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Markov Regime-Switching Tests: Asymptotic Critical Values

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  • Steigerwald, Douglas
  • Carter, Andrew

Abstract

Empirical research with Markov regime-switching models often requires the researcher not only to estimate the model but also to test for the presence of more than one regime. Despite the need for both estimation and testing, methods of estimation are better understood than are methods of testing. We bridge this gap by explaining, in detail, how to apply the newest results in the theory of regime testing, developed by Cho and White [Cho, J. S., and H. White 2007. “Testing for Regime Switching.” Econometrica 75 (6): 1671–1720.]. A key insight in Cho and White is to expand the null region to guard against false rejection of the null hypothesis due to a small group of extremal values. Because the resulting asymptotic null distribution is a function of a Gaussian process, the critical values are not obtained from a closed-form distribution such as the χ². Moreover, the critical values depend on the covariance of the Gaussian process and so depend both on the specification of the model and the specification of the parameter space. To ease the task of calculating critical values, we describe the limit theory and detail how the covariance of the Gaussian process is linked to the specification of both the model and the parameter space. Further, we show that for linear models with Gaussian errors, the relevant parameter space governs a standardized index of regime separation, so one need only refer to the tabulated critical values we present. While the test statistic under study is designed to detect regime switching in the intercept, the test can be used to detect broader alternatives in which slope coefficients and error variances may also switch over regimes.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Paper provided by Department of Economics, UC Santa Barbara in its series University of California at Santa Barbara, Economics Working Paper Series with number qt5rn986z6.

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Date of creation: 12 Aug 2011
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Handle: RePEc:cdl:ucsbec:qt5rn986z6

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Keywords: Social and Behavioral Sciences; mixture model; regime switching; numeric approximation;

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References

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  1. René Garcia, 1995. "Asymptotic Null Distribution of the Likelihood Ratio Test in Markov Switching Models," CIRANO Working Papers 95s-07, CIRANO.
  2. Andrew V. Carter & Douglas G. Steigerwald, 2012. "Testing for Regime Switching: A Comment," Econometrica, Econometric Society, vol. 80(4), pages 1809-1812, 07.
  3. Jin Seo Cho & Halbert White, 2007. "Testing for Regime Switching," Econometrica, Econometric Society, vol. 75(6), pages 1671-1720, November.
  4. Stephen G. Cecchetti & Pok-sang Lam & Nelson C. Mark, 1988. "Mean Reversion in Equilibrium Asset Prices," NBER Working Papers 2762, National Bureau of Economic Research, Inc.
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Cited by:
  1. Avouyi-Dovi, Sanvi & Ano Sujithan, Kuhanathan, 2013. "The links between some European financial factors and the BRICS credit default swap spreads," Economics Papers from University Paris Dauphine 123456789/11721, Paris Dauphine University.

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