Spurious regression between long memory series due to mis-specified structural breaks

ABSTRACT

This article examines the spurious regression phenomenon between long memory series if the generating mechanism of individual series is assumed to follow a stationary/nonstationary process with mis-specified breaks. By using least-squares regression, the t-ratio becomes divergent and spurious regression is present. The intuition behind this is that the long memory series with change points can increase persistency in the level of regression errors and cause such spurious relationship. Simulation results indicate that the extent of spurious regression heavily relies on memory index, sample size, and location of break. As a remedy, we employ a four-stage procedure motivated by Maynard, Smallwood and Wohar (2013, Econ. Rev., 32, 318–360) to alleviate the size distortions. Finally, an empirical illustration using some stock price data from Shanghai Stock Exchange is reported.

KEYWORDS:

• Long memory
• Spurious regression
• Structural breaks
• t-Ratio

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05, 62F03

Acknowledgments

We thank the editor, an associate editor, and the anonymous referee for their constructive and insightful comments and suggestions that greatly improved the article. However, any remaining errors are our own.

Additional information

Funding

Supported in part by a National Natural Science Foundation of China Grant No. 71473194, No. 71273206 and No. 71103143, Shaanxi Natural Science Foundation of China Grant No. 2013KJXX-40 and No. 16JK1500.