Abstract
We propose a new robust test to detect changes in the autocovariance function of a time series. The test is based on empirical autocovariances of a robust transformation of the original time series. Because of the transformation, we do not require any finite moments of the original time series, making the test especially suitable for heavy tailed time series. We furthermore propose a lag weighting scheme, which puts emphasis on changes of the autocovariance at smaller lags. Our approach is compared to existing ones in some simulations.
Highlights
Testing for second order stationarity goes back to Quenouille (1958) and Jenkins (1961)
Tests that check stationarity of the spectrum are presented in Picard (1985), Giraitis and Leipus (1992), and Rozenholc (2001) and a wavelet periodogram is used in Nason (2013) and Cardinali and Nason (2018)
YtYt+l, we look at max k=1,...,T
Summary
Testing for second order stationarity goes back to Quenouille (1958) and Jenkins (1961). In Jin, Wang, and Wang (2015) estimated autocovariances of subsamples are compared to the estimation based on the whole time series. Several tests have been proposed for linear models, see Bai (1993), Bai (1994), Andrews (1993), Davis, Huang, and Yao (1995), and Akashi, Dette, and Liu (2018). CUSUM-type tests to detect changes in one or several autocovariances have been derived in Berkes, Gombay, and Horvath (2009), Lee, Ha, Na, and Na (2003), and Dette, Wu, and Zhou (2015). A test based on the auto-copula has been proposed in Bucher, Fermanian, and Kojadinovic (2019). We want to fill this gap with a CUSUM type test based on robustified autocovariances.
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