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Resampling in the frequency domain of time series to determine critical values for change-point tests

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  • Kirch Claudia

Abstract

We study a model with an abrupt change in the mean and dependent errors that form a linear process. Different kinds of statistics are considered, such as maximum-type statistics (particularly different CUSUM procedures) or sum-type statistics. Approximations of the critical values for change-point tests are obtained through permutation methods in the frequency domain. The theoretical results show that the original test statistics and their corresponding frequency permutation counterparts follow the same distributional asymptotics. The main step in the proof is to obtain limit theorems for the corresponding rank statistics and then deduce the permutation asymptotics conditionally on the given data.Some simulation studies illustrate that the permutation tests usually behave better than the original tests if performance is measured by the α- and β-errors respectively.

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  • Kirch Claudia, 2007. "Resampling in the frequency domain of time series to determine critical values for change-point tests," Statistics & Risk Modeling, De Gruyter, vol. 25(3), pages 237-261, July.
    • Handle: RePEc:bpj:strimo:v:25:y:2007:i:3/2007:p:25:n:3
    DOI: 10.1524/stnd.2007.0902
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    References listed on IDEAS

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    1. Jushan Bai, 1994. "Least Squares Estimation Of A Shift In Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(5), pages 453-472, September.
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    3. Kokoszka, Piotr & Leipus, Remigijus, 1998. "Change-point in the mean of dependent observations," Statistics & Probability Letters, Elsevier, vol. 40(4), pages 385-393, November.
    4. Hidalgo, Javier, 2003. "An alternative bootstrap to moving blocks for time series regression models," LSE Research Online Documents on Economics 6850, London School of Economics and Political Science, LSE Library.
    5. Antoch, Jaromír & Husková, Marie, 2001. "Permutation tests in change point analysis," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 37-46, May.
    6. Javier Hidalgo, 2003. "An Alternative Bootstrap to Moving Blocks for Time Series Regression Models," STICERD - Econometrics Paper Series 452, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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