Testing for constant unconditional variance in heavy-tailed time series

Abstract

The paper demonstrates that the limiting distribution of the CUMSUMQ statistic can be expressed as a function of Brownian or stable-Lévy excursions stochastic processes, depending on the tail index of the time series, which can be well approximated by Generalized Extreme Value (GEV) distributions. Response surfaces to compute critical values and p-values for the CUMSUMQ statistic in finite samples are estimated considering the tail index. The paper introduces a modified version of the Iterative Cumulative Sum of Squares (ICSS) algorithm that incorporates the tail index into the detection of multiple structural breaks in the unconditional variance. The proposed methodology is illustrated through an empirical application to 80 log-exchange rate returns against the US dollar.