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Frequency Domain Tests for Residual Serial Correlation in Cointegration Regressions[Note 1. The first author is grateful to Sanggyu Lee and ...]
Author(s) -
Choi In,
Mark Nelson
Publication year - 1997
Publication title -
oxford bulletin of economics and statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.131
H-Index - 73
eISSN - 1468-0084
pISSN - 0305-9049
DOI - 10.1111/1468-0084.00082
Subject(s) - mathematics , residual , cointegration , consistency (knowledge bases) , autocorrelation , statistics , econometrics , frequency domain , statistical hypothesis testing , asymptotic distribution , sample (material) , mathematical analysis , algorithm , chemistry , geometry , chromatography , estimator
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.