Abstract
In this paper we consider the problem of testing for a parameter change in AR(1)-GARCH(1,1) models based on the residual cusum test. It is shown that the limiting distribution of the residual cusum test statistic is the sup of a Brownian bridge. Through a simulation study, it is demonstrated that the proposed test performs adequately. A real data analysis is provided for illustration.
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References
Billingsley, P.: Convergence of Probability Measures, 2nd edn. Wiley, New York (1999)
Carrasco, M., Chen, X.: Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18, 17–39 (2002)
Csörgő, M., Horváth, L.: Limit Theorems in Change-Point Analysis. Jhon Wiley & Sons Ltd., West Sussex (1997)
Hamilton, J.D.: Time Series Analysis. Princeton University Press, New Jersey (1994)
Inclán, C., Tiao, G.C.: Use of cumulative sums of squares for retrospective detection of changes of variances. J. Amer. Statist. Assoc. 89, 913–923 (1994)
Kang, J., Lee, S.: Parameter change test for random coefficient integer-valued autoregressive processes with application to polio data analysis. J. Time Series Anal. 30, 239–258 (2009)
Kim, M., Lee, S.: Test for tail index change in stationary time series with Pareto type marginal distribution. Bernoulli 15, 325–356 (2009)
Lee, S., Ha, J., Na, O., Na, S.: The Cusum Test for Parameter Change in Time Series Models. Scand. J. Statist. 30, 781–796 (2003)
Lee, S., Nishiyama, Y., Yosida, N.: Test for parameter change in diffusion processes by cusum statistics based on one-step estimators. Ann. Inst. Statist. Math. 58, 211–222 (2006)
Lee, S., Park, S.: The cusum of squares test for scale changes in infinite order moving average processes. Scand. J. Statist. 28, 625–644 (2001)
Lee, S., Song, J.: Test for parameter change in ARMA models with GARCH errors. Statist. Probab. Letters 78, 1990–1998 (2008)
Lee, S., Tokutsu, Y., Maekawa, K.: The residual cusum test for parameter change in regression models with ARCH errors. J. Japan Statist. Soc. 34, 173–188 (2004)
Na, S., Lee, J., Lee, S.: Change point test for copula ARMA-GARCH models. J. Time Series Anal. 33, 554–569 (2012)
Na, O., Lee, J., Lee, S.: Change point detection in SCOMDY models. AStA Advancs in Statistical Analysis 97, 215–238 (2013)
Page, E.S.: A test for change in a parameter occurring at an unknown point. Biometrika 42, 523–527 (1955)
Picard, D.: Testing and estimating change-points in time series. Adv. Appl. Prob. 17, 841–867 (1985)
Peligrad, M.: Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random varaibles. In: Eberlein, E., Taqqu, M.S. (eds.) Dependence in Probability and Statistics, pp. 193–223. Birkhäuser, Boston (1986)
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© 2014 Springer International Publishing Switzerland
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Lee, S., Lee, J. (2014). Residual Based Cusum Test for Parameter Change in AR-GARCH Models. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S. (eds) Modeling Dependence in Econometrics. Advances in Intelligent Systems and Computing, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-319-03395-2_6
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DOI: https://doi.org/10.1007/978-3-319-03395-2_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03394-5
Online ISBN: 978-3-319-03395-2
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