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Test for tail index constancy of GARCH innovations based on conditional volatility

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Abstract

This study considers the problem of testing whether the tail index of the GARCH innovations undergoes a change according to the values of conditional volatilities. Special attention is paid to power-transformed and threshold generalized autoregressive conditional heteroscedasticity processes that can accommodate the GARCH family. We show that the proposed test asymptotically follows a functional of a standard Brownian motion under some regularity conditions. To evaluate our method, we carry out a simulation study and real data analysis using the return series of the Google stock price and DowJones index.

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Acknowledgements

We thank the Editor, an AE and referee for their careful reading and valuable comments and suggestions. This research is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and future Planning (No. 2018R1A2A2A05019433).

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Authors and Affiliations

  1. APEC Climate Center, Busan, 48058, Korea

    Moosup Kim

  2. Department of Statistics, Seoul National University, Seoul, 08826, Korea

    Sangyeol Lee

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  1. Moosup Kim
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  2. Sangyeol Lee
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Correspondence to Sangyeol Lee.

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Kim, M., Lee, S. Test for tail index constancy of GARCH innovations based on conditional volatility. Ann Inst Stat Math 71, 947–981 (2019). https://doi.org/10.1007/s10463-018-0669-6

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  • DOI: https://doi.org/10.1007/s10463-018-0669-6

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