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Unit Root Tests with Markov-Switching

  • Randolph
  • Xiao Qin
  • Tan Gee Kwang
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Diba and Grossman (1988) and Hamilton and Whiteman (1985) recommended unit root tests for rational bubbles. They argued that if stock prices are not more explosive than dividends, then it can be concluded that rational bubbles are not present. Evans (1991) demonstrated that these tests will fail to detect the class of rational bubbles which collapse periodically. When such bubbles are present, stock prices will not appear to be more explosive than the dividends on the basis of these tests, even though the bubbles are substantial in magnitude and volatility. Hall et al. (1999) show that the power of unit root test can be improved substantially when the underlying process of the sample observations is allowed to follow a first-order Markov process. Our paper applies unit root tests to the property prices of Hong Kong and Seoul, allowing for the data generating process to follow a three states Markov chain. The null hypothesis of unit root is tested against the explosive bubble or stable alternative. Simulation studies are used to generate the critical values for the one-sided test. The time series used in the tests are the monthly price and rent indices of Seoul's housing (1986:1 to 2003:6) and Hong Kong's retail premise (1980:12 to 2003:1). The investigations show that only one state appears to be highly likely in both cases. The switching unit root tests failed to find explosive bubbles in the price series, which might be due to the fact that the power of test is weak in the presence of heteroscedasticity

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Paper provided by Econometric Society in its series Econometric Society 2004 Australasian Meetings with number 145.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:ausm04:145
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  1. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
  2. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
  3. Diba, Behzad T & Grossman, Herschel I, 1988. "Explosive Rational Bubbles in Stock Prices?," American Economic Review, American Economic Association, vol. 78(3), pages 520-30, June.
  4. Hall, Stephen G & Psaradakis, Zacharias & Sola, Martin, 1999. "Detecting Periodically Collapsing Bubbles: A Markov-Switching Unit Root Test," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(2), pages 143-54, March-Apr.
  5. Bhargava, Alok, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Wiley Blackwell, vol. 53(3), pages 369-84, July.
  6. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-30, September.
  7. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  8. Giuseppe Cavaliere, 2003. "Asymptotics for unit root tests under Markov´┐Żregime-switching," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 193-216, 06.
  9. Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
  10. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  11. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
  12. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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