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

  • Moosup Kim
  • Sangyeol Lee


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.


Constancy test for tail index Heavy-tailed distribution Conditional volatility GARCH model PTTGARCH model 



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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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2018

Authors and Affiliations

  1. 1.APEC Climate CenterBusanKorea
  2. 2.Department of StatisticsSeoul National UniversitySeoulKorea

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