Multiple Choice Test Bank Questions No Feedback – Chapter 1
Correct answers denoted by an asterisk.
1. The linear relationship between two variables (y and x) can be represented by the equation
y  a  bx . Which of the following statements is true?
(I) Parameter a is termed the intercept
(II) Parameter a is termed the slope
(III) Parameter b is termed the gradient
(IV) Parameter b is termed the constant.
(a) I and IV only
(b)* I and III only
(c) II and III only
(d) II and IV only.
2. Assume that the relationship between a company’s stock price (y) and dividends paid per
share (x) is linear. If the slope of the equation is 0.50 and the intercept is 30, what would be the
expected stock price if the dividend paid was 3?
(a) 33
(b) 30.50
(c)* 31.5
(d) 30.
3. Which of the following values are closes to the roots of the following quadratic equation:
y  x 2  4 x  1?
(a) 0 and 4
(b) 1 and 4
(c) 0.5 and 3
(d)* 0.3 and 3.7.
4. Consider the following graphs.
(A)
(B)
Which of the following statements is true?
(a) A is depicts a non-linear relationship between y and x
(b) B is depicts a linear relationship between y and x
(c)* A and B depict linear and non-linear relationships between y and x, respectively
(d) A and B depict non-linear and linear relationships between y and x, respectively.
5. Which of the following statements is true about graph (A) above?
(a)* The intercept of the graph is positive and its slope is negative
(b) The intercept of the graph is negative and its slope is positive
(c) Both the intercept and slope of the graph are positive
(d) It is impossible to say anything about the intercept and slope without seeing the
mathematical equation.
6. The simplest possible way of writing 3x5  7x3 is:
(a) 21 x5  x3
(b) 21 x15
(c) * 21x8
(d) 21x53.
7. What are the roots of the equation y = 2x2 + 2x – 4?
(a)
(b)
(c)
(d)
* –2 and 1
–1 and 2
–2 and 2
–2 (repeated).
8. What are the roots of the equation y = x2 + 2x – 6 closest to?
(a) –4 and 2
(b) * –3.65 and 1.65
(c) –7.3 and 3.3
(d) Both complex.
9. ‘x to the power 3’ could be written:
(a)
(b)
(c)
(d)
3x
3x3
* x3
3x  3x  3x.
10. Another way of writing elog(x) is:
(a)
(b)
(c)
(d)
*1
log(x)
ex
x.
11. Log(1) is:
(a)
(b)
(c)
(d)
1
*0
2.71828…
Undefined.
2
12. Writing out all the terms in the expression
2
 x
i 1 j 1
(a)
(b)
(c)
(d)
* x11 + x12 + x21 + x22
x11  x12  x21  x22
x1 + x2
x11 + x22.
13.
 y is equal to:
ij
would lead to:
5
i 1
(a)
(b)
(c)
(d)
* 5y
y
y5
5y5.
14. What is the (first order) derivative of the function y  x 2  4 x  1?
(a) 2x  4 x  1
(b) 2 x 2  4 x
(c)* 2x  4
(d) 2 x  4  1.
15. What is the second order derivative of the function y  6 x4  3x3  4 x 2  2 ?
(a) 24 x 3  9 x 2  8 x
(b)* 72 x 2  18 x  8
(c) 24 x3  9 x 2  8
(d) 6 x 4  3x3  4 x 2 .
16. The derivative of log(5x) is:
(a)
(b)
(c)
(d)
5/x
* 1/x
5log(x)
5/log(x).
17. The derivative of e4x-2 is:
(a)
(b)
(c)
(d)
4/(4x-2)
(4x-2)e4
(4x-2)e4x-2
* 4e4x-2.
18. If A is of dimension 1  4 and B is of dimension 4  1, what is the most accurate term to
describe the result of the matrix multiplication AB?
(a)
(b)
(c)
(d)
* A scalar
A column vector
A row vector
A matrix.
3 1
 4
19. If matrices A  2  4 6  and B  4   , what is AB?
8
 2 2


 160 
(a)*  512 
 192 


 20 
(b)  64 
 24 
 
 40 
(c)  128 
 48 


 80 
(d)  256  .
 96 


20. The rank of matrices A and B from Question 19 are:
(a) 1 and 2, respectively
(b)* 2 and 1, respectively
(c) 1 and 3, respectively
(d) 3 and 1, respectively.
21. For two conformable matrices A and B, expanding the parentheses of (AB)-1 gives:
(a)
(b)
(c)
(d)
A-1B-1
* B-1A-1
BA
AB.
3 1
22. What is the inverse of matrix C  
?
 4 6
 0.43 0.07 
(a) 

 0.29 0.21 
 0.43 0.07 
(b)* 

 0.29 0.21 
 0.43 0.07 
(c) 

 0.29 0.21 
 0.43 0.07 
(d) 
.
 0.29 0.21
23. The rank of a square matrix is also:
(a)
(b)
(c)
(d)
The product of the eigenvalues
The sum of the eigenvalues
* The number of non-zero eigenvalues
The number of correlated rows or columns.
24. The trace of matrix C is
(a)* 9
(b) 8
(c) 7
(d) 6.
25. The point where the capital market line is tangential to the efficient frontier is
(a) The point where the portfolio returns are minimised
(b) The point where the portfolio returns are maximised
(c) The point where the portfolio’s Sharpe ratio is minimised
(d)* The point where the portfolio’s Sharpe ratio is maximised.
26. The central limit theorem states that
(a)* The sampling distribution of the mean of any random sample of observations will tend
towards the normal distribution with mean equal to the population mean as the sample size
tends to infinity
(b) The sampling distribution of the mean of any random sample of observations will tend
towards the normal distribution with mean equal to the population mean as the sample size
tends to zero
(c) The cumulative distribution function of the mean of any random sample of observations will
tend towards the normal distribution with mean equal to the population mean as the sample
size tends to infinity
(d) The probability distribution function of the mean of any random sample of observations will
tend towards the normal distribution with mean equal to the population mean as the sample
size tends to infinity.
27. Consider the following data series: 11, 10, 6, 8, 4, 3, 7. What is its semi-interquartile range
of this series?
(a) 6
(b) 5
(c) 4
(d)* 3.
28. Consider the following two graphs:
(A)
(B)
Which of the following statements is true if A represents a normal distribution?
(I) The skewness of the distribution plot A is 0 and its kurtosis is 3
(II) The skewness of the distribution plot B is 0 and its kurtosis is 3
(III) The excess kurtosis of the distribution plot A is 3
(IV) The excess kurtosis of the distribution plot B is 0.
(a) Both (I) and (III) are true
(b) Only (III) is true
(c)* Only (I) is true
(d) Both (I) and (IV) are true.
29. Suppose that we have a function given by y = a1 + a2x. a1 and a2 are, respectively,
(a) The domain and range of the function
(b) The order and power of the function
(c) * The intercept and slope of the function
(d) The slope and intercept of the function.
30. What are the roots of the equation y = 3 + 4x + 2x2?
(a) 2 and –4
(b) 0.5 and –2
(c) 2 and 2
(d) * This function has no real roots.
31. (x3)2 simplifies to
(a) x5
(b) * x6
(c) x
(d) The expression cannot be simplified.
32. Which of the following three equations is/are correct regarding the summation operator?
𝐾
𝐾
∑𝐾
𝑖=1 𝑥𝑖 + ∑𝑖=1 𝑧𝑖 = ∑𝑖=1(𝑥𝑖 + 𝑧𝑖 )
(i)
𝐾
𝐾
∑𝐾
𝑖=1 𝑥𝑖 𝑧𝑖 = ∑𝑖=1 𝑥𝑖 ∑𝑖=1 𝑧𝑖
(ii)
𝐾
∑𝐾
𝑖=1 𝑐𝑥𝑖 = 𝑐 ∑𝑖=1 𝑥𝑖
(iii)
(a)
(b)
(c)
(d)
(iii) only
* (i) and (iii) only
(i) and (ii) only
(i), (ii) and (iii).
33. What is ∏3𝑘=1 𝑘 3 ?
(a) * 216
(b) 35
(c) 6
(d) 7776.
34. The second order derivative of a quadratic function will be:
(a) A cubic function
(b) A quadratic function
(c) A linear function
(d) * A constant.
35. Using the chain rule or otherwise, what is the (first) derivative of the following function? y =
(2x2 + 4x – 6)3
(a) 3(2x2 + 4x – 6)2
(b) (4x + 4)2
(c) * 3(2x2 + 4x – 6)2(4x + 4)
(d) 3(2x2 + 4x – 6)3(4x + 4)2.
Multiple Choice Test Bank Questions No Feedback – Chapter 2
Correct answers denoted by an asterisk.
1. Financial econometrics can best be described as
(a)* The application of statistical techniques to problems in finance
(b) The application of mathematical models to problems in economics
(c) The application of financial techniques to problems in economics
(d) None of the above.
2. Which of the following is a serious problem encountered by applied econometricians in economics?
(a) Small samples problems
(b) Measurement error
(c) Data revisions
(d)* All of the above.
3. Which of these is a characteristic of financial data?
(a) They are observed at much lower frequencies than macroeconomic data
(b) The number of observations is usually very small
(c)* They are considered to be very noisy
(d) It is easy to separate underlying trends from random and uninteresting features.
4. Data that have been collected over a period of time on one or more variables is referred to as
(a) Cross-sectional data
(b) Time-cross-sectional data
(c)* Time-series data
(d) Panel data.
5. Data that have been collected on one or more variables at a single point in time is referred to as
(a)* Cross-sectional data
(b) Time-cross-sectional data
(c) Time series data
(d) Panel data.
6. Data that have both time series and cross-sections is referred to as
(a) Cross-sectional data
(b) Time-cross-sectional data
(c) Time-series data
(d)* Panel data.
7. An individual invested £106.40 in the stock market and the value of his investment two years later is
£138.22. What are the simple and continuously compounded returns on his investment?
(a) 26% and 30%, respectively
(b) –29% and -34%, respectively
(c)* 30% and 26%, respectively
(d) 30% and 30%, respectively.
8. An individual has £10000 capital to invest in the stock market. He invests 30% of his capital in stock A,
25% in stock B and 45% in Stock C. What is the return on his/her portfolio assuming that the simple
returns on stocks A, B and C are 5%, 10% and 12%, respectively?
(a)* 9.0%
(b) 9.7%
(c) 9.3%
(d) 9%.
The average nominal annual rent in the US denominated in dollars and the CPI (2008 levels) are given in
the table below:
Year
Average annual rent (US Dollars)
CPI (2008 levels)
2008
9908
100
2009
9998
99.7
2010
10012
101.3
2011
10180
104.5
2012
10396
106.7
9. What is the 2008 average annual rent in 2012 terms?
(a) 9743
(b)* 10572
(c) 9286
(d) 11093.
