Frequency Domain Tests for Residual Serial Correlation in Cointegration Regressions
| Author | Nelson Mark,In Choi |
| Published date | 01 November 1997 |
| DOI | http://doi.org/10.1111/1468-0084.00082 |
| Date | 01 November 1997 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 59, 4 (1997)
0305-9049
PRACTITIONERS CORNER
Frequency Domain Tests for Residual Serial
Correlation in Cointegration Regressions*
In Choi and Nelson Mark
I. INTRODUCTION
Since the influental work by Durbin and Watson (1951), many researchers
have developed tests for the null of no serial correlation in standard
linear regression residuals. Prime examples of these tests are Godfrey’s
(1978a, 1978b) Lagrange Multiplier (LM) tests, which have often been
used in empirical applications. The LM tests are easy to implement,
because only the null model needs to be estimated by the ordinary least
squares methods. However, the frequency domain tests have some advan-
tages over the LM tests in the context of cointegrating regressions.1
Alternative procedures that may be used for testing serial correlation are
the Box and Pierce (1970) and Ljung and Box (1978) tests that were
originally developed for ARMA models. But the asymptotic validity of
these tests has not been established in the context of cointegrating
regressions.
Therefore, the purpose of this paper is to introduce tests that can test
the null of no serial correlation in cointegrating regression residuals
against the alternative of general serially correlated residuals. Such tests
have not yet been introduced in the literature. The tests are formulated in
the frequency domain by using the spectral measure estimates. The main
idea for the tests is to compare the two different estimates for the
spectral measure; one is obtained without any restrictions on the shape of
spectral measures and the other with the restriction that the given time
series is a white noise process. Hence, when the null of a white noise
process is violated, the tests statistics will diverge. This implies that tests
have asymptotic power against any stationary processes that are not white
noise processes.
*The first author is grateful to Sanggyu Lee and Joon Park for helpful suggestions.
1Advantages of the frequency domain tests over the LM tests are explained in detail in
previous versions of this paper, which can be obtained from the first author upon request.
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