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Estimating multiple breaks in nonstationary autoregressive models. (English) Zbl 07306303
Summary: T. T. l. Chong [Econ. Lett. 49, No. 4, 351–357 (1995; Zbl 0875.90170)] and J. J. L. Velázquez [J. Differ. Equations 206, No. 2, 315–352 (2004; Zbl 1063.35068)] proposed a sample-splitting method to estimate a multiple-break model. However, their studies focused on stationary time series models, in which the identification of the first break depends on the magnitude and the duration of the break, and a testing procedure is needed to assist the estimation of the remaining breaks in subsamples split by the break points found earlier. In this paper, we focus on nonstationary multiple-break autoregressive models. Unlike the stationary case, we show that the duration of a break does not affect whether it will be identified first. Rather, it depends on the stochastic order of magnitude of signal strength of the break under the case of constant break magnitude and also the square of the magnitude of the break under the case of shrinking break magnitude. Since the subsamples usually have different stochastic orders in nonstationary autoregressive models with breaks, one can therefore determine which break will be identified first. We apply this finding to the models proposed in [P. C. B. Phillips and J. Yu, Quant. Econ. 2, No. 3, 455–491 (2011; Zbl 1235.91143)] and [P. C. B. Phillips et al., “Explosive behavior in the 1990s Nasdaq: When did exuberance escalate asset values?”, Int. Econ. Rev. 52, No. 1, 201–226 (2011; doi:10.1111/j.1468-2354.2010.00625.x); Int. Econ. Rev. 56, No. 4, 1043–1078 (2015; Zbl 1404.62111); ibid. 56, No. 4, 1079–1134 (2015; Zbl 1404.62112)]. We propose an estimation procedure as well as the asymptotic theory for the model. Some extensions to more general models are provided, and the hypothesis test with the null hypothesis being the unit root model is examined. Results of numerical simulations and an empirical study are given to illustrate the finite-sample performance.
MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
62P20 Applications of statistics to economics
Software:
basta
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References:
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