10. What is the 2012 average annual rent in 2008 terms?
(a)* 9743
(b) 10572
(c) 9286
(d) 11093.
11. The numerical score assigned to the credit rating of a bond is best described as what type of
number?
(a) Continuous
(b) Cardinal
(c)* Ordinal
(d) Nominal.
12. Suppose that we wanted to sum the 2007 returns on ten shares to calculate the return on a portfolio
over that year. What method of calculating the individual stock returns would enable us to do this?
(a)* Simple
(b) Continuously compounded
(c) Neither approach would allow us to do this validly
(d) Either approach could be used and they would both give the same portfolio return.
13. If we wish to compare the spread of two series with considerably different mean values, which of
the following measures would be the most appropriate?
(a) The semi-interquartile range
(b) The standard deviation
(c) The range
(d) * The coefficient of variation.
14. For a series with a negative skew in its distribution (a long left tail), which of the following best
describes the relationship between its measures of central tendency?
(a) mean > median > mode
(b) * mode > median > mean
(c) mode > mean > median
(d) median > mode > mean.
15. Which of the following statements is TRUE concerning the correlation between two series?
(a) * It is unit-free
(b) It scales with the product of the units of the two series
(c) It scales with the ratio of the units of the two series
(d) It will take the value –1 if there is no association between the two series.
16. What is the sum of the following infinite set of terms? 5, 2.5, 1.25, 0.625, …
(a) Infinity
(b) 5
(c) 20
(d) * 10.
17. What is the sum of the first 12 terms in the following sequence? 12, 24, 48, …
(a) * 49,140
(b) 24,576
(c) 768
(d) 98,292.
18. If I have £10,000 now and I want it to grow by 50% within eight years, what interest rate,
compounded annually, is required (to one decimal place)?
(a) * 5.2%
(b) 6.2%
(c) 4.6%
(d) 7.4%.
19. If a savings account pays a nominal interest rate of 10% per year, compounded monthly, what is the
effective interest rate to one decimal place?
(a) 11.2%
(b) 9.5%
(c) 10.0%
(d) * 10.5%.
20. If you place £10,000 in a savings account, how long would it take to reach £20,000 assuming an
annual interest rate of 3%, continuously compounded, rounded to the nearest year?
(a) 26
(b) 34
(c) *23
(d) 20.
21. What would be a fair price to pay today, to the nearest dollar, for a zero coupon bond having exactly
six years to maturity and to be redeemed at $1000 if the annual discount rate is 6%?
(a) $1000
(b) * $747
(c) $864
(d) $553.
22. Which of the following statements is FALSE concerning the internal rate of return?
(a) For projects where the cashflow payments change sign, there can be more than one internal rate of
return
(b) The internal rate of return is the discount rate that sets the net present value of all of the cashflows
to be received equal to the asset’s purchase price
(c) * In order to calculate an internal rate of return, all of the incoming cashflows must be identical
(d) We cannot calculate a different internal rate of return for each cashflow.
Multiple Choice Test Bank Questions No Feedback – Chapter 3
Correct answers denoted by an asterisk.
1. Regression is concerned with describing and evaluating the relationship between
(a) A dependent variable and regressands
(b) An independent variable and regressors
(c)* A dependent variable and regressors
(d) An effect variable and explained variables.
2. What does a positive linear relationship between x and y in a simple regression imply?
(a) Increases in the independent variable are usually accompanied by increases in the regressor
(b) The relationship between x and y cannot be explained by a straight line
(c) Decreases in the independent variable is usually accompanied by increases in the regressors
(d)* Increases in the regressor are usually accompanied by increases in the dependent variable.
3. Which of these is NOT a reason for adding a disturbance term to a regression model
yt     xt  ut ?
(a) Some determinants of the effect variable may be omitted from the model
(b) Some determinants of the effect variable may be unobservable
(c)* Some determinants of the independent variable may be omitted from the model
(d) There may be errors in the way that the dependent variable is measured which cannot be modelled.
4. Which of these is not a standard method for estimating econometric models?
(a) Ordinary least squares
(b) The method of moments
(c)* Method of generalised squared moments
(d) Maximum likelihood.
5. The method of estimating econometric models which involves fitting a line to the data by minimising
the sum of squared residuals is the
(a)* Method of ordinary least squares
(b) Method of moments
(c) Method of generalised squared moments
(d) Method of maximum likelihood.
6. Suppose you have 5-year annual data on the excess returns on a fund manager’s portfolio (‘fund ABC’)
and the excess returns on a market index (where rABC is the return on fund ABC, rf is the risk-free rate
and rM is the return on the market index):
Year t
Excess return on fund ABC
Excess return on market index
rABC ,t  rf ,t
rM ,t  rf ,t
1
14.0
16.0
2
32.0
21.7
3
11.6
6.0
4
21.2
16.2
5
17.4
11.0
What is the estimated alpha ( ̂ ) for Fund ABC?
(a) 2.3
(b)* 3.3
(c) 4.3
(d) 5.3.
7. Given the data in Question 6, what is the estimated beta ( ˆ ) of Fund ABC?
(a) 3.1
(b) 2.1
(c)* 1.1
(d) None of the above.
8. Suppose that the unbiased estimator of the standard deviation of the disturbance (s) is 5.1. What is the
nearest value to the standard errors of the estimated CAPM alpha ( ̂ ) of Fund ABC from Question 6?
(a) 3.5
(b) 4.5
(c) 5.5
(d)* 6.5.
9. The estimated alpha ( ̂ ) and beta ( ˆ ) of a rival fund, Fund DEF, are 2.3 and 3.1, respectively. If the
expected market risk premium is 12%, what would we expect the excess return of Fund DEF to be?
(a)* 39.5%
(b) 30.7%
(c) 5.4%
(d) 64.8%.


10. What is the most appropriate interpretation of the assumption cov ui , u j  0 concerning the
regression disturbance terms?
(a) The errors are nonlinearly independent of one another
(b) The errors are linearly dependent of one another
(c) The covariance of the errors is constant and finite over all its values
(d)* The errors are linearly independent of one another.
11. The estimators ̂ and ˆ determined by OLS will be the Best Linear Unbiased Estimators (BLUE) if
which of the following assumptions hold?
(I) The errors have zero mean
(II) The variance of the errors is constant and finite over all values of the independent variable(s)
(III) The errors are linearly independent of one another
(IV)There is no relationship between the error and corresponding independent variables
(a) I and II only
(b) I, II and III only
(c) II, III and IV only
(d)* I, II, III, and IV.
12. Standard errors
(a) Give us an idea of the deviation of the errors from their mean
(b) Measure the reliability of the independent variables
(c)* Give us an idea of the precision of estimates of  and 
(d) Measure the reliability of the dependent variables.
Suppose you have calculated the following regression results:
yˆ t  1.25  0.64 xt . The standard errors of ̂ and ˆ are 1.22 and 0.58, respectively.
13. Using the test of significance approach, what is the test statistic value of a hypothesis to test whether
the true value of  statistically different from zero?
(a)* 1.10
(b) 0.91
(c) –0.62
(d) Cannot say without more information.
14. Assuming there are 1000 observations in your sample, what are the test statistic and critical value of
a two-sided hypothesis test of whether the true value of  statistically different from zero be given a 5%
significance level?
(a)* 1.10 and 1.96, respectively
(b) 0.91 and 1.65, respectively
(c) –0.62 and 1.96, respectively
(d) Cannot say without more information.
15. Consider a bivariate regression model with coefficient standard errors calculated using the usual
formulae. Which of the following statements is/are correct regarding the standard error estimator for the
slope coefficient?
(i)
(ii)
(iii)
(iv)
(a)
(b)
(c)
(d)
It varies positively with the square root of the residual variance (s)
It varies positively with the spread of X about its mean value
It varies positively with the spread of X about zero
It varies positively with the sample size T
* (i) only
(i) and (iv) only
(i), (ii) and (iv) only
(i), (ii), (iii) and (iv).
16. In a time-series regression of the excess return of a mutual fund on a constant and the excess return
on a market index, which of the following statements should be true for the fund manager to be
considered to have ‘beaten the market’ in a statistical sense?
(a) * The estimate for  should be positive and statistically significant
(b) The estimate for  should be positive and statistically significantly greater than the risk-free rate of
return
(c) The estimate for  should be positive and statistically significant
(d) The estimate for  should be negative and statistically significant.
17. What result is proved by the Gauss–Markov theorem?
(a) That OLS gives unbiased coefficient estimates
(b) That OLS gives minimum variance coefficient estimates
(c) * That OLS gives minimum variance coefficient estimates only among the class of linear unbiased
estimators
(d) That OLS ensures that the errors are distributed normally.
18. The type I error associated with testing a hypothesis is equal to
(a) One minus the type II error
(b) The confidence level
(c) * The size of the test
(d) The size of the sample.
19. Which of the following is a correct interpretation of a ‘95% confidence interval’ for a regression
parameter?
(a) * We are 95% sure that the interval contains the true value of the parameter
(b) We are 95% sure that our estimate of the coefficient is correct
(c) We are 95% sure that the interval contains our estimate of the coefficient
(d) In repeated samples, we would derive the same estimate for the coefficient 95% of the time.
20. Which of the following statements is correct concerning the conditions required for OLS to be a
usable estimation technique?
(a)
(b)
(c)
(d)
* The model must be linear in the parameters
The model must be linear in the variables
The model must be linear in the variables and the parameters
The model must be linear in the residuals.
21. Which of the following is NOT a good reason for including a disturbance term in a regression equation?
(a) It captures omitted determinants of the dependent variable
(b) * To allow for the non-zero mean of the dependent variable
(c) To allow for errors in the measurement of the dependent variable
(d) To allow for random influences on the dependent variable.
22. Which of the following is NOT correct with regard to the p-value attached to a test statistic?
(a) * p-values can only be used for two-sided tests
(b) It is the marginal significance level where we would be indifferent between rejecting and not rejecting
the null hypothesis
(c) It is the exact significance level for the test
(d) Given the p-value, we can make inferences without referring to statistical tables.
23. Which one of the following is NOT an assumption of the classical linear regression model?
(a)
(b)
(c)
(d)
24.
The explanatory variables are uncorrelated with the error terms.
The disturbance terms have zero mean
* The dependent variable is not correlated with the disturbance terms
The disturbance terms are independent of one another.
Which of the following is the most accurate definition of the term ‘the OLS estimator’?
(a) It comprises the numerical values obtained from OLS estimation
(b) * It is a formula that, when applied to the data, will yield the parameter estimates
(c) It is equivalent to the term ‘the OLS estimate’
(d) It is a collection of all of the data used to estimate a linear regression model.
