Testing conditional heteroscedasticity with systematic sampling of time series

Abstract

It is well known that conditional heteroscedasticity is exhibited by many economic and financial time series such as stock prices or returns. Empirical analysis is often based on a subseries obtained through systematically sampling from an underlying time series and we analyze how that can affect testing for heteroscedasticity. The results show the distribution of the test statistics is changed by systematic sampling, causing a serious power loss that increases with the sampling interval. Consequently, the tests often fail to reject the hypothesis of no conditional heteroscedasticity, leading to the wrong decision and missing the true nature of the data-generating process.

Keywords:

• Conditional heteroscedasticity
• Lagrange multiplier test
• portmanteau test
• power loss
• systematic sampling

Acknowledgements

The author is very grateful to Profs. Hyung-Tae Hae and Serge Provost for kindly providing the Mathematica code for the computation of the approximate distribution of quadratic forms based on Laguerre polynomials required for the portmanteau statistic. The author is also grateful to the Editor and to an anonymous referee whose valuable suggestions and comments helped to improve the paper.