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"Generalized Extreme Value Approximation to the CUMSUMQ Test for Constant Unconditional Variance in Heavy-Tailed Time Series"

Author

Listed:
  • Josep Lluís Carrion-i-Silvestre

    (AQR-IREA Research Group. Departament d’Econometria, Estadística i Economia Aplicada. Universitat de Barcelona. Av. Diagonal, 690. 08034 Barcelona. Spain.)

  • Andreu Sansó

    (Department d’Economia Aplicada. Universitat de les Illes Balears and MOTIBO Research Group, Balearic Islands Health Research Institute (Idisba).)

Abstract
This paper focuses on testing the stability of the unconditional variance when the stochastic processes may have heavy-tailed distributions. Finite sample distributions that depend both on the effective sample size and the tail index are approximated using Extreme Value distributions and summarized using response surfaces. A modification of the Iterative Cumulative Sum of Squares (ICSS) algorithm to detect the presence of multiple structural breaks is suggested, adapting the algorithm to the tail index of the underlying distribution of the process. We apply the algorithm to eighty absolute log-exchange rate returns, finding evidence of (i) infinite variance in about a third of the cases, (ii) finite changing unconditional variance for another third of the time series - totalling about one hundred structural breaks - and (iii) finite constant unconditional variance for the remaining third of the time series.

Suggested Citation

  • Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2023. ""Generalized Extreme Value Approximation to the CUMSUMQ Test for Constant Unconditional Variance in Heavy-Tailed Time Series"," IREA Working Papers 202309, University of Barcelona, Research Institute of Applied Economics, revised Jul 2023.
    • Handle: RePEc:ira:wpaper:202309
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    References listed on IDEAS

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    Keywords

    CUMSUMQ test; Unconditional variance; Multiple structural changes; Heavy tails; Generalized Extreme Value distribution. JEL classification: C12; C22.;
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