25. Two researchers have identical models, data, coefficients and standard error estimates. They test
the same hypothesis using a two-sided alternative, but researcher 1 uses a 5% size of test while
researcher 2 uses a 10% test. Which one of the following statements is correct?
(a)
(b)
(c)
(d)
Researcher 2 will use a larger critical value from the t-tables
* Researcher 2 will have a higher probability of type I error
Researcher 1 will be more likely to reject the null hypothesis
Both researchers will always reach the same conclusion.
26. Consider an increase in the size of the test used to examine a hypothesis from 5% to 10%. Which one
of the following would be an implication?
(a)
(b)
(c)
(d)
* The probability of a Type I error is increased
The probability of a Type II error is increased
The rejection criterion has become more strict
The null hypothesis will be rejected less often.
27. What is the relationship, if any, between the normal and t-distributions?
(a)
(b)
(c)
(d)
A t-distribution with zero degrees of freedom is a normal
A t-distribution with one degree of freedom is a normal
* A t-distribution with infinite degrees of freedom is a normal
There is no relationship between the two distributions.
Multiple Choice Test Bank Questions No Feedback – Chapter 4
Correct answers denoted by an asterisk.
1. Consider a standard normally distributed variable, a t-distributed variable with d degrees of
freedom, and an F-distributed variable with (1, d) degrees of freedom. Which of the following
statements is FALSE?
(a) The standard normal is a special case of the t-distribution, the square of which is a special
case of the F-distribution
(b) * Since the three distributions are related, the 5% critical values from each will be the same
(c) Asymptotically, a given test conducted using any of the three distributions will lead to the
same conclusion
(d) The normal and t- distributions are symmetric about zero while the F-distribution takes only
positive values.
2. If our regression equation is y = X + u, where we have T observations and k regressors, what
will be the dimension of ̂ using the standard matrix notation
(a) T  k
(b) T  1
(c) * k  1
(d) k  k.
Question 3 refers to the following regression estimated on 64 observations:
yt = 1 + 2X2t + 3X3t + 4X4t + ut
3. Which of the following null hypotheses could we test using an F-test?
(i) 2 = 0
(ii) 2 = 1 and 3 + 4 = 1
(iii) 34 = 1
(iv) 2 -3 -4 = 1.
(a) (i) and (ii) only
(b) (ii) and (iv) only
(c) (i), (ii), (iii), and (iv)
(d)* (i), (ii), and (iv) only.
For Question 4, you are given the following data
 1.3 2.1  1.4
 1.6
( X ' X ) 1   2.1 0.8 1.9 ,( X ' y )   2.9 ,
 1.4 1.9 3.4 
 0.8 
s 2  0.86, T  103
The regression equation is
yt = 1 + 2X2t + 3X3t + ut
4. Which of the following is the correct value for ̂ 1 ?
(a) * 2.89
(b) 1.30
(c) 0.84
(d) We cannot determine the value of ̂ 1 from the information given in the question.
5. Consider the following regression estimated using 84 observations:
yt = 1 + 2X2t + 3X3t + 4X4t + ut
Suppose that a researcher wishes to test the null hypothesis: 2 = 1 and 3 + 4 = 1. The
TABULATED value of the F-distribution that we would compare the result of testing this
hypothesis with at the 10% level would be approximately
(a) 19.48
(b) 2.76
(c) * 2.37
(d) 3.11.
6.
(a)
(b)
(c)
(d)
What is the relationship, if any, between t-distributed and F-distributed random variables?
A t-variate with z degrees of freedom is also an F(1, z)
* The square of a t-variate with z degrees of freedom is also an F(1, z)
A t-variate with z degrees of freedom is also an F(z, 1)
There is no relationship between the two distributions.
7. Which one of the following statements must hold for EVERY CASE concerning the residual
sums of squares for the restricted and unrestricted regressions?
(a)
(b)
(c)
(d)
URSS > RRSS
URSS  RRSS
RRSS > URSS
* RRSS  URSS.
8. Which one of the following is the most appropriate as a definition of R2 in the context that
the term is usually used?
(a) It is the proportion of the total variability of y that is explained by the model
(b) * It is the proportion of the total variability of y about its mean value that is explained by
the model
(c) It is the correlation between the fitted values and the residuals
(d) It is the correlation between the fitted values and the mean.
9. Suppose that the value of R2 for an estimated regression model is exactly one. Which of the
following are true?
(i)
(ii)
(iii)
(i)
All of the data points must lie exactly on the line
All of the residuals must be zero
All of the variability of y about its mean has been explained by the model
The fitted line will be horizontal with respect to all of the explanatory variables.
(a) (ii) and (iv) only
(b) (i) and (iii) only
(c) * (i), (ii), and (iii) only
(d) (i), (ii), (iii), and (iv).
10. Consider the following two regressions
yt  1   2 x2t   3 yt 1  ut
yt   1   2 x2t   3 yt 1  ut
Which of the following statements are true?
(i)
(ii)
(iii)
(iv)
(a)
(b)
(c)
(d)
The RSS will be the same for the two models
The R2 will be the same for the two models
The adjusted R2 will be different for the two models
The regression F-test will be the same for the two models.
(ii) and (iv) only
* (i) and (iii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv).
11. Which of the following are often considered disadvantages of the use of adjusted R2 as a
variable addition/variable deletion rule?
(i)
(ii)
(iii)
(iv)
(a)
(b)
(c)
(d)
Adjusted R2 always rises as more variables are added
Adjusted R2 often leads to large models with many marginally significant or marginally
insignificant variables
Adjusted R2 cannot be compared for models with different explanatory variables
Adjusted R2 cannot be compared for models with different explained variables.
* (ii) and (iv) only
(i) and (iii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv).
12. Which of these is a mathematical expression of the residual sum of squares?
(I) uˆ ' uˆ
(II) uˆ1uˆ2 ...uˆT 
(III) uˆ1  uˆ2  ...  uˆT
(a) * I only
(b) I and II only
(c) I and III only
(d) I, II and III.
13. If you are interested in conducting a multiple hypotheses test to determine whether  2 and
 3 are both unity for a regression y  1  2 x2  3 x3  4 x4  u , what would the restricted
regression be?
(a) y  1   4 x4  u
(b)  y  x2   1  2  3 x3  4 x4  u
(c)*  y  x2  x3   1  4 x4  u
(d)  y  x4   1  2 x2  3 x3  u .
14. What would the restricted regression be if you are interested in testing the null hypothesis
H 0 : 2  0 and 3  0 against the alternative hypothesis H1 :  2  0 or 3  0 for a regression
y  1   2 x2  3 x3  4 x4  u ,?
(a)* y  1   4 x4  u
(b)  y  x2   1  2  3 x3  4 x4  u
(c)  y  x2  x3   1  4 x4  u
(d)  y  x4   1  2 x2  3 x3  u .
15. Assuming that the restricted sum of squares of the restricted regression in Question 14 is
436.1 and the unrestricted sum of squares is 397.2, what would the conclusion of the
hypothesis test be? (The significance level is 5%.)
(a)* Reject the null hypothesis
(b) Do not reject the null hypothesis
(c) Reject the alternative hypothesis
(d) Cannot say.
16. Which of these statements is a characteristic of the stepwise regression procedure?
(I) It chooses the jointly most ‘important’ explanatory variable from a set of candidate variables
(II) It can start with no variables in the regression and then it selects first the variable with the
lowest p-value
(III) It can start with no variables in the regression and then it selects first the variable with the
highest p-value
(a) I only
(b) II only
(c) III only
(d)* Both I and II.
17. Trying many variables in a regression without basing the selection of candidate variables on
a financial or economic theory is popularly referred to as
(a) Data fitting
(b) Data clipping
(c)* Data mining
(d) None of the above.
18. Why is R2 a commonly used and perhaps better measure of how well a regression model fits
the data than the residual sum of squares (RSS)?
(a) The RSS is often too large
(b) The RSS does not depend on the scale of the dependent variable whereas the R2 does
(c)* The RSS depends on the scale of the dependent variable whereas the R2 does not
(d) The RSS depends on the scale of the independent variable whereas the R2 does not.
Use the following to answer Questions 19 and 20.
Assuming you have two regression models yt  1   2 x2t  3 x3t  ut and
yt  1  2 x4t  3 x5t  vt .
19. How can the two models be validly compared to determine the model that better
represents the data yt?
(a) By observing their respective R2
(b) By observing their respective Adjusted R2
(c) By estimating an encompassing or hybrid model
(d)* All of the above.
20. What is the relevant encompassing model required to compare the two regression models?
(a)* yt   1   2 x2t   3 x3t   4 x4t   5 x5t  wt
(b) yt   1   2 x2t   3 x3t   5 x5t  wt
(c)  1  yt   2 x2t   3 x3t   4 x4t   5 x5t  wt
(d) Encompassing models cannot be used to compare these specifications.
21. Which of these statements is NOT true about quantile regressions?
(a) No distributional assumptions are required to optimally estimate the parameters
(b) It is a non-parametric technique
(c)* It is a parametric technique
(d) The response variable is usually assumed to be independently distributed and
homoscedastic.
Multiple Choice Test Bank Questions No Feedback – Chapter 5
Correct answers denoted by an asterisk.
2. A researcher conducts a Breusch–Godfrey test for autocorrelation using 3 lags of the residuals
in the auxiliary regression. The original regression contained 5 regressors including a constant
term, and was estimated using 105 observations. What is the critical value using a 5%
significance level for the LM test based on T R2?
(a) 1.99
(b) 2.70
(c) * 7.81
(d) 8.56.
2. Which of the following would NOT be a potential remedy for the problem of multicollinearity
between regressors?
(a) Removing one of the explanatory variables
(b) * Transforming the data into logarithms
(c) Transforming two of the explanatory variables into ratios
(d) Collecting higher frequency data on all of the variables.
3. Which of the following conditions must be fulfilled for the Durbin–Watson test to be valid?
(i) The regression includes a constant term
(ii) The regressors are non-stochastic
(iii) There are no lags of the dependent variable in the regression
(iv) There are no lags of the independent variables in the regression.
(a)* (i), (ii), and (iii) only
(b) (i) and (ii) only
(c) (i), (ii), (iii), and (iv)
(d) (i), (ii), and (iv) only.
4. If the residuals of a regression on a large sample are found to be heteroscedastic which of the
following might be a likely consequence?
(i) The coefficient estimates are biased
(ii) The standard error estimates for the slope coefficients may be too small
(iii) Statistical inferences may be wrong.
(a) (i) only
(b) * (ii) and (iii) only
(c) (i), (ii), and (iii)
(d) (i) and (ii) only.
5. The value of the Durbin–Watson test statistic in a regression with 4 regressors (including the
constant term) estimated on 100 observations is 3.6. What might we suggest from this?
