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

Josep Carrion-i-Silvestre and Andreu Sansó

No 202309, IREA Working Papers from University of Barcelona, Research Institute of Applied Economics

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.

Keywords: CUMSUMQ test; Unconditional variance; Multiple structural changes; Heavy tails; Generalized Extreme Value distribution. JEL classification: C12; C22. (search for similar items in EconPapers)
Pages: 38 pages
Date: 2023-07, Revised 2023-07
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-rmg
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Working Paper: Generalized Extreme Value Approximation to the CUMSUMQ Test for Constant Unconditional Variance in Heavy-Tailed Time Series (2023)
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