Chapter 1
Introduction
‘Introductory Econometrics for Finance’ © Chris Brooks 2019
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Introduction:
The Nature and Purpose of Econometrics
• What is Econometrics?
– Literal meaning is “measurement in economics”, it is a discipline of statistics
• Definition of financial econometrics:
– The application of statistical and mathematical techniques to problems in
finance.
• Specialized for using and developing mathematical and statistical
tools for:
• Empirical estimation of relationships in finance and economics
• Testing theories in finance and economics
• Making predictions and forecasts
• Evaluating government and business policy
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Introduction:
The Nature and Purpose of Econometrics
• Econometrics uses nonexperimental (observational) data
• Regression analysis is the major tool in econometrics
• Why study econometrics?
– Important to be able to apply theories in finance and economics to real world
data.
– Theory may be ambiguous as to the effect of some policy change, and in any
case theory rarely tells us how large the effect might be.
– Forecasting economic variables (inflation, interest rates, housing starts, and
so on).
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Examples of the kind of problems that
may be solved by an Econometrician
1. Testing whether financial markets are weak-form informationally
efficient.
2. Testing whether the CAPM or APT represent superior models for the
determination of returns on risky assets.
3. Measuring and forecasting the volatility of bond returns.
4. Explaining the determinants of bond credit ratings used by the ratings
agencies.
5. Modelling long-term relationships between prices and exchange rates.
‘Introductory Econometrics for Finance’ © Chris Brooks 2019
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Examples of the kind of problems that
may be solved by an Econometrician (cont’d)
6. Determining the optimal hedge ratio for a spot position in oil.
7. Testing technical trading rules to determine which makes the most
money.
8. Testing the hypothesis that earnings or dividend announcements have
no effect on stock prices.
9. Testing whether spot or futures markets react more rapidly to news.
10. Forecasting the correlation between the returns to the stock indices of
two countries.
‘Introductory Econometrics for Finance’ © Chris Brooks 2019
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Steps involved in the formulation of
econometric models
Economic or Financial Theory (Previous Studies)
Formulation of an Estimable Theoretical Model
Collection of Data
Model Estimation
Is the Model Statistically Adequate?
No
Reformulate Model
Yes
Interpret Model
Use for Analysis
‘Introductory Econometrics for Finance’ © Chris Brooks 2019
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Steps in Econometric Analysis
(a) Economic/Finance model
• For example, consumption function
C = f (Y ;W);
(1)
• where C is consumption, Y is income, W is wealth, and f is
some function (typically unknown).
• Of course there are other factors affecting consumption, but
equation (1) captures the essence of the problem.
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Steps in Econometric Analysis
(b) Econometric model
• Usually the economic model does not specify exactly the
functional form. In addition the economic model is assumed to
be exact in the simplified world satisfying the simplifying
assumptions.
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Steps in Econometric Analysis
• The task of econometrics is to turn the economic model to an
operational one. Usually this amounts to a linear
approximation,
C = β0 + β1Y + β2W + u;
(2)
• where β0, β1 and β2 are parameters of the model, to be
estimated from the data, and u is (unobservable) random error
or disturbance term, which determines the stochastic
properties of the model.
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Types of Data and Notation
• There are 4 types of data which econometricians might use for
analysis:
1. Time series data
2. Cross-sectional data
3. Pooled Cross-sections
4. Panel data, a combination of 1. & 2.
• The data may be quantitative (e.g. exchange rates, stock
prices, number of shares outstanding), or qualitative (e.g. day
of the week).
‘Introductory Econometrics for Finance’ © Chris Brooks 2019
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Types of Data and Notation
(1) Cross-sectional
• data on one or more variables collected at a single point in time.
• From econometric point of view it is important that the observations
consist a random sample from the underlying population.
• Examples
– A poll of usage of internet stock broking services
– Cross-section of stock returns on the New York Stock Exchange
– A sample of bond credit ratings for UK banks
• Examples of problems that could be tackled using a cross-sectional
regression
– The relationship between company size and the return to investing in its shares
– The relationship between a country’s GDP level and the probability that the
government will default on its sovereign debt.
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Types of Data and Notation
Example 1: firm cross-sectional data on roe and other variables
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Types of Data and Notation
(2) Time Series Data
• A time series consist of observations on a variable(s) over time.
Typical examples are daily share prices, interest rates, CPI values.
• An important additional feature over cross-sectional data is the
ordering of the observations, which may convey important
information.
• Another additional feature is data frequency which may require
special attention.
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Types of Data and Notation
• Examples:
Series
GNP or unemployment
government budget deficit
money supply
value of a stock market index
Frequency
monthly, or quarterly
annually
weekly
as transactions occur
• Examples of problems that could be tackled using a time-series regression
– How the value of a country’s stock index has varied with that country’s
macroeconomic fundamentals.
– How the value of a company’s stock price has varied when it announced the
value of its dividend payment.
– The effect on a country’s currency of an increase in its interest rate
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Types of Data and Notation
Example 2: time data subset of Fama/French three factor model data
(https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.
html)
The three factors used are SMB (small minus big), HML (high minus
low) and the portfolio's return less the risk free rate of return
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Types of Data and Notation
(3) Pooled Cross-sections
• Both time series and cross-section features.
• An example is a data set where a number of firms are randomly selected,
say in 1990, and another sample is selected in 2000. (i.e., data consist of
two different random samples.)
• If in both samples the same features are measured, combining both years
forms a pooled cross-section data set.
• Pooled cross-section data is analyzed much the same way as usual crosssection data.
• However, many times it is important to pay special attention to the fact that
there are 10 years in between.
• Usually the interest is whether there are some important changes between
the time points. Statistical tools are usually the same as those used for
analysis of differences between two independently sampled populations.
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Types of Data and Notation
(4) Panel Data
• Panel data (longitudinal data) consists of time series for each crosssectional member (i.e., same individuals) in the data set. That is one has
series of history from each individual/firm.
• Example 3: city panel data on n=64 firms for two years per city
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Types of Data and Notation
• i : index for the i-th observation in cross-sectional data
– Xi = observation i on the cross-sectional random variable X
• n: sample size (total number of observations)
• t : index for the time period
– Yt = value of Y in period t.
• T: total number of observations on the time series random variable
• Panel data uses a combination of cross-sectional and time-series
notations
– Zit = value of observation i on the random variable Z in period t
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What are the Special Characteristics
of Financial Data?
•
•
•
•
Frequency & quantity of data
– The data can be high frequency, i.e. daily or even every minute.
– Stock market prices are measured every time there is a trade or somebody posts a new
quote.
Quality
– Recorded asset prices are usually those at which the transaction took place. Little
possibility for measurement error.
Financial Data is affected by risk
– Most financial data is affected by not just return but also risk, which requires specialist
modelling.
Financial data is ‘noisy’
– It is often difficult to pick up patterns in the data due to the variable nature of financial
data.
– A slight uptick or downtick in a security's or market's price and/or volume representing
little or no actual change in its fundamentals
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Causality and Ceteris Paribus
• Causality: Cause and effect x  y
– For example, eating too much fast food without any physical activity leads to
weight gain.
• Ceteris Paribus: "Holding other relevant factors fixed".
– For example, it can be predicted that if the price of coffee increases—ceteris
paribus—the quantity of coffee demanded by buyers will decrease.
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