(a) The residuals are positively autocorrelated
(b) * The residuals are negatively autocorrelated
(c) There is no autocorrelation in the residuals
(d) The test statistic has fallen in the intermediate region.
6. Which of the following is NOT a good reason for including lagged variables in a regression?
(a) Slow response of the dependent variable to changes in the independent variables
(b) Over-reactions of the dependent variables
(c) The dependent variable is a centred moving average of the past 4 values of the series
(d) * The residuals of the model appear to be non-normal.
7. What is the long-run solution to the following dynamic econometric model?
yt = 1 + 2X2t + 3X3t + ut
(a) y = 1 + 2X2 + 3X3
(b) yt = 1 + 2X2t + 3X3t
(c) y = - (2/ 1) X2 - (3 / 1)X3
(d) * There is no long-run solution to this equation.
8. Which of the following would you expect to be a problem associated with adding lagged values
of the dependent variable into a regression equation?
(a) * The assumption that the regressors are non-stochastic is violated
(b) A model with many lags may lead to residual non-normality
(c) Adding lags may induce multicollinearity with current values of variables
(d) The standard errors of the coefficients will fall as a result of adding more explanatory
variables.
9. A normal distribution has coefficients of skewness and excess kurtosis which are, respectively,
(a) * 0 and 0
(b) 0 and 3
(c) 3 and 0
(d) Will vary from one normal distribution to another.
10. Which of the following would probably NOT be a potential ‘cure’ for non-normal residuals?
(a) * Transforming two explanatory variables into a ratio
(b) Removing large positive residuals
(c) Using a procedure for estimation and inference which did not assume normality
(d) Removing large negative residuals.
11. What would be the consequences for the OLS estimator if autocorrelation is present in a
regression model but ignored?
(a) It will be biased
(b) It will be inconsistent
(c) * It will be inefficient
(d) All of (a), (b), and (c) will be true.
12. If OLS is used in the presence of heteroscedasticity, which of the following will be likely
consequences?
(i)
(ii)
(iii)
(iv)
Coefficient estimates may be misleading
Hypothesis tests could reach the wrong conclusions
Forecasts made from the model could be biased
Standard errors may inappropriate.
(a) * (ii) and (iv) only
(b) (i) and (iii) only
(c) (i), (ii), and (iii) only
(d) (i), (ii), (iii), and (iv).
13. If a residual series is negatively autocorrelated, which one of the following is the most likely
value of the Durbin–Watson statistic?
(a)
(b)
(c)
(d)
Close to zero
Close to two
* Close to four
Close to one.
14. If the residuals of a model containing lags of the dependent variable are autocorrelated,
which one of the following could this lead to?
(a)
(b)
(c)
(d)
Biased but consistent coefficient estimates
* Biased and inconsistent coefficient estimates
Unbiased but inconsistent coefficient estimates
Unbiased and consistent but inefficient coefficient estimates.
15. Which one of the following is NOT a symptom of near multicollinearity?
(a)
(b)
(c)
(d)
The R2 value is high
The regression results change substantively when one particular variable is deleted
* Confidence intervals on parameter estimates are narrow
Individual parameter estimates are insignificant.
16. Which one of the following would be the most appropriate auxiliary regression for a Ramsey
RESET test of functional form?
(a) * yt  0  1 yˆ t 2  vt
(b) yt 2  0  1 x2t   2 x3t   4 x22t  5 x32t  6 x2t x3t  vt
2
2
(c) uˆt   0  1 yˆ t  vt
(d) ut   0  1 x2 t   2 x3t   4 x22t   5 x32t   6 x2 t x3t  vt .
17. If a regression equation contains an irrelevant variable, the parameter estimates will be
(a)
(b)
(c)
(d)
* Consistent and unbiased but inefficient
Consistent and asymptotically efficient but biased
Inconsistent
Consistent, unbiased and efficient.
18. Put the following steps of the model-building process in the order in which it would be
statistically most appropriate to do them:
(i) Estimate model
(ii) Conduct hypothesis tests on coefficients
(iii) Remove irrelevant variables
(iv) Conduct diagnostic tests on the model residuals.
(a)
(b)
(c)
(d)
(i) then (ii) then (iii) then (iv)
(i) then (iv) then (ii) then (iii)
* (i) then (iv) then (iii) then (ii)
(i) then (iii) then (ii) then (iv).
19. Test statistics for the LM test and the Wald test are usually constructed to follow a
(a)* χ2 distribution and F-distribution, respectively
(b) χ2 distribution and t-distribution, respectively
(c) F-distribution and χ2 distribution, respectively
(d) t-distribution and χ2 distribution, respectively.
20. Which of these statements is true?
(I) The F-distribution has 2 degrees of freedom parameters
(II) Asymptotically, the LM test and the Wald test are equivalent
(III) The results from the LM and Wald tests may differ somewhat in small samples
(IV) The F-distribution is a special case of the t-distribution.
(a) I only
(b) I and II
(c)* I, II, and III
(d) I, II, III, and IV.
21. The assumption of homoscedasticity can be written mathematically as
(a)* var  ut    2  
(b) var  ut    2  
(c) var  ut    2  
(d) var  ut    2   .
22. Assuming you are interested in conducting a Goldfeld–Quandt test at a 5% significance level
and the regression model is estimated on each sub-sample with residual variances s12  0.15 and
s22  0.14 , T1  12 , T2  14 and k  2 . What would your conclusion be?
(a) Do not reject the null hypothesis of heteroscedasticity
(b) Reject the null hypothesis of homoscedasticity
(c) Reject the null hypothesis of heteroscedasticity
(d)* Do not reject the null hypothesis of homoscedasticity.
23. Which of these is a test for heteroscedasticity?
(a) Breusch–Godfrey test
(b)* White test
(c) Bera–Jarque test
(d) Breusch–Jagan test.
24. Which of these is NOT a viable ‘solution’ for heteroscedasticity?
(a) Using generalised least squares if the form of heteroscedasticity is known
(b) Transforming the variables into logs
(c) Using heteroscedasticity-consistent standard error estimates
(d)* Taking the first differences of the series.
(A)
(B)
25. The graphs above are time series plots of residuals from two separate regressions. Which of
these combinations is true?
(a)* A shows negative autocorrelation and B shows positive autocorrelation
(b) A shows positive autocorrelation and B shows negative autocorrelation
(c) A shows heteroscedasticity and B shows homoscedasticity
(d) A shows homoscedasticity and B shows heteroscedasticity.
26. Assuming a researcher runs the following regression ut  ut 1  vt where ut is residual from
a regression. If the researcher conducts a hypothesis test with null hypothesis of H 0 :   0
against an alternative hypothesis of H1 :   0 , what type of test is he or she conducting?
(a) Test for heteroscedasticity
(b)* Test for autocorrelation
(c) Test for non-normality
(d) Test for homoscedasticity.
27. Assuming the researcher now runs the following regression
ut  1ut 1  2ut 2  ...   rut r  vt where ut is residual from a regression. If the researcher
conducts a test with a null hypothesis of H 0 : 1  0 and  2  0 and ... and  r  0 against an
alternative hypothesis of H1 : 1  0 or  2  0 or ... or  r  0 , what type of test is he or she
conducting?
(a) Test for rth order of heteroscedasticity
(b)* Test for rth order of autocorrelation
(c) Test for rth order of non-normality
(d) Test for rth order of homoscedasticity.
28. Which of these is not a consequence of ignoring autocorrelation if it is present?
(a) The coefficient estimates derived using OLS are inefficient
(b) Standard error estimates are inappropriate
(c)* The coefficient estimates derived using OLS are biased
(d) The coefficient estimates derived using OLS are not the best linear unbiased estimators.
29. Which of these is a viable solution to the problem of multicollinearity?
(I) Ignore it
(II) Drop one of the collinear variables
(III) Transform the highly correlated variables into a ratio
(IV) Take the logs of the variables
(a) I only
(b) I and II only
(c)* I, II, and III only
(d) I, II, III, and IV.
30. Which of the following statements are true about parameter stability tests?
(I) Parameter stability tests test the assumption that the estimated parameters of a model are
constant for the entire sample
(II) Chow test and predictive failure tests are two types of parameter stability tests
(III) Backward and forward predictive failure tests are two types of parameter stability tests
(IV) Parameter stability tests examine violations of the classical linear regression model
assumptions.
(a) I only
(b) I and II only
(c)* I, II, and III only
(d) I, II, III, and IV.
31. Simultaneous equations bias is a situation where
(a)* There is a two-way causal relationship between the explanatory and explained variable
(b) There is a two-way causal relationship between two selected explanatory variables
(c) There is a two-way causal relationship between two selected independent variables
(d) There is a two-way causal relationship between the residuals of two regression models.
Multiple Choice Test Bank Questions No Feedback – Chapter 6
Correct answers denoted by an asterisk.
1. Consider the following model estimated for a time series
yt = 0.3 + 0.5 yt-1 - 0.4 t-1 + t
where t is a zero mean error process.
What is the (unconditional) mean of the series, yt ?
(a) * 0.6
(b) 0.3
(c) 0.0
(d) 0.4.
2. Consider the following single exponential smoothing model:
St =  Xt + (1-) St-1
You are given the following data:
̂ =0.1, Xt=0.5,St-1=0.2
If we believe that the true DGP can be approximated by the exponential smoothing model, what
would be an appropriate 2-step-ahead forecast for X? (i.e., a forecast of Xt+2 made at time t)
(a) 0.2
(b) * 0.23
(c) 0.5
(d) There is insufficient information given in the question to form more than a one-step- ahead
forecast.
3. Consider the following MA(3) process
yt = 0.1 + 0.4ut-1 + 0.2ut-2 – 0.1ut-3 + ut
What is the optimal forecast for yt, 3 steps into the future (i.e., for time t+2 if all information until
time t–1 is available), if you have the following data?
ut-1 = 0.3; ut-2 = –0.6; ut-3 = –0.3
(a)
(b)
(c)
(d)
0.4
0.0
* 0.07
–0.1.
4. Which of the following sets of characteristics would usually best describe an autoregressive
process of order 3 (i.e., an AR(3))?
(a) * A slowly decaying acf, and a pacf with 3 significant spikes
(b) A slowly decaying pacf and an acf with 3 significant spikes
(c) A slowly decaying acf and pacf
(d) An acf and a pacf with 3 significant spikes.
5. A process, xt, which has a constant mean and variance, and zero autocovariance for all nonzero lags is best described as
(a) * A white noise process
(b) A covariance stationary process
(c) An autocorrelated process
(d) A moving average process.
6. Which of the following conditions must hold for the autoregressive part of an ARMA model to
be stationary?
(a) * All roots of the characteristic equation must lie outside the unit circle
(b) All roots of the characteristic equation must lie inside the unit circle
(c) All roots must be smaller than unity
(d) At least one of the roots must be bigger than one in absolute value.
