A robust test for autocorrelation in the presence of a structural break in variance

Abstract

It has been known that when there is a break in the variance (unconditional heteroskedasticity) of the error term in linear regression models, a routine application of the Lagrange multiplier (LM) test for autocorrelation can cause potentially significant size distortions. We propose a new test for autocorrelation that is robust in the presence of a break in variance. The proposed test is a modified LM test based on a generalized least squares regression. Monte Carlo simulations show that the new test performs well in finite samples and it is especially comparable to other existing heteroskedasticity-robust tests in terms of size, and much better in terms of power.

Keywords:

• LM test
• variance break
• GLS regression
• variance-ratio test

Acknowledgements

Tae-Hwan Kim is grateful for financial support from the National Research Foundation of Korea – a grant funded by the Korean Government (NRF-2009-327-B00088).

Notes

1. We have also tried the least squares (LS) method by Bai 17 to estimate τˆ. However, the results are not better than those from the QMLE method. All the results based on the LS method are not reported but available upon request.

2. It is noted that allowing a one-time break in the error variance is a special case of the locally stationary autoregressive process considered in Kitagawa and Akaike 18, where k structural breaks, not only in the error variance but also in all of the regression coefficients, are permitted in autoregressive models. Hence, the QML variance estimators in Equation (8) can also be obtained using the Householder transformation-based procedure developed by Kitagawa and Akaike 18.

3. In the auxiliary regression, we replace missing values with zero in order to improve the finite sample property following the suggestion in Kiviet [?].

4. We use the same parameter values as in Godfrey and Tremayne 6 to make our simulation results comparable with theirs.

5. Godfrey and Tremayne 6 considered three different forms of HCCME, which results in three different tests denoted by and in their paper. According to our preliminary simulations, all of these three tests perform similarly. Therefore, we report the results of only, but the complete set of results is available upon request.