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Optimal test for Markov switching

Author

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  • Marine Carrasco
  • Liang Hu

Abstract

We propose a new test for the stability of parameters in a Markov switching model where regime changes are driven by an unobservable Markov chain. Testing in this context is more challenging than testing in structural change and threshold models because, besides the presence of nuisance parameters that are not identified under the null hypothesis, there is the additional difficulty due to the singularity of the information matrix under the null. We derive a class of information matrix-type tests and show that they are equivalent to the likelihood ratio test. Hence, our tests are asymptotically optimal. Besides their optimality properties, these tests are more general than the competing tests proposed by Garcia (1998) and Hansen (1992). Indeed, the underlying Markov chain driving the regime changes may have a finite or continuous state space, as long as it is exogenous. It is not restricted to linear models either. Therefore, our technique applies for instance to testing stability in random coefficient GARCH models. We use this test to investigate the presence of rational collapsing bubbles in stock markets. There is bubble if the stock price is disconnected from the market fundamental value. We regress the stock price on dividends and use the residual as proxy for the bubble size. Using US data, we find that the residuals are stationary, which could be hastily interpreted as evidence against the presence of bubbles. However, our Markov switching test strongly rejects the linearity, suggesting that at least two regimes should be used to fit the data. Estimating a two-state Markov switching model (Hamilton, 1989) reveals that one regime has a unit root, while the other is mean reverting, which is consistent with periodically collapsing bubbles

Suggested Citation

  • Marine Carrasco & Liang Hu, 2004. "Optimal test for Markov switching," 2004 Meeting Papers 374, Society for Economic Dynamics.
  • Handle: RePEc:red:sed004:374
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    2. Lanouar Charfeddine & Dominique Guegan, 2008. "Is it possible to discriminate between different switching regressions models? An empirical investigation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00368358, HAL.
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    15. Spyros Andreopoulos, 2006. "The real interest rate, the real oil price, and US unemployment revisited," Bristol Economics Discussion Papers 06/592, Department of Economics, University of Bristol, UK.
    16. Silvestro Di Sanzo, 2009. "Testing for linearity in Markov switching models: a bootstrap approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 18(2), pages 153-168, July.
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    19. Gross, Marco & Binder, Michael, 2013. "Regime-switching global vector autoregressive models," Working Paper Series 1569, European Central Bank.

    More about this item

    Keywords

    econometrics; speculative bubbles; Markov switching; test;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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