Chapter 13. Time Series Regression
In this section we discuss single equation regression techniques that are important for the
analysis of time series data: testing for serial correlation, estimation of ARMA models,
using polynomial distributed lags, and testing for unit roots in potentially nonstationary
time series.
The chapter focuses on the specification and estimation of time series models. A number
of related topics are discussed elsewhere: standard multiple regression techniques are dis-
cussed in Chapters 11 and 12, forecasting and inference are discussed extensively in
Chapters 14 and 15, vector autoregressions are discussed in Chapter 20, and state space
models and the Kalman filter are discussed in Chapter 22.
Serial Correlation Theory
A common finding in time series regressions is that the residuals are correlated with their
own lagged values. This serial correlation violates the standard assumption of regression
theory that disturbances are not correlated with other disturbances. The primary problems
associated with serial correlation are:
OLS is no longer efficient among linear estimators. Furthermore, since prior residu-
als help to predict current residuals, we can take advantage of this information to
form a better prediction of the dependent variable.
Standard errors computed using the textbook OLS formula are not correct, and are
generally understated.
If there are lagged dependent variables on the right-hand side, OLS estimates are
biased and inconsistent.
EViews provides tools for detecting serial correlation and estimation methods that take
account of its presence.
In general, we will be concerned with specifications of the form:
(13.1)
where is a vector of explanatory variables observed at time t, is a vector of vari-
ables known in the previous period,
b
and
g
are vectors of parameters, is a disturbance
term, and is the innovation in the disturbance. The vector may contain lagged
values of u, lagged values of
e
, or both.
y
t
x
t
′¯u
t
+=
u
t
z
t 1
−
′°"
t
+=
x
t
z
t 1
−
u
t
"
t
z
t 1
−
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