Changes of structure in financial time series and the GARCH model

Abstract

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 shifts.integrated periodogram, spectral distribution, functional central limit theorem, Kiefer--Muller process, Brownian bridge, sample autocorrelation, change point, GARCH process, long range dependence, IGARCH, non-stationarity