Change of structure in financial time series, long range dependence and the GARCH model

Abstract

Functionals of a two-parameter integrated periodogram have been used for a long time for detecting changes in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram having as limit a Gaussian field. In the case of GARCH(p; q) processes a statistic closely related to the integrated periodogram can be used for the purpose of change detection in the model. We derive a central limit theorem for this statistic under the hypothesis of a GARCH(p; q) sequence with a finite 4th moment. When applied to real-life time series our method gives clear evidence of the fast pace of change in the data. One of the straightforward conclusions of our study is the infeasibility of modeling long return series with one GARCH model. The parameters of the model must be updated and we propose a method to detect when the update is needed. Our study supports the hypothesis of global non-stationarity of the return time ser...

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