econometrics

1. Introduction to
Financial Econometrics
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Econometrics
• Literally means “measurement in economics”
• practically it means “the application of statistical
techniques to problems in economics”
• focus on problems in financial economics
• explain the behavior of a financial variable

3. Econometrics (Gerhard 1968)
• application of mathematical statistics to economic
data
• to lend empirical support to the models
constructed
• by mathematical economics and
• to obtain numerical results
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4. Econometrics (Goldberger 1964).
Econometrics may be defined
• as the social science
• in which the tools of economic theory,
mathematics, and statistical inference
• are applied to the analysis of economic
phenomena.
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• Economic theory makes statements or hypotheses that
are mostly qualitative in nature (the law of demand)
• the law does not provide any numerical measure of
the relationship.
• Economic statistics collect, process, and present
economic data in charts and tables.
• It does not go any further. The one who does that is
the econometrician.
• Econometrics is mainly interested in the empirical
verification of economic theory.
Econometrics

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• Statement of theory or hypothesis.
• Specification of the mathematical model of the theory
• Specification of the statistical, or econometric, model
• Collecting the data
• Hypothesis testing
• Forecasting or prediction
• Using the model for control or policy purposes.
Econometric methodology

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Econometric Model Building
Assess implications for theory
Interpret model
Satisfactory
Re-estimate model using better techniques
Collect better data
Reformulate model
Unsatisfactory
5. Evaluate estimation results
4. Estimate model
3. Collect data
2. Derive estimable model
1. Understand finance theory

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Econometrics versus Financial
Econometrics
Little difference between econometrics and financial
econometrics beyond emphasis
– Data samples
• Economics-based econometrics often suffers from paucity of
data
• Financial economics often suffers from infoglut and signal to
noise problems even in short data samples
– Time scales
• Economic data releases often regular calendar events
• Financial data are likely to be real-time or tick-by-tick

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Financial Data
What sorts of financial variables do we usually want
to explain?
oPrices - stock prices, stock indices, exchange rates
oReturns - stock returns, index returns Volatility
oCorporate finance variables

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Cross Sectional Data
data on one or more variables collected at a single point
in time
e.g. company size and the return on its shares in 2014
Using a Cross-Sectional Regression
• The relationship between company size and the
return
• The relationship between a country’s GDP level and
default on its sovereign debt.

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Time Series Data
data arranged chronologically, at regular intervals
Using a Time Series Regression
• How the value of a country’s stock index has varied
with that country’s macroeconomic fundamentals.
• How a company’s stock returns has varied when it
announced the value of its dividend

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Panel Data
Panel Data has the dimensions of both time series
and cross-sections
e.g. the daily prices of a number of stocks over two
years.
– It is common to denote each observation by the letter t
and the total number of observations by T for time
series data,
– and to denote each observation by the letter i and the
total number of observations by N for cross-sectional
data.

13. Econometric Model of Consumption with
effect of GDP
• The relationships between economic variables are
generally inexact.
• variables like size of family, ages of the members
in the family, family religion, etc., affect
consumption expenditure. .
• To allow for the inexact relationships between
economic variables is modified as follows:
Y = β1 + β2X + u
• where u, known as the disturbance, or error, term,

14. linear regression model
Y is linearly related to X, but that the relationship
between the two is not exact; it is subject to
individual variation.

15. Obtaining Data
To obtain the numerical values of β1 and β2, we need
data. which relate to the personal consumption
expenditure (PCE) and the gross domestic product
(GDP).

16. Regression Line

17. Estimation of Econometric Model
• Regression analysis is the main tool
we obtain the following estimates of β1 and β2, namely,
−184.08 and 0.7064.
• Thus, the estimated consumption function is:
Yˆ = −184.08 + 0.7064Xi
• The slope coefficient was about 0.70
• an increase in real income of 1 rupee led, on average,
to an increase of about 70 cents in real consumption.

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Financial Data
• Financial data have some defining characteristics
that shape the econometric approaches that can be
applied
– outliers
– trends
– mean-reversion
– volatility clustering

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Outliers

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Trends

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Mean-Reversion (with Outliers)

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More Mean-Reversion

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Volatility Clustering

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Basic Data Analysis
• All pieces of empirical work should begin with
some basic data analysis
– Eyeball the data/carefully looking into data
– Summarize the properties of the data series
– Examine the relationship between data
series

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Basic Data Analysis
• Eyeballing the data helps establish presence of
– trends versus mean reversion
– volatility clusters
– key observations
• outliers
–data errors?
• turning points
• regime changes

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Basic Data Analysis
Summary statistics
– Average level of variable
• Mean, median, mode
– Variability around this central tendency
• Standard deviations, variances,
maxima/minima
– Distribution of data
• Skewness, kurtosis

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Basic Data Analysis
• Since we are usually concerned with explaining one
variable using another
– “trading volume depends positively on volatility”
• relationships between variables are important
– cross-plots, multiple time-series plots
– correlations (covariances)
– multi-collinearity

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The basic story
• y is a function of x
• y depends on x
• y is determined by x
“the spot exchange rate depends on relative price
levels and interest rates…”

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Terminology
• y is the x’s are the
– predictand predictors
– regressand regressors
– explained variable explanatory variables
– dependent variable independent variables
– endogenous variable exogenous variables
– left hand side variable right hand side variables

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Data
• Suppose we have n observations on y and x:
cross section
yi = α + β xi + ui i = 1, 2, …, n
time series
yt = α + β xt + ut t = 1, 2, …, n

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Errors
• Where does the error come from?
– Randomness of (human) nature
– Omitted variables
• men and markets are more complex than the
models we use to describe them.
• Everything else is captured by the error term

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Objectives of model building
• to get good point estimates of α and β given
the data
• to understand how confident we should be in
those estimates
• both will allow us to make statistical
inferences
– on the true form of the relationship between y and
x (“test the theory”)

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Simple Regression: An Example
following data on the excess returns on a fund manager’s
portfolio (“fund XXX”) together with the excess returns
on a market index:
We want to find whether there is a relationship between x
and y given the data that we have.
Year, t Excess return
= rXXX,t – rft
Excess return on market index
= rmt - rft
1 17.8 13.7
2 39.0 23.2
3 12.8 6.9
4 24.2 16.8
5 17.2 12.3

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Finding the Line of Best Fit
• We can use the general equation for a straight line,
y = α + βx
to get the line that best “fits” the data.
• Is this realistic? No. So what we do is to add a
random disturbance term, u into the equation.
yt =  + xt + ut
where t = 1, 2, 3, 4, 5

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Determining the Regression
Coefficients
• So how do we determine what  and  are?
• Choose  and  so that the distances from the
data points to the fitted lines are minimised
• so that the line fits the data as closely as possible
• The most common method used to fit a line to the
data is known as OLS (ordinary least squares).

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Ordinary Least Squares
What we actually do is
• take each vertical distance between the data
point and the fitted line
• square it and
• minimize the total sum of the squares (hence
least squares).

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y = - 1.7366 + 1.6417x
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5 10 15 20 25

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Thanks