INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 122 We will mostly be concerned with first-order
autoregressive autocorrelation, often denoted AR (1). AR (1) appears to be the most common type of autocorrelation approximation. It is described as positive or negative according to the sign of
ρ. Note that if
ρ is 0, there is no autocorrelation occurrence. There are two major things that
will be discussed in this unit, which are
1. Test for the presence of serial correlation. Estimate the regression equation when the errors are serially correlated.
Durbin-Watson Test (DW) The simplest and most commonly used model is one where the errors and have a correlation. For this model one can think of testing hypotheses about on the basis of
, the correlation between the
least squares residuals and . A commonly used statistic for this purpose which is related to is the DW statistic, which will be denote by. It is defined as
∑ (
)
∑
…[4.17] Where is the
estimated residual for period . DW can be rewritten as
∑
∑
∑
∑
∑
∑
…[4.18] Since and are approximately equal if the sample is large, we have
( ) If The sampling distribution of depends on the values of the explanatory variables
and hence DW derived upper ( ) limits and lower ( ) limits for the significance levels for
. There are tables to test the hypothesis of zero autocorrelation against the hypothesis of first-order positive autocorrelation. (For negative autocorrelation we interchange (
) ( )
), hence;