7. Which of the following statements are true concerning time-series forecasting?
(i) All time-series forecasting methods are essentially extrapolative
(ii) Forecasting models are prone to perform poorly following a structural break in a series
(iii) Forecasting accuracy often declines with prediction horizon
(iv) The mean squared errors of forecasts are usually very highly correlated with the profitability
of employing those forecasts in a trading strategy.
(a) (i), (ii), (iii), and (iv)
(b) * (i), (ii), and (iii) only
(c) (ii), (iii) only
(d) (ii) and (iv) only.
8. If a series, yt, follows a random walk (with no drift), what is the optimal 1-step-ahead forecast
for y?
(a)
(b)
(c)
(d)
* The current value of y
Zero
The historical unweighted average of y
An exponentially weighted average of previous values of y.
9. Consider a series that follows an MA(1) with zero mean and a moving average coefficient of
0.4. What is the value of the autocorrelation function at lag 1?
(a)
(b)
(c)
(d)
0.4
1
*0.34
It is not possible to determine the value of the autocovariances without knowing the
disturbance variance.
10. Which of the following statements are TRUE?
(i)
(ii)
(iii)
(iv)
(a)
(b)
(c)
(d)
An MA(q) can be expressed as an AR(infinity) if it is invertible
An AR(p) can be written as an MA(infinity) if it is stationary
The (unconditional) mean of an ARMA process will depend only on the intercept and on
the AR coefficients and not on the MA coefficients
A random walk series will have zero pacf except at lag 1.
(ii) and (iv) only
(i) and (iii) only
(i), (ii), and (iii) only
* (i), (ii), (iii), and (iv).
11. Consider the following picture and suggest the model from the following list that best
characterises the process:
0.9
0.8
acf
pacf
0.7
acf and pacf
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9
10
-0.1
Lags
(a)
(b)
(c)
(d)
An AR(1)
An AR(2)
* An ARMA(1,1)
An MA(3).
The acf is clearly declining very slowly in this case, which is consistent with their being an
autoregressive part to the appropriate model. The pacf is clearly significant for lags 1
and 2, but the question is: does it them become insignificant for lags 2 and 4, indicating
an AR(2) process, or does it remain significant, which would be more consistent with a
mixed ARMA process? Well, given the huge size of the sample that gave rise to this acf
and pacf, even a pacf value of 0.001 would still be statistically significant. Thus an ARMA
process is the most likely candidate, although note that it would not be possible to tell
from the acf and pacf which model from the ARMA family was more appropriate. The
DGP for the data that generated this plot was y_t = 0.9 y_(t–1) – 0.3 u_(t–1) + u_t.
12. Which of the following models can be estimated using ordinary least squares?
(i) An AR(1)
(ii) An ARMA(2,0)
(iii) An MA(1)
(iv) An ARMA(1,1).
(a)
(b)
(c)
(d)
(i) only
* (i) and (ii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv).
13. If a series, y, is described as ‘mean-reverting’, which model from the following list is likely to
produce the best long-term forecasts for that series y?
(a)
(b)
(c)
(d)
A random walk
* The long term mean of the series
A model from the ARMA family
A random walk with drift.
14. Consider the following AR(2) model. What is the optimal 2-step-ahead forecast for y if all
information available is up to and including time t, if the values of y at time t, t-1 and t-2 are –
0.3, 0.4 and –0.1, respectively, and the value of u at time t-1 is 0.3?
yt = –0.1 + 0.75yt-1 – 0.125yt-2 + ut
(a)
(b)
(c)
(d)
–0.1
0.27
* –0.34
0.30.
15. What is the optimal three-step-ahead forecast from the AR(2) model given in Question 14?
(a)
(b)
(c)
(d)
–0.1
0.27
–0.34
* –0.31.
16. Suppose you had to guess at the most likely value of a one hundred-step-ahead forecast for
the AR(2) model given in Question 14 – what would your forecast be?
(a) -0.1
(b) 0.7
(c) * –0.27
(d) 0.75.
17. Which of these is NOT a consequence of working with non-stationarity variables?
(a) Shocks will be persistent
(b) Unjustifiably high R2
(c) The standard assumptions for asymptotic analysis will be invalid
(d)* It leads to data mining.
18. Three characteristics of a weakly stationary process are
(I) E  yt   
(II) E  yt    yt      2  
(III) E  yt1    yt 2      t 2t1 t1 , t2 .
What do the mathematical expressions I, II, and III imply?
(a) Constant variance, constant mean, and constant autocovariance, respectively
(b) Constant autocovariance structure, constant mean, and constant variance, respectively
(c) Constant mean, constant autocorrelation, and constant autocovariance, respectively
(d)* Constant mean, constant variance, and constant autocovariance structure, respectively.
Use the following to answer Questions 19 and 20. Suppose that you have estimated the first
five autocorrelation coefficients using a series of length 81 observations and found them to be
Lag
Autocorrelation coefficient
1
0.412
2
-0.205
3
-0.332
4
0.005
5
0.543
19. Which autocorrelation coefficients are significantly different from zero at the 5% level?
(a) The first and fifth autocorrelation coefficient
(b) The first, second, third, and fifth autocorrelation coefficient
(c)* The first, third, and fifth autocorrelation coefficient
(d) The second and fourth autocorrelation coefficient.
20. What is the appropriate Box–Pierce test statistic?
(a) 4.78
(b)* 47.83
(c) 59.05
(d) 5.91.
21. Consider the following MA(2) process yt  ut  1ut 1  2ut 2 where the errors follow a
standard normal distribution. What is the variance of yt ?
(a) E u 2   2u 2   2u 2 
t
1
t 1
2
t 2
(b)  2  12 2   22 2
(c) 1  12   22
(d)* All of the above.
22. A model where the current value of a variable depends upon only the values that the
variable took in previous periods plus an error term is called
(a)* An autoregressive model
(b) An autoregressive moving average model
(c) An autoregressive integrated moving average model
(d) A periodic lag model.
23. Is the following process yt  3 yt 1  2.75 yt 2  0.75 yt 3  ut stationary?
(a) Yes
(b)* No
(c) Partly stationary
(d) Cannot say.
24. What type of a process is yt  ut  1 yt 1  2 yt 2  ...   p yt  p  1ut 1   2ut 2  ...   qut q  ut
?
(a) An autoregressive model
(b)* An autoregressive moving average model
(c) An autoregressive integrated moving average model
(d) A periodic lag model.
25. Which of these is an appropriate way to determine the order of an ARMA model required to
capture the dynamic features of a given data?
(a) Graphically plotting the time series of the data
(b) Determining the number of parameters that maximises the information criteria
(c)* Determining the number of parameters that minimises the information criteria
(d) None of the above.
26. A recursive forecasting framework is one where
(a)* The initial estimation date is fixed but additional observations are added one at a time to
the estimation period
(b) The length of the in-sample period used to estimate the model is fixed so that the start date
and end date successively increase by one observation
(c) The initial estimation date changes as additional observations are added one at a time to the
estimation period
(d) The length of the out-of-sample period used to estimate the model is fixed so that the start
date and end date successively increase by one observation.
27. A rolling window forecasting framework is one where
(a) The initial estimation date is fixed but additional observations are added one at a time to the
estimation period
(b)* The length of the in-sample period used to estimate the model is fixed so that the start
date and end date successively increase by one observation
(c) The initial estimation date changes as additional observations are added one at a time to the
estimation period
(d) The length of the out-of-sample period used to estimate the model is fixed so that the start
date and end date successively increase by one observation.
Use the following to answer Questions 28 to 30.
A researcher is interested in forecasting the house price index in Country Z. The observed price
index values from 1996 to 2000 are 101, 103 104, 107 and 111. The researcher uses two
different forecasting models, A and B. The forecasts for the price index using Model A are
100.5, 102.4, 103.2, 106 and 111 whilst the forecast using Model B are 100.8, 102.2, 104, 104.2
and 112.1.
28. What are the closest to the mean squared errors for model A and B’s forecasts?
(a) 0.58 and 0.98, respectively
(b) 0.98 and 0.58, respectively
(c)* 0.45 and 1.95, respectively
(d) 1.95 and 0.45, respectively.
29. What are the closest to the mean absolute errors from models A and B?
(a)* 0.58 and 0.98, respectively
(b) 0.98 and 0.58, respectively
(c) 0.45 and 1.95, respectively
(d) 1.95 and 0.45, respectively.
30. Based on the MAE and MSE forecast evaluation metrics, which of these statements are
true?
(a)* Model A outperforms Model B at forecasting the house price index
(b) Model A underperforms Model B at forecasting the house price index
(c) Model A and Model B perform equally well at forecasting the house price index
(d) We cannot tell which model does best.
Multiple Choice Test Bank Questions No Feedback – Chapter 7
Correct answers denoted by an asterisk.
1. Which of the following are characteristics of vector autoregressive (VAR) models?
(i) They are typically a-theoretical and data driven
(ii) They can easily lead to overfitting
(iii) All variables on the right hand side of the equation are pre-determined
(iv) Their interpretation is often difficult from a theoretical perspective.
(a) * (i), (ii), (iii), and (iv)
(b) (i), (ii), and (iv) only
(c) (i) and (ii) only
(d) (i) and (iv) only.
For Questions 2 and 3, consider the following set of simultaneous equations:
 0   1Y2t   2Y3t   4 X 1t  u1t
Y2t   0   1Y1t   2 X 1t   3 X 2t   4 X 3t  u 2t
Y3t 
 0   1Y1t  u 3t
Y1t 
(1)
( 2)
(3)
Assume that the Y’s are endogenous and the X’s exogenous variables, and that the error terms
are uncorrelated.
2. Which of the following statement is true of equation (3)?
(a) According to the order condition, it is not identified
(b) According to the order condition, it is just identified
(c) * According to the order condition, it is over-identified
(d) There is insufficient information given in the question to determine whether the equation is
identified or not.
3. Estimation of equation (2) on its own using OLS would result in
(a) Consistent and unbiased coefficient estimates
(b) Consistent coefficient estimates which might be biased in small samples
(c) Inconsistent but unbiased coefficient estimates
(d) * Coefficient estimates that are neither unbiased nor consistent.
4. Which of the following statements is INCORRECT?
(a) Equations that are part of a recursive system can be validly estimated using OLS
(b) Unnecessary use of two-stage least squares (2SLS) – i.e., on a set of right hand side variables
that are in fact exogenous – will result in consistent but inefficient coefficient estimates
(c) 2SLS is just a special case of instrumental variables (IV) estimation
(d) * 2SLS and indirect least squares (ILS) are equivalent for over-identified systems.
5. Which of the following could be viewed as a disadvantage of the vector autoregressive (VAR)
approach to modelling?
