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.