A general approach to testing for autocorrelation

Testing for the presence of autocorrelation in a time series is a common task for researchers working with time series data. The standard Q test statistic, introduced by Box and Pierce (1970) and refined by Ljung and Box (1978), is applicable to univariate time series and to testing for residual autocorrelation under the assumption of strict exogeneity.   Breusch (1978) and Godfrey (1978) in effect extended the L-B-P approach to testing for autocorrelations in residuals in models with weakly exogenous regressors. However, each of these readily-available tests have important limitations. We use the results of Cumby and Huizinga (1992) to extend the implementation of the Q test statistic of L-B-P-B-G to cover a much wider ranges of hypotheses and settings: (a) tests for the presence of autocorrelation of order p through q, where under the null hypothesis there may be autocorrelation of order p-1 or less; (b) tests following estimation in which regressors are endogenous and estimation is by IV or GMM methods; and (c) tests following estimation using panel data. We show that the Cumby-Huizinga test, although developed for the large-T setting, formally identical to the test developed by Arellano and Bond (1991) for AR(2) in a large-N panel setting.