(a) We do not need to specify which variables are endogenous and which are exogenous
(b) Standard form VARs can be estimated equation-by-equation using OLS
(c) * VARs often contain a large number of terms
(d) VARs can be expressed using a very compact notation.
6. Consider the following bivariate VAR(2):
y1t  10  11 y1t 1  12 y1t 2  13 y 2t 1  14 y 2t 2  u1t
y 2t   20   21 y1t 1   22 y1t 2   23 y 2t 1   24 y 2t 2  u 2t
Which of the following coefficient significances are required to be able to say that y1 Grangercauses y2 but not the other way around?
(a) 13 and 14 significant; 21 and 22 not significant
(b) * 21 and 22 significant; 13 and 14 not significant
(c) 21 and 23 significant; 11 and 13 not significant
(d) 11 and 13 significant; 21 and 23 not significant.
7. Which of the following statements is TRUE concerning VAR impulse response functions?
(i) Impulse responses help the researcher to investigate the interactions between the variables
in the VAR
(ii) An impulse response analysis is where we examine the effects of applying unit shocks to all of
the variables at the same time
(iii) Impulse responses involve calculating the proportion of the total forecast error variance of a
given variable that is explained by innovations to each variable
(iv) If the 2 standard error bars around the impulse responses for a given lag span (i.e., include)
the x-axis, it would be said that the response is statistically significant.
(a) (i), (ii), (iii), and (iv)
(b) (i), (ii), and (iii) only
(c) (i) only
(d) * (i) and (ii) only.
8. In the context of simultaneous equations modelling, which of the following statements is
TRUE concerning an exogenous variable?
(a)
(b)
(c)
(d)
The values of exogenous variables are determined within the system
* The exogenous variables are assumed to be fixed in repeated samples
Reduced form equations will not contain any exogenous variables on the RHS
Reduced form equations will contain only exogenous variables on the LHS.
9. Comparing the information criteria approach with the likelihood ratio test approach to
determining the optimal VAR lag length, which one of the following statements is true?
(a)
(b)
(c)
(d)
The choice of stiffness of penalty term will not affect the model choice
The validity of information criteria relies upon normal residuals
* Conducting a likelihood ratio test could lead to a sub-optimal model selection
An application of the univariate information criteria to each equation will give identical
results to the application of a multivariate version of the criteria to all of the equations
jointly.
10. The second stage in two-stage least squares estimation of a simultaneous system would be
to
(a) Estimate the reduced form equations
(b) * Replace the endogenous variables that are on the RHS of the structural equations with
their reduced form fitted values
(c) Replace all endogenous variables in the structural equations with their reduced form fitted
values
(d) Use the fitted values of the endogenous variables from the reduced forms as additional
variables in the structural equations.
11. Which of these assumptions is violated when an equation is estimated using OLS when it is
in fact part of a simultaneous structural system?
(a) E  X ' u   0
(b)* E  X ' u   0


(c) E  X ' X  X ' u  0
1
(d) None of the above.
12. A variable x is defined as ________ if its value is determined outside of the equation or
system of equations. What is the blank?
(a) Endogenous
(b)* Exogenous
(c) Homogeneous
(d) Heterogeneous.
13. Which of these is not an appropriate method of estimating equations that are from a
simultaneous system?
(a) Indirect least squares
(b) Two-stage least squares
(c)* Aggregate least squares
(d) Instrumental variables.
14. Which of these statements is true about vector autoregressive models?
(I) They allow the value of a variable to depend on more than just its own lags
(II) All variables are endogenous
(III) The researcher does not need to specify which variables are endogenous or exogenous
(IV) All variables are exogenous
(a) I only
(b) I and II only
(c)* I, II, and III only
(d) I, II, III, and IV.
15. Which of these is an approach used to determine the appropriate lag lengths of VAR
models?
(a) Graphically plotting the time series of the data
(b) Selecting the number of lags that maximises the information criteria
(c)* Selecting the number of lags that minimises the information criteria
(d) None of the above.
16. Assuming that you have a VAR model with 2 variables (A and B) including many lags, how
can you test whether A cause Granger-causes changes in B?
(a) By observing if the differences in correlation between A and B are statistically significant
(b)* Impose restrictions that all the coefficients of the lags of A are equal to 0 in the equation
for B of the VAR model and test the joint hypothesis within the F-test framework
(c) Impose restrictions that all the coefficients of the lags of B are equal to 0 in the equation for
A of the VAR model and test the joint hypothesis within the F-test framework
(d) None of the above.
17. Impulse responses:
(a)* Trace out the responsiveness of the dependent variables in the VAR to shocks to each of
the variables
(b) Are a different term for variance decompositions
(c) Trace out the responsiveness of the residuals in the VAR to shocks to each of the variables
(d) Give the proportion of the movements in the dependent variables that are due to their own
shocks versus shocks to other variables.
18. Variance decompositions
(a) Trace out the responsiveness of the dependent variables in the VAR to shocks to each of the
variables
(b) Will always give the same conclusions as impulse responses
(c) Trace out the responsiveness of the residuals in the VAR to shocks to each of the variables
(d)* Give the proportion of the movements in the dependent variables that are due to their
own shocks versus shocks to other variables.
Multiple Choice Test Bank Questions No Feedback – Chapter 8
Correct answers denoted by an asterisk.
1. Which of the following are probably valid criticisms of the Dickey–Fuller methodology?
(i) The tests have a unit root under the null hypothesis and this may not be rejected due to
insufficient information in the sample
(ii) The tests are poor at detecting a stationary process with a unit root close to the non-stationary
boundary
(iii) The tests are highly complex to calculate in practice
(iv) The tests have low power in small samples.
(a) (i), (ii), (iii), and (iv)
(b) * (i), (ii), and (iv) only
(c) (i) and (iii) only
(d) (ii) only.
2. Which of the following are problems associated with the Engle–Granger approach to modelling
using cointegrated data?
(i) The coefficients in the cointegrating relationship are hard to calculate
(ii) This method requires the researcher to assume that one variable is the dependent variable
and the others are independent variables
(iii) The Engle–Granger technique can only detect one cointegrating relationship
(iv) The Engle-Granger technique does not allow the testing of hypotheses involving the actual
cointegrating relationship.
(a) (i), (ii), (iii), and (iv)
(b) * (ii), (iii), and (iv) only
(c) (ii), (iii) only
(d) (ii) and (iv) only.
3. Consider the following vector error correction (VECM) model:
yt = yt-5 + 1yt-1 + 2yt-2 + 3yt-3 + 4yt-4 + ut
where yt is a k  1 vector of variables, and ut is a k  1 vector of disturbances.
Which of the following statements is true of the VECM?
(a) Johansen’s test for cointegration centres on the rank of the matrix 1
(b) If the variables yt are cointegrated,  will be of full rank
(c) If the rank of  is zero, the variables are cointegrated
(d) * Provided that all of the series in y are non-stationary, the rank of  can be at most
k-1.
4. Consider the following matrix:
3 6
X 

1 2 
What are its characteristic roots?
(a) * 5 and 0
(b) 5 and 5
(c) 3 and 2
(d) 0 and 0.
5. You have the following data for Johansen’s max rank test for cointegration between 4
international equity market indices:
r
max
5% Critical Value
0
40.03
30.26
1
26.81
23.84
2
13.42
17.72
3
8.66
10.71
How many cointegrating vectors are there?
(a) 0
(b) 1
(c) * 2
(d) 3.
6. Which criticism of Dickey–Fuller (DF)-type tests is addressed by stationarity tests, such as the
KPSS test?
(a) * DF tests have low power to reject the null hypothesis of a unit root, particularly in small
samples.
(b) DF tests are always over-sized.
(c) DF tests do not allow the researcher to test hypotheses about the cointegrating vector
(d) DF tests can only find at most one cointegrating relationship.
7. Consider the following data generating process for a series yt:
yt    1.5 yt 1  ut
Which one of the following most accurately describes the process for yt?
(a)
(b)
(c)
(d)
A random walk with drift
A non-stationary process
A deterministic trend process
* An explosive process.
8. Which one of the following best describes most series of asset prices?
(a) An independently and identically distributed (iid, i.e., ‘completely random’) process
(b) * A random walk with drift
(c) An explosive process
(d) A deterministic trend process.
9. If there are three variables that are being tested for cointegration, what is the maximum
number of linearly independent cointegrating relationships that there could be?
(a)
0
(b)
1
(c)
*2
(d)
3.
10. If the number of non-zero eigenvalues of the pi matrix under a Johansen test is 2, this
implies that
(a)
* There are 2 linearly independent cointegrating vectors
(b)
There are at most 2 linearly independent cointegrating vectors
(c)
There are 3 variables in the system
(d)
There are at least 2 linearly independent cointegrating vectors.
11. If a Johansen ‘max’ test for a null hypothesis of 1 cointegrating vectors is applied to a
system containing 4 variables, which eigenvalues would be used in the test?
(a)
The largest 1
(b)
* The second largest
(c)
The second smallest
(d)
The smallest.
12. Consider the testing of hypotheses concerning the cointegrating vector(s) under the
Johansen approach. Which of the following statements is correct?
(a) If the restriction is (are) rejected, the number of cointegrating vectors will rise
(b) If the restriction(s) is (are) rejected, the number of eigenvalues will fall
(c) Whether the restriction is supported by the data or not, the eigenvalues are likely to change
at least slightly upon imposing the restriction(s)
(d) * All linear combinations of the cointegrating vectors are themselves cointegrating vectors.
13. Which of these is a characteristic of a stationary series?
(a) Constant mean
(b) Constant autocovariances for each given lag
(c) Constant variance
(d)* All of the above.
14. Which of the following are consequences of using non-stationary data in regressions?
(I) Shocks will be persistent
(II) It can lead to spurious regressions
(III) t-ratios will not follow a t-distribution
(IV) The F-statistic will not follow an F-distribution.
(a) I only
(b) I and II only
(c) I, II, and III only
(d)* I, II, III, and IV.
15. What is the impact of shocks to an AR(1) with no drift yt     yt 1  ut if   1 ?
(a) Shocks will gradually die away
(b) Shocks will persist in the system and never die away
(c) Shocks will start to increase after the next observation but gradually die away
(d)* Shocks become more and more influential as time goes on.
16. What is the impact of shocks to an AR(1) with no drift yt     yt 1  ut if   1 ?
(a) Shocks will gradually die away
(b)* Shocks persist in the system and never die away
(c) Shocks will start to increase after the next observation but gradually die away
(d) Shocks become more and more influential as time goes on.
17. To induce stationarity in a deterministic trend-stationary process
(a)* Regress the non-stationary series on the time trend and use the residuals
(b) Difference the series once
(c) Difference the series twice
(d) No action is necessary because the process is already stationary.
