Block bootstrap testing for changes in persistence with heavy-tailed innovations

ABSTRACT

This article considers the detection of changes in persistence in heavy-tailed series. We adopt a Dickey–Fuller-type ratio statistic and derive its null asymptotic distribution of test statistic. We find that the asymptotic distribution depends on the stable index, which is often typically unknown and difficult to estimate. Therefore, the block bootstrap method is proposed to detect changes without estimating κ. The empirical sizes and power values are investigated to show that the block bootstrap test is valid. Finally, the validity of the method is demonstrated by analyzing the exchange rate of RMB and US dollars.

KEYWORDS:

• Block bootstrap test
• Changes in persistence
• Dickey–Fuller-type ratio statistic
• Heavy tailed.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03
• 62F05

Acknowledgments

The authors are grateful to the anonymous referee and the editor for their careful reading of the manuscript and their helpful comments which lead to a better presentation of the manuscript.

Funding

This work is supported by the National Natural Science Foundation of China (No. 11226217,71501115), the Postdoctoral Science Foundation (No.2012M510772), and the Postdoctoral Science Special Foundation (No.2013T60266).