Monitoring changes in the error distribution of autoregressive models based on Fourier methods

TEST - Tập 21 - Trang 605-634 - 2011
Zdeněk Hlávka1, Marie Hušková1, Claudia Kirch2, Simos G. Meintanis3
1Faculty of Mathematics and Physics, Department of Statistics, Charles University in Prague, Praha 8, Czech Republic
2Institute of Stochastics, Karlsruhe Institute of Technology, Karlsruhe, Germany
3Department of Economics, National and Kapodistrian University of Athens, Athens, Greece

Tóm tắt

We develop a procedure for monitoring changes in the error distribution of autoregressive time series while controlling the overall size of the sequential test. The proposed procedure, unlike standard procedures which are also referred to, utilizes the empirical characteristic function of properly estimated residuals. The limit behavior of the test statistic is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test and corresponding results on the finite–sample performance of the new method are presented. As it turns out the procedure is not only able to detect distributional changes but also changes in the regression coefficient.

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