Distribution-free tests for time series models specification

Miguel A. Delgado , Carlos Velasco

We consider a class of time series specification tests based on quadratic forms of weighted sums of residuals autocorrelations. Asymptotically distribution-free tests in the presence of estimated parameters are obtained by suitably transforming the weights, which can be optimally chosen to maximize the power function when testing in the direction of local alternatives. We discuss in detail an asymptotically optimal distribution-free alternative to the popular Box-Pierce when testing in the direction of AR or MA alternatives. The performance of the test with small samples is studied by means of a Monte Carlo experiment.

Mots clés: C12; C14; C22; Optimal tests; Residuals autocorrelation function; Specification tests; Time series models; Dynamic regression model

Miguel A. Delgado, Carlos Velasco. Distribution-free tests for time series models specification. Econometrics, 2009, 155 (2), pp.128. ⟨10.1016/j.jeconom.2009.09.022⟩. ⟨hal-00628276⟩