On Markov error‐correction models, with an application to stock prices and dividends

This paper considers Markov error-correction (MEC) models in which deviations from the long-run equilibrium are characterized by different rates of adjustment. To motivate our analysis and illustrate the various issues involved, our discussion is structured around the analysis of the long-run properties of US stock prices and dividends. It is shown that the MEC model is flexible enough to account for situations where deviations from the long-run equilibrium are nonstationary in one of the states of nature and allows us to test for such a possibility. An empirical specification procedure to establish the existence of MEC adjustment in practice is also presented. This is based on a multi-step test procedure that exploits the differences between the global and local characteristics of systems with MEC adjustment. Copyright © 2004 John Wiley & Sons, Ltd.

[1]  C. Granger,et al.  Co-integration and error correction: representation, estimation and testing , 1987 .

[2]  B. LeBaron,et al.  A test for independence based on the correlation dimension , 1996 .

[3]  Zacharias Psaradakis,et al.  Power Properties of Nonlinearity Tests for Time Series with Markov Regimes , 2002 .

[4]  Jianfeng Yao,et al.  On stability of nonlinear AR processes with Markov switching , 2000, Advances in Applied Probability.

[5]  G. Evans Pitfalls in Testing for Explosive Bubbles in Asset Prices , 1991 .

[6]  Clive W. J. Granger,et al.  Comments on testing economic theories and the use of model selection criteria , 1995 .

[7]  Clive W. J. Granger,et al.  Testing for neglected nonlinearity in time series models: A comparison of neural network methods and alternative tests , 1993 .

[8]  Peter Schmidt,et al.  Some Properties of Tests for Specification Error in a Linear Regression Model , 1977 .

[9]  J. Zakoian,et al.  Stationarity of Multivariate Markov-Switching ARMA Models , 2001 .

[10]  S. Johansen Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models , 1991 .

[11]  Donald W. K. Andrews,et al.  An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator , 1992 .

[12]  S. V. Norden Regime Switching as a Test for Exchange Rate Bubbles , 1996 .

[13]  H. White,et al.  Information criteria for selecting possibly misspecified parametric models , 1996 .

[14]  Kenneth A. Froot,et al.  Intrinsic Bubbles: the Case of Stock Prices , 1989 .

[15]  Brendan McCabe,et al.  Can Economic Time Series Be Differenced to Stationarity , 1996 .

[16]  C. Granger,et al.  REGIME-SENSITIVE COINTEGRATION WITH AN APPLICATION TO INTEREST-RATE PARITY , 1997, Macroeconomic Dynamics.

[17]  P. Phillips,et al.  Asymptotic Properties of Residual Based Tests for Cointegration , 1990 .

[18]  Christian Haefke,et al.  Forecasting Austrian IPOs: An Application of Linear and Neural Network Error-Correction Models , 1996 .

[19]  Norman R. Swanson,et al.  Further developments in the study of cointegrated variables , 2010 .

[20]  J. Nyblom Testing for the Constancy of Parameters over Time , 1989 .

[21]  W. Newey,et al.  A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelationconsistent Covariance Matrix , 1986 .

[22]  Bruce E. Hansen,et al.  Erratum: The likelihood ratio test under nonstandard conditions: Testing the Markov switching model of GNP , 1996 .

[23]  Switching error-correction models of house prices in the United Kingdom , 1997 .

[24]  J. Stock,et al.  Testing for Common Trends , 1988 .

[25]  D. Andrews,et al.  Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative , 1992 .

[26]  Robert J. Shiller,et al.  Cointegration and Tests of Present Value Models , 1987, Journal of Political Economy.

[27]  James Davidson,et al.  A non-linear error correction mechanism based on the bilinear model 1 The data used in this study ar , 1998 .

[28]  D. Peel,et al.  Transactions Costs and Nonlinear Adjustment in Real Exchange Rates; An Empirical Investigation , 1997, Journal of Political Economy.

[29]  D. Andrews Tests for Parameter Instability and Structural Change with Unknown Change Point , 1993 .

[30]  E. Fama,et al.  The Equity Premium , 2001 .

[31]  Peter C. B. Phillips,et al.  Statistical Inference in Instrumental Variables Regression with I(1) Processes , 1990 .

[32]  Robert J. Vigfusson,et al.  Avoiding the Pitfalls: Can Regime-Switching Tests Reliably Detect Bubbles? , 1998 .

[33]  Bruce E. Hansen,et al.  Testing for parameter instability in linear models , 1992 .

[34]  Zacharias Psaradakis,et al.  ON THE DETERMINATION OF THE NUMBER OF REGIMES IN MARKOV‐SWITCHING AUTOREGRESSIVE MODELS , 2002 .

[35]  Zacharias Psaradakis,et al.  Detecting periodically collapsing bubbles: a Markov‐switching unit root test , 1999 .