102 The Basics of financial economeTrics
■ (^) Autocorrelation of residuals is quite common in time series financial
data. In time series analysis, autocorrelation is also referred to as serial
correlation and lagged correlation.
■ (^) If a residual t is positive (negative) and the residual that follows, t + 1,
tends to be positive (negative), this behavior is said to be persistent and
is referred to as positive autocorrelation. If, instead, a positive (negative)
residual t tends to be followed by a negative (positive) residual t + 1, this
is referred to as negative autocorrelation.
■ (^) Significant autocorrelation in a time series means that, in a probabilistic
sense, the series is predictable because future values are correlated with
current and past values.
■ (^) The presence of autocorrelation complicates hypothesis testing of the
regression coefficients. This is because although the regression coeffi-
cient estimates are unbiased, they are not best linear unbiased estimates
so that the variances may be significantly underestimated and the result-
ing hypothesis tests questionable. When significant autocorrelation is
present, the Aitken’s generalized least squares (GLS) estimator, which is
an optimal linear unbiased estimated, can be employed.
■ (^) The most popular test for the presence of autocorrelation of the residu-
als is the Durbin-Watson test, or more specifically, the Durbin-Watson
d-statistic.
■ (^) Autoregressive moving average (ARMA) models are used for dealing
with the problem of autocorrelation in time series data.