Changes of structure in financial time series and the Garch model
DOI:
https://doi.org/10.57805/revstat.v2i1.8Keywords:
integrated periodogram, spectral distribution, functional central limit theorem, Kiefer-Müller process, Brownian bridge, sample autocorrelation, change point, GARCH process, long range dependence, IGARCH, non-stationarityAbstract
In this paper we propose a goodness of fit test that checks the resemblance of the spectral density of a GARCH process to that of the log-returns. The asymptotic behavior of the test statistics are given by a functional central limit theorem for the integrated periodogram of the data. A simulation study investigates the small sample behavior, the size and the power of our test. We apply our results to the S&P500 returns and detect changes in the structure of the data related to shifts of the unconditional variance. We show how a long-range dependence type behavior in the sample ACF of absolute returns might be induced by these changes.
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Copyright (c) 2004 REVSTAT-Statistical Journal
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