Testing serial correlation in a general d-factor model with possible infinite variance

Abstract

It is well-known that the presence of serial correlation may result in an inefficient or even biased estimation in time series analysis. In this paper, we consider testing serial correlation in a general d-factor model when the model errors follow the GARCH process, which is frequently used in modeling financial data. Two empirical likelihood-based testing statistics are suggested as a way to deal with problems that might come up with infinite variance. Both statistics are shown to be chi-squared distributed asymptotically under mild conditions. Simulations confirm the excellent finite-sample performance of both tests. Finally, to emphasize the importance of using our tests, we explore the impact of the exchange rate on the stock return using both monthly and daily data from eight countries.

Keywords:

• Empirical likelihood
• weighted empirical likelihood
• GARCH process
• infinite variance
• serial correlation

JEL Classification:

• C12
• C22
• G1

Acknowledgments

We thank the Associate Editor and the referees for their insightful comments which greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Yawen Fan's research is supported by the Science and Technology research project of Education Department of Jiangxi Province (No. GJJ200545), Postgraduate Innovation Project of Jiangxi Province (No. YC2021–B124) and NSSF of China (No. 21BTJ035). Xiaohui Liu's research was supported by NSF of China (No. 11971208 and 11601197), the National Major Social Science Project of China (No. 21&ZD152), the Outstanding Youth Fund Project of the Science and Technology Department of Jiangxi Province (No. 20224ACB211003), and the Science and Technology research project of Education Department of Jiangxi Province (No. GJJ2200539).