Testing the Autocorrelation Structure of Disturbances in Ordinary Least Squares and Instrumental Variables Regressions

Abstract

This paper derives the asymptotic distribution for a vector of sample autocorrelations of regression residuals from a quite general linear model. The asymptotic distribution forms the basis for a test of the null hypothesis that the regression error follows a moving average of order q [greaterthan or equal] 0 against the general alternative that autocorrelations of the regression error are non-zero at lags greater than q. By allowing for endogenous, predetermined and/or exogenous regressors, for estimation by either ordinary least squares or a number of instrumental variables techniques, for the case q>0, and for a conditionally heteroscedastic error term, the test described here is applicable in a variety of situations where such popular tests as the Box-Pierce (1970) test, Durbin's (1970) h test, and Godfrey's (1978b) Lagrange multiplier test are net applicable. The finite sample properties of the test are examined in Monte Carlo simulations where, with a sample sizes of 50 and 100 observations, the test appears to be quite reliable.