Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-12T02:53:26.365Z Has data issue: false hasContentIssue false
  • English
  • Français

STABILITY OF REGIME SWITCHING ERROR CORRECTION MODELS UNDER LINEAR COINTEGRATION

Published online by Cambridge University Press:  06 September 2007

Pentti Saikkonen
Pentti Saikkonen
Affiliation:
University of Helsinki
Get access Rights & Permissions [Opens in a new window]

Abstract

The paper obtains conditions that ensure stationarity of linear long-run equilibrium relations and differenced observations in vector autoregressive error correction models with nonlinear short-run dynamics. The considered models include various threshold error correction models and their smooth transition counterparts. These models assume that the form of the short-run dynamics depends on values of observable transition functions that determine the regime in which the considered process evolves. In related models studied in the paper the transition functions are unobservable. These models are obtained by making the transition functions of threshold error correction models dependent on an unobservable random term. Previous stationarity conditions obtained for these kinds of regime switching error correction models are extended by using recent developments on nonlinear autoregressive models based on the theory of Markov chains and the concept of joint spectral radius of a set of square matrices. In addition to stationarity, existence of second-order moments and beta mixing is also established. The results of the paper enhance the understanding of the considered nonlinear error correction models and pave the way for the development of their asymptotic estimation and testing theory.Financial support from the Research Unit of Economic Structures and Growth (RUESG) in the University of Helsinki and the Yrjö Jahnsson Foundation is gratefully acknowledged. The author thanks Anders Rahbek for stimulating discussions on the topic of this paper and Helmut Lütkepohl and an anonymous referee for useful comments.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 1 , February 2008 , pp. 294 - 318
Copyright
© 2008 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Balke, N.S. & T.B. Fomby (1997) Threshold cointegration. International Economic Review 38, 627–645.Google Scholar
Bec, F. & A. Rahbek (2004) Vector equilibrium correction models with non-linear discontinuous adjustments. Econometrics Journal 7, 628–651.Google Scholar
Blondel, V.D. & Y. Nesterov (2005) Computationally efficient approximations of the joint spectral radius. SIAM Journal of Matrix Analysis 27, 256–272.Google Scholar
Cline, D.B.H. & H.H. Pu (1998) Verifying irreducibility and continuity of a nonlinear time series. Statistics and Probability Letters 40, 139–148.Google Scholar
Corradi, V., N. Swanson, & H. White (2000) Testing for stationarity-ergodicity and for comovements between nonlinear discrete time Markov processes. Journal of Econometrics 96, 39–73.Google Scholar
Doukhan, P. (1994) Mixing. Properties and Examples. Springer-Verlag.
Escribano, A. (2004) Nonlinear error correction: The case of money demand in the U.K. (1878–2000). Macroeconomic Dynamics 8, 76–116.Google Scholar
Escribano, A. & S. Mira (2002) Nonlinear error correction models. Journal of Time Series Analysis 23, 509–522.Google Scholar
Gripenberg, G. (1997) Computing the joint spectral radius. Linear Algebra and Its Applications 234, 43–60.Google Scholar
Johansen, S. (1995) Likelihood Based Inference on Cointegration in the Vector Autoregressive Model. Oxford University Press.
Kapetanios, G., Y. Shin, & A. Snell (2006) Testing for cointegration in nonlinear smooth transition error correction models. Econometric Theory 22, 279–303.Google Scholar
Liebscher, E. (2005) Towards a unified approach for proving geometric ergodicity and mixing properties of nonlinear autoregressive processes. Journal of Time Series Analysis 26, 669–689.Google Scholar
Lütkepohl, H. (1996) Handbook of Matrices. Wiley.
Meyn, S.P. & R.L. Tweedie (1993) Markov Chains and Stochastic Stability. Springer-Verlag.
Saikkonen, P. (2005) Stability results for nonlinear error correction models. Journal of Econometrics 127, 69–81.Google Scholar
Shih, M.-H., J.-W. Wu, & C