s
Brighton Business School
Undergraduate Programmes
BSc(Hons) Economics & Finance
BSc(Hons) Finance & Investment
Level Six Examination
May 2015
EC388: Financial Econometrics
Instruction to candidates:
Time allowed: 2 Hours
Rubric: You are require to answer THREE questions from a total of six
All questions carry 100 marks
(Mark allocations within questions are shown in brackets).
Show all workings/calculations clearly.
Nature of examination: unseen, closed book
Allowable material: non-programmable calculators
Attachments:
Statistical tables (t-table, DW table)
Formula sheet
Page 1 of 7
EC388: Financial Econometrics
(May 2015)
Question 1
Consider the simple linear model:
Yt = 0 + 1Xt + ut
a)
where
ut ~ NID(0, σ2)
Y2 = 2708
XY = 530
You are given the following information
X = 30
X2 = 110
Y = 160
T=10
Using the matrix approach compute the Ordinary Least Squares (OLS) estimates for 0 and 1, and
the corresponding variance-covariance matrix.
(60 marks)
b)
Assuming that the assumption in regard to the error process is correct then the estimated
coefficients are ‘BLUE’. Explain this statement.
(10 marks)
c)
Use a significance level of 0.05 to implement a test of the following hypotheses
H0: 1 = 0
Vs
H1: 1  0
Vs
H1: 1 > 2
and
H0: 1 = 2
What do you conclude?
(30 marks)
Page 2 of 7
EC388: Financial Econometrics
(May 2015)
Question 2
A simple demand for money model is specified as:
mt = 0 + 1yt + ut
ut  NID(0,2)
t = 1,....,30
where, mt denotes the natural logarithm of real money balances, and yt denotes the natural
logarithm of real income and ut is an error term that is assumed to satisfy the standard
assumptions.
a)
It is hypothesised that the model omits a relevant variable, i.e. the rate of interest. Explain
fully, using appropriate formulae and expressions, the implications this has for the estimated
coefficient 1.
(40 marks)
b)
The model is re-estimated with the a suitable nominal interest rate (e.g. the 3 month treasury
bill rate) and the following coefficient estimates are obtained:
mt
= 1.25
(0.052)
+
0.709 yt – 0.006 Rt
(0.109)
(0.002)
where, mt and yt are defined as above, and Rt denotes the nominal interest expressed as a
percentage. The estimated standard errors are reported in parentheses beneath the relevant
coefficient estimate.
i)
Does this model conform to monetary theory?
ii)
Comment on the statistical significance of the estimated coefficients and carefully interpret
their estimated impact on money demand.
(20 marks)
c)
The researcher observes a possible structural break in the data. Outline a method that can
be used to test for a structural break in the data.
(30 marks)
Page 3 of 7
EC388: Financial Econometrics
(May 2015)
(10 marks)
Question 3
An import demand function is specified as
mt =  0 +  1 y t +  2 p t + u t
where,
mt denotes the natural logarithm of real import demand,
yt denotes the natural logarithm of real income, and
pt denotes the natural logarithm of real import price and ut is the error term.
a)
It is hypothesised that the variance in the error term is heteroscedastic and related to
income. Explain fully, using appropriate expressions, how you would test this hypothesis if
heteroscedasticity is of known form.
(40 marks)
b)
It is now assumed that heteroscedasticity is of unknown form and the variable that is the
source of heteroscedasticity cannot be identified. Using appropriate expressions, explain
fully how you would test for heteroscedasticity in this case.
(50 marks)
c)
If the relationship were to be estimated by OLS what would be the consequences?
(10 marks)
Page 4 of 7
EC388: Financial Econometrics
(May 2015)
Question 4
A researcher investigating the relationship between the inflation rate and the unemployment rate
for the US between 1948 and 1996 using annual data reports the following results:
INFt = 1.427 (1.719)
0.468 UNt
(0.189)
ut  NID (0,2)
t = 1,....,49
R2 0.052, DW = 0.803, F= 2.616 [0.1125]
where,
INF denotes the inflation rate at time t and,
UN denotes the unemployment rate at time t.
The estimated standard errors are reported in parentheses beneath the relevant variable and u t is
an error term that is assumed to satisfy the standard assumptions.
a)
Comment briefly on the estimated relationship.
(10 marks)
b)
Using the information above test this model for first order autocorrelation using the DW
procedure.
(30 marks)
c)
The researcher re-estimates the equation and the following results are reported:
INFt = 2.431 - 0.468 UNt + 0.728 INFt-1 u t  NID (0,2)
(1.719)
(0.289)
(0.126)
R2 0.467,
DW = 1.477,
F= 19.719 [0.000]
Is there any evidence of autocorrelation in this model?
d)
t = 1,....,48
(40 marks)
What are the possible causes of autocorrelation?
(10 marks)
e)
What are the consequences on the estimated coefficients and estimated standard errors if
autocorrelation is present in the data?
(10 marks)
Page 5 of 7
EC388: Financial Econometrics
(May 2015)
Question 5
A financial analyst investigating the volatility of daily returns to the S&P500 postulates the
estimation of two alternative models:
Model 1:
yt = μ + βXt + ut ,
where ut ~ N(0, 1) and
σ 2u t  α 0  α 1 u 2t 1  ,...,  α p u 12 p
Model 2:
yt = μ + βXt + ut
where ut ~ N(0, 1) and
σ 2u t  α 0  α 1 u 2t 1  γσ 2t 1
In both models yt is the daily returns on the S&P500, 𝜎𝑢2 is the variance of the error term ut, and Xt
is a vector of regressors assumed to affect the returns to the S&P500.
a)
What class of regression models are models 1 and 2 examples?
(10 marks)
b)
Why would either model be superior to OLS in modelling returns in financial markets?
(10 marks)
c)
Why is model 2 preferred to model 1, by researchers and financial analysts, when modelling
volatility?
(10 marks)
d)
What range of values are likely for the coefficients; , 0, 1, and γ in model 2?
(30 marks)
e)
The analyst now contemplates the estimation of two further models
Model 3: yt = μ + βXt + ut
where ut ~ N(0, 1) and
σ 2u t  α 0  α 1 u 2t 1  γσ 2t 1  u 2t 1 D
Model 4: yt = μ + β1 Xt + β2 𝜎𝑢2 + ut
where ut ~ N(0, 1) and
σ 2u t  α 0  α 1 u 2t 1  γσ 2t 1
Carefully explain the rationale for choosing either of these models over model 2.
(40 marks)
Page 6 of 7
EC388: Financial Econometrics
(May 2015)
Question 6
a)
Define the following:
i)
A stationary process;
(10 marks)
ii)
A random walk;
(10 marks)
iii)
An integrated process of order n.
(10 marks)
b)
Explain fully, using appropriate mathematical expressions, how you would test for
stationarity in a univariate time series using the Dickey-Fuller (DF) and Augmented DickeyFuller (ADF) procedure.
(60 marks)
c)
Outline a test to help distinguish a trended stationary process from a difference stationary
process.
(10 marks)
Page 7 of 7
EC388: Financial Econometrics
(May 2015)