18. The plotted series in the following graph is an example of a:
(a) Stationary process
(b)* Deterministic trend process
(c) White noise prices
(d) Random walk with drift.
19. A researcher would like to test for a unit root in a series. She runs the regression
yt   yt 1  ut . What should her null hypothesis be assuming that she adopts the Dickey–
Fuller test approach?
(a)*   0
(b)   1
(c)   0
(d)   1 .
20. Assuming the researcher in Question 19 would like to run an augmented Dickey–Fuller test
instead. What is the appropriate regression she would have to run and the null hypothesis of
the test?
p
(a)* yt   yt 1   i yt i  ut and   0 , respectively
i 1
p
(b) yt   yt 1   i yt i  ut and   1 , respectively
i 1
p
(c) yt   yt 1   i yt i  ut and   0 , respectively
i 1
p
(d) yt   yt 1   i yt i  ut and   1 , respectively.
i 1
21. Two variables are said to be cointegrated if
(a) If the two variables are I(0) and a linear a combination of the two are I(1)
(b) If the two variables are I(1) and a linear a combination of the two are I(1)
(c) If the two variables are I(0) and a linear a combination of the two are I(0)
(d)* If the two variables are I(1) and a linear a combination of the two are I(0).
22. Assume that you are trying to model the relationship between house prices and rents. If you
find that both series are non-stationary and a linear combination of the two series is stationary,
which of the following is true?
(I) Regressing the levels of house prices on the levels of rents could lead to spurious regressions
(II) House prices and rents are cointegrated
(III) An appropriate linear combination of house prices and rents is I(1)
(IV) House prices and rents are not cointegrated.
(a) I only
(b)* I and II only
(c) I, II, and III only
(d) I, II, III, and IV only.
Multiple Choice Test Bank Questions No Feedback – Chapter 9
Correct answers denoted by an asterisk.
1. Volatility clustering is
(a) The tendency for financial asset returns to have distributions that exhibit fat tails
(b)* The tendency for financial asset return volatility to appear in bunches
(c) The tendency for volatility to rise more following a large price fall than following a price rise
of the same magnitude
(d) All of the above.
2. Which of the following is TRUE about ARCH and GARCH models?
(I) They are used for modelling and forecasting volatility
(II) They are non-linear models
(III) They can both be estimated using OLS
(IV) Series estimated using these models must have a unit root process.
(a) I only
(b)* I and II only
(c) I, II, and III only
(d) I, II, III, and IV.
3. Which of these cannot be used to test for non-linearity?
(a) Portmanteau tests
(b)* White test
(c) Ramsey’s RESET test
(d) The BDS test.
4. Which of the following statements are true regarding volatility:
(I) It measures the total risk of financial assets
(II) It can be used in computing value-at-risk
(III) It is a component of the Black–Scholes formula for deriving the prices of traded options
(IV) It can be estimated using the variance of asset returns.
(a) I only
(b) I and II only
(c) I, II, and III only
(d)* I, II, III, and IV.
5. What are the names of the following models?
(I)  t2   0  1ut21
(II)  t2   0  1ut21   t21
(III)  t2  0  1ut21  2ut22  ...  qut2q
(IV)  t2  0  1ut21  2ut22  ...   put2 p  1 t21  2 t22  ...  q t2q
(a) GARCH (1), ARCH (1,1), GARCH(q) and ARCH(p,q), respectively
(b)* ARCH(1), GARCH(1,1), ARCH(q) and GARCH(p,q), respectively
(c) ARCH(1), EGARCH(1,1), ARCH(q) and EGARCH(p,q), respectively
(d) EGARCH (1), ARCH(1,1), EGARCH (q) and ARCH(p,q), respectively.
6. What is an appropriate approach to testing for ‘ARCH effects’?
(a)* Run a regression, collect the residuals, regress the squared residuals on their lags and
conduct a hypothesis test to check whether the coefficients of the lagged squared residuals are
equal to zero
(b) Run a regression, collect the fitted values, regress the fitted values on their squared lags and
conduct a hypothesis test to check whether the coefficients of the lagged squared fitted values
are equal to zero
(c) Employ White’s test
(d) All of the above.
7. Which of these is an appropriate technique used in estimating models from the GARCH
family?
(a)* Maximum likelihood
(b) Instrumental variables
(c) Indirect least squares
(d) Ordinary least squares.
8. What are the steps required to estimate an ARCH/GARCH model?
(a) First specify the appropriate equations for the correlation and the variance, then specify LLF
and the computer will generate parameter values that maximise the LLF
(b) First specify the appropriate equations for the median and the variance, then specify LLF
and the computer will generate parameter values that maximise the LLF
(c)* First specify the appropriate equations for the mean and the variance, then specify LLF and
the computer will generate parameter values that maximise the LLF
(d) None of the above.
9. GJR and EGARCH are types of GARCH models that allow for:
(a) An asymmetric response of returns to positive and negative shocks in the dependent
variable
(b) An asymmetric response of returns to positive and negative shocks to its lagged values
(c) A symmetric response of volatility to positive and negative shocks
(d)* An asymmetric response of volatility to positive and negative shocks.
10. Assume that you have estimated a GJR model of monthly stock returns and you obtain the
following equations:
yt  0.125
 t2  1.102  0.115ut21  0.641 t21  0.175ut21I t 1
Suppose that  t21  0.721, what would be the fitted conditional variance for time t if uˆt 1  0.5
and then if uˆt 1  0.5 ?
(a) 1.62 and 1.67, respectively
(b) 1.64 and 1.59, respectively
(c)* 1.59 and 1.64, respectively
(d) 1.67 and 1.62, respectively.
11. Suppose that a researcher estimates a GARCH(1,1) model and obtains a log likelihood
function (LLF) value of 71.22. She is interested in testing whether an ARCH(1) model is a better
model at describing volatility. If she estimates a model which imposes the necessary restrictions
and obtains an LLF value of 68.21, what would be the conclusion of her likelihood ratio test
(assuming a 5% significance level)?
(a) Statistical evidence suggesting that ARCH(1) is better than GARCH(1,1)
(b)* Statistical evidence suggesting that ARCH(1) is not better than GARCH(1,1)
(c) Statistical evidence suggesting that GARCH(1,1) is better than ARCH(1)
(d) We cannot say because we would need to know the number of observations.
12. What would typically be the shape of the news impact curve for a series that exactly
followed a GARCH(1,1) process?
(a) It would be asymmetric, with a steeper curve on the left than the right
(b) It would be asymmetric, with a steeper curve on the right than the left
(c) * It would be symmetric about zero
(d) It would be discontinuous about zero.
13. Which of the following are NOT features of an IGARCH(1,1) model?
(i) Forecasts of the conditional variance will converge upon the unconditional variance as the
horizon tends to infinity
(ii) The sum of the coefficients on the lagged squared error and the lagged conditional variance
will be unity
(iii) Forecasts of the conditional variance will decline gradually towards zero as the horizon
tends to infinity
(iv) Such models are never observed in reality.
(a) * (ii) only
(b) (ii) and (iv) only
(c) (ii), (iii), and (iv) only
(d) (i), (ii), (iii), and (iv)
.
14. Which of the following would represent the most appropriate definition for implied
volatility?
(a) * It is the volatility of the underlying asset’s returns implied from the price of a traded
option and an option pricing model
(b) It is the volatility of the underlying asset’s returns implied from a statistical model such as
GARCH
(c) It is the volatility of an option price implied from a statistical model such as GARCH
(d) It is the volatility of an option price implied from the underlying asset volatility.
15. Suppose that a researcher wanted to obtain an estimate of realised (‘actual’) volatility.
Which one of the following is likely to be the most accurate measure of volatility of stock
returns for a particular day?
(a) The price range (high minus low) on that day
(b) The squared return on that day
(c) * The sum of the squares of hourly returns on that day
(d) The squared return on the previous day.
16. Which of the following is the most plausible test regression for determining whether a
series y contains ‘ARCH effects’?
(a)
yt2   0  1 y t 1 2 y t  2  3 y t  3  4 y t  4  5 y t  5 ut
(b)
* yt2  0  1 yt 1 2 yt  2 3 yt 3 4 yt  4 5 yt 5 ut
(c)
yt  0  1 yt 1 2 yt  2 3 yt 3 4 yt  4 5 yt 5 ut
(d)
yt  0  1 yt 1 2 yt  2 3 yt 3 4 yt  4 5 yt 5 ut .
2
2
2
2
2
3
2
2
4
2
2
5
2
2
6
17. Consider the following conditional variance equation for a GJR model.
ht = 0 + 1 ut21 +ht-1+ut-12It-1
where It-1 = 1 if ut-1 < 0
= 0 otherwise
For there to be evidence of a leverage effect, which ONE of the following conditions must hold?
(a)
(b)
(c)
(d)
0 positive and statistically significant
*  positive and statistically significant
 statistically significantly greater than 0
1+ statistically significantly less than  .
18. Consider the three approaches to conducting hypothesis tests under the maximum
likelihood framework. Which of the following statements are true?
(i)
(ii)
(iii)
(iv)
(a)
(b)
(c)
(d)
The Wald test is based on estimation only under the null hypothesis
The likelihood ratio test is based on estimation under both the null and the alternative
hypotheses
The Lagrange multiplier test is based on estimation under the alternative hypothesis
only
The usual t- and F-tests are examples of Wald tests.
* (ii) and (iv) only
(i) and (iii) only
(i), (ii), and (iv) only
(i), (ii), (iii), and (iv).
19. Which one of the following problems in finance could not be usefully addressed by either a
univariate or a multivariate GARCH model?
(a)
(b)
(c)
(d)
(e)
Producing option prices
Producing dynamic hedge ratios
Producing time-varying beta estimates for a stock
* Producing forecasts of returns for use in trading models
Producing correlation forecasts for value at risk models.
Multiple Choice Test Bank Questions No Feedback – Chapter 10
Correct answers denoted by an asterisk.
1. Threshold autoregressive and Markov switching models:
(a)* Allow us to potentially capture regime switches in a dependent variable
(b) Forecast correlations of two distinct series
(c) Maximise the threshold of autoregressive models
(d) All of the above.
To check for seasonality (day-of-the-week effect) in stock returns of South Korea, Malaysia, the
Philippines, Taiwan, and Thailand, Brooks and Persand (2001) regress daily returns in each of
these countries’ stock market on five dummy variables D1 to D5 representing each day of the
week – i.e., D1 for Mondays, D2 for Tuesdays, D3 for Wednesdays, D4 for Thursdays and D5 for
Fridays:
rt   1D1t   2 D2t   3 D3t   4 D4t   5 D5t  ut
Their results were:
2. Which market(s) did not display any evidence of day-of-the-week effect?
(a) Thailand, Malaysia and Taiwan
(b) Philippines only
(c) South Korea only
(d)* South Korea and Philippines.
