Chapter 12
Properties of regression models with time
series data
Overview
This chapter begins with a statement of the regression model assumptions for regressions using time series data,
paying particular attention to the assumption that the disturbance term in any time period be distributed
independently of the regressors in all time periods.
There follows a general discussion of autocorrelation: the
meaning of the term, the reasons why the disturbance term may be subject to it, and the consequences of it for
OLS estimators.
The chapter continues by presenting the Durbin–Watson test for AR(1) autocorrelation and
showing how the problem may be eliminated.
Next it is shown why OLS yields inconsistent estimates when the
disturbance term is subject to autocorrelation and the regression model includes a lagged dependent variable as
an explanatory variable.
Then the chapter shows how the restrictions implicit in the AR(1) specification may be
tested using the common factor test, and this leads to a more general discussion of how apparent autocorrelation
may be caused by model misspecification.
This in turn leads to a general discussion of the issues involved in
model selection and, in particular, to the general-to-specific methodology.
Learning outcomes
After working through the corresponding chapter in the text, studying the corresponding slideshows, and doing
the starred exercises in the text and the additional exercises in this guide, you should be able to:
state the regression model assumptions for regressions with time series data and explain the implications of
the assumption that the disturbance term be distributed independently of the regressors in all time periods
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explain the concept of autocorrelation and the difference between positive and negative autocorrelation
describe how the problem of autocorrelation may arise
describe the consequences of autocorrelation for OLS estimators, their standard errors, and
t
and
F
tests, and
how the consequences change if the model includes a lagged dependent variable
perform the Durbin–Watson
d
test for AR(1) autocorrelation and, where appropriate, the Durbin
h
test
explain how the problem of AR(1) autocorrelation may be eliminated
describe the restrictions implicit in the AR(1) specification
perform the common factor test
explain how apparent autocorrelation may arise as a consequence of the omission of an important variable or
the mathematical misspecification of the regression model.
demonstrate that the static, AR(1), and ADL(1,0) specifications are special cases of the ADL(1,1) model
explain the principles of the general-to-specific approach to model selection and the defects of the specific-
to-general approach
October 2007

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