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Unit Root Tests with Markov-Switching

Author

Listed:
  • Randolph
  • Xiao Qin
  • Tan Gee Kwang

Abstract

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

Suggested Citation

  • Randolph & Xiao Qin & Tan Gee Kwang, 2004. "Unit Root Tests with Markov-Switching," Econometric Society 2004 Australasian Meetings 145, Econometric Society.
  • Handle: RePEc:ecm:ausm04:145
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    References listed on IDEAS

    as
    1. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
    2. Giuseppe Cavaliere, 2003. "Asymptotics for unit root tests under Markov regime-switching," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 193-216, June.
    3. 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 143-154, March-Apr.
    4. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    5. 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 1057-1072, June.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Diba, Behzad T & Grossman, Herschel I, 1988. "Explosive Rational Bubbles in Stock Prices?," American Economic Review, American Economic Association, vol. 78(3), pages 520-530, June.
    8. Hamilton, James D., 1986. "State-space models," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 50, pages 3039-3080 Elsevier.
    9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    10. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    11. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    12. 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 357-384, March.
    13. Evans, George W, 1991. "Pitfalls in Testing for Explosive Bubbles in Asset Prices," American Economic Review, American Economic Association, vol. 81(4), pages 922-930, September.
    14. Qin XIAO & Randolph TAN GEE KWANG, "undated". "Kalman Filter Estimation of Property Price Bubbles in Seoul," EcoMod2004 330600164, EcoMod.
    15. Alok Bhargava, 1986. "On the Theory of Testing for Unit Roots in Observed Time Series," Review of Economic Studies, Oxford University Press, vol. 53(3), pages 369-384.
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    Keywords

    unit root; three states markov switching; explosive rational bubbles;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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