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Empirical likelihood for break detection in time series. (English) Zbl 1349.62383
Summary: Structural breaks have become an important research topic in time series analysis and in many fields of application, e.g. econometrics, hydrology, seismology, engineering and industry, chemometrics, and medicine. In most phenomena encountered in the real world modeling assuming no change of structure may obviously lead to inconsistent estimates and poor forecasts. Much research work has been carried out in the past decades and efforts mostly concentrated on the identification of points in time where structural breaks possibly occur and on the development of statistical tests of absence of breaks. Common procedures are the CUSUM based statistics and the F based statistics proposed by Bai and Perron in several papers and technical reports. The need of specification of a probability distribution for conducting the statistical tests has been often a drawback in practical applications. If the distribution is misspecified the test may turn to be unreliable. In this paper a distribution free procedure for identification of change points and testing for structural breaks is proposed based on the empirical likelihood and the empirical likelihood ratio statistics. A comparison with the F test and the CUSUM test is performed on both simulated and real world data. The size and power of the test is comparable with existing procedures and the identification procedure is generally accurate and effective.
62M07 Non-Markovian processes: hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62G30 Order statistics; empirical distribution functions
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