Empirical Likelihood-Based Tests for Serial Correlation with Possible Infinite Variance

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 when the model error follows a GARCH process which is frequently used in modelling financial data. Two empirical likelihood-based testing statistics are proposed to deal with possible infinite variance issues that may occur. Both statistics are shown to be chi-squared distributed asymptotically under mild conditions. Simulations confirm the good 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