3. A Markov process can be written mathematically as:
(a) P  a  yt  b | y1 , y2 ,... yt 1   P a  yt  b | yt 1 , yt 2 
(b) P  a  yt  b | y1 , y2 ,... yt 1   P a  yt  b | yt 2 
(c)* P  a  yt  b | y1 , y2 ,... yt 1   P a  yt  b | yt 1 
(d) P  a  yt  b | y1 , y2 ,... yt 1   P a  yt  b | yt 2  .
4. The unknown parameters of a Markov switching model are usually estimated using:
(a)* Maximum likelihood
(b) Instrumental variables
(c) Indirect least squares
(d) Ordinary least squares.
5. The key difference between threshold autoregressive and Markov switching models is that:
(a) The latter can be estimated using ordinary least squares while the latter is estimated using
the indirect least squares estimation technique
(b) Under the latter, the state variable is assumed to be known and observable, while it is latent
under the former
(c)* Under the former, the state variable is assumed to be known and observable, while it is
latent under the latter
(d) None of the above.
6. Which of these equations is a self-exciting threshold autoregressive (SETAR) model?
(a)* yt  1  1 yt 1  u1t if yt k  r
yt  1  1 yt 1  u1t if yt k  r
(b) yt  1  1 yt 1  u1t if st  k  r
yt  1  1 yt 1  u1t if st  k  r
(c) yt  1  1 yt 1  u1t if t  k  r
yt  1  1 yt 1  u1t if t  k  r
(d) yt  1  1 yt 1  u1t if ut  k  r
yt  1  1 yt 1  u1t if ut  k  r .
7. To compare the goodness of fit of Markov switching and threshold autoregressive models
with linear models, one can compare the residual sums of squares of the two types of models
using an F-test. Is the statement true?
(a) Yes
(b)* No
(c) If the autoregressive model is restricted
(d) Cannot say without knowing the number of regimes in the regime switching models.
8. Suppose that a researcher wishes to test for calendar (seasonal) effects using a dummy
variables approach. Which of the following regressions could be used to examine this?
(i)
(ii)
(iii)
(iv)
A regression containing intercept dummies
A regression containing slope dummies
A regression containing intercept and slope dummies
A regression containing a dummy variable taking the value 1 for one observation and
zero for all others.
(a) (ii) and (iv) only
(b) (i) and (iii) only
(c) * (i), (ii), and (iii) only
(d) (i), (ii), (iii), and (iv).
9. If a series possesses the ‘Markov property’, what would this imply?
(i)
(ii)
(iii)
(iv)
(a)
(b)
(c)
(d)
The series is path-dependent
All that is required to produce forecasts for the series is the current value of the series
plus a transition probability matrix
The state-determining variable must be observable
The series can be classified as to whether it is in one regime or another regime, but it
can only be in one regime at any one time.
* (ii) only
(i) and (ii) only
(i), (ii), and (iii) only
(i), (ii), (iii), and (iv).
10. Consider the following two equations in a state space model, where yt is the observed
series, and ut and t are noise terms.
The two equations would respectively be termed as:
(a) * The measurement equation and the transition equation
(b) The data equation and the Markov equation
(c) The transition equation and the parameter model
(d) The measurement equation and the Markov process.
11. The ratio of the variance of the error term t to the variance of the error term ut is used as
the basis of a test for:
(a) * Whether it is necessary to allow for time-varying parameters
(b) Whether the observed series, yt, is excessively noisy
(c) Whether the Markov property holds
(d) Whether the Kalman filter will be efficient.
12. Consider the following two equations in a state space model, where yt is the observed
series, and ut and t are noise terms.
What would be the hyperparameters for this model?
(a) The transition matrix, Tt
(b) The state variable, t
(c) The estimated values of the noise terms (i.e., the values of ut and t)
(d) * The variances of the noise terms (i.e., the variances of ut and t)’
Multiple Choice Test Bank Questions No Feedback – Chapters 11-14
Correct answers denoted by an asterisk.
1. Which of these are advantages of using panel data?
(I) We can address a broader range of issues and tackle more complex problems than would be
possible with pure time-series or pure cross-sectional data alone
(II) It allows us to increase the number of degrees of freedom
(III) It allows us to increase the power of the tests
(IV) We can remove the impact of certain forms of omitted variables bias in regression results.
(a) I only
(b) I and II only
(c) I, II, and III only
(d)* I, II, III, and IV.
2. Which of these is a type of panel estimator approach?
(I) Fixed effects
(II) Random effects
(III) Seemingly unrelated regression effects
(IV) Time-varying effects.
(a) I only
(b)* I and II only
(c) I, II, and III only
(d) I, II, III, and IV.
3. Entity fixed effects models
(a)* Allow the intercept in the regression model to differ cross-sectionally but not over time,
while all of the slope estimates are fixed both cross-sectionally and over time
(b) Allow the slope in the regression model to differ cross-sectionally but not over time, while
the intercept estimates are fixed both cross-sectionally and over time
(c) Allow the intercept in the regression model to differ over time, while all of the slope
estimates are different both cross-sectionally and over time
(d) Any of the above could be true depending on the model specification.
4. Running a cross-sectional regression on the time-averaged values of the variables is known as
a:
(a) Within estimator
(b)* Between estimator
(c) Cross-sectional estimator
(d) Demeaned estimator.
5. The acronym LSDV in panel model estimation stands for
(a) Least squares dependent variable
(b) Limited squares dependent variable
(c)* Least squares dummy variable
(d) Limiting squares dummy variable.
6. Which of the following is a mathematical expression of a time-fixed effects model?
(a) yit     xit  uit
(b) yit     xit  i   it
(c) yit     xit  it , it   i  vit
(d)* yit     xit  t   it .
7. What of the following is a mathematical expression of a random effects model?
(a) yit     xit  uit
(b) yit     xit  i   it
(c)* yit     xit  it , it   i  vit
(d) yit     xit  t   it .
8. To test for unit roots in panel data, Levin, Lin and Chu (2002) develop a test based on the
equation yi ,t  i  t  i t  i yi ,t 1   i yi ,t 1  vit . What is the appropriate null hypothesis
for this test?
(a) * H 0 : i    0
(b) H 0 :  i  0
(c) H 0 : i  0
(d) . H 0 :   0
9. Logit and probit models are more appropriate than linear probability models because:
(a) Logit and probit can estimate probabilities that are negative
(b) Logit and probit cannot estimate probabilities that are greater than one
(c) Logit and probit cannot estimate probabilities that are negative but not greater than one
(d)* Logit and probit cannot estimate probabilities that are negative or greater than one.
10. Which of the following statements about logit and probit models is true?
(I) They cannot be estimated by ordinary least squares
(II) They can be estimated using maximum likelihood
(III) They can be estimated using non-linear least squares
(IV) They can be estimated using instrumental variables.
(a) I only
(b) I and II only
(c)* I, II, and III only
(d) I, II, III, and IV.
11. If the maximised value of the log-likelihood function for a logit model is 34.55 and for a
restricted model where all of the slope parameters are set to zero is 30.67, what is the pseudoR2?
(a) 0.13
(b)* –0.13
(c) 0.11
(d) –0.11.
12. Appropriate modelling of limited dependent variables that are assigned numerical values
having a natural ordering can be done using:
(I) Probit models
(II) Logit models
(III) Ordered probit models
(IV) Ordered logit models.
(a) I only
(b) I and II only
(c) II and III only
(d)* III and IV only.
13. In the context of an event study, a cumulative abnormal return:
(a) Is calculated by summing the individual returns over all the firms separately for each day
(b) * Is calculated by summing the individual returns over time for each firm separately
(c) Takes the geometric product of the individual returns over all the firms separately for each
day
(d) Takes the geometric product of the individual returns over time for each firm separately.
14. Which of the following statements is TRUE concerning the calendar time methodology
sometimes used in event studies?
(a) It will weight all the firms in the sample that underwent the event equally
(b) It can involve the calculation of a buy-and-hold abnormal return
(c) If the slope parameter in the test regression is positive and significant, this will provide
evidence of an abnormal return in the event study
(d) *It will give more weight in the sample to firms which underwent the event at a time when
few other firms did so.
15. The traditional Fama–MacBeth approach to tests of the CAPM involves:
(a) * A set of time-series regressions to estimate the betas for each stock and then a crosssectional regression to estimate the risk premium
(b) A set of cross-sectional regressions to estimate the betas and then a time-series regression
to estimate the risk premium
(c) A single cross-sectional regression to estimate the CAPM beta
(d) A time-series regression to estimate the betas for each stock and then another time-series
regression to estimate the risk premium.
16. In the Fama–MacBeth regressions, the parameter estimates in the second stage are
interpreted as:
(a) Factor loadings
(b) * Factor risk premia
(c) Average returns for each stock
(d) The volatilities of returns for each stock.
17. In the Fama–MacBeth regressions, the parameter estimates in the first stage are
interpreted as:
(a) * Factor loadings
(b) Factor risk premia
(c) Average returns for each stock
(d) The volatilities of returns for each stock.
18. In Fama–French (1993)- and Carhart (1994)-type models, for there to be no evidence of
outperformance by a fund manager, we would require:
(a) The intercept is positive but not statistically significant
(b) The intercept is not positive and significant and slope estimates are all insignificant
(c) * The intercept is not positive and significant
(d) The slope estimates are all insignificant.
19. If we use the block maximum approach to estimating the parameters of a member of the
extreme value family of distributions and we select a large number of short blocks, which of the
following is a likely disadvantage?
(a) * A number of data points would be classified as extreme when they are not, leading to bias
in the shape parameter estimate
(b) Too few data points would be classified as extreme, leading to excessive noise in the shape
parameter estimate
(c) Too few data points would be classified as extreme, leading to bias in the shape parameter
estimate
(d) A number of data points would be classified as extreme when they are not, leading to
excessive noise in the shape parameter estimate.
20. Which of the following distributions would be most appropriate for modelling the central
part of the distribution of a set of stock returns?
(a) Gumbel
(b) Fréchet
(c) Weibull
(d) * Normal.
21. If we use the peaks-over-threshold approach to estimating the parameters of an extreme
value distribution, if we use a value of U, the threshold, that is too high (i.e., too far into the
tail), which of the following is a likely disadvantage?
(a) A number of data points would be classified as extreme when they are not, leading to bias in
the shape parameter estimate
(b) * Too few data points would be classified as extreme, leading to excessive noise in the shape
parameter estimate
(c) Too few data points would be classified as extreme, leading to bias in the shape parameter
estimate
(d) A number of data points would be classified as extreme when they are not, leading to
excessive noise in the shape parameter estimate.