Frequency Domain Tests for Residual Serial Correlation in Cointegration Regressions

Abstract

This paper introduces tests for residual serial correlation in cointegrating regressions. The tests are devised in the frequency domain by using the spectral measure estimates. The asymptotic distributions of the tests are derived and test consistency is established. The asymptotic distributions are obtained by using the assumptions and methods that are different from those used in Grenander and Rosenblatt (1957) and Durlauf (1991). Small‐scale simulation results are reported to illustrate the finite sample performance of the tests under various distributional assumptions on the data generating process. The distributions considered are normal and t‐distributions. The tests are shown to have stable size at sample sizes as large as 50 or 100. Additionally, it is shown that the tests are reasonably powerful against the ARMA residuals. An empirical application of the tests to investigate the ‘weak‐form’ efficiency in the foreign exchange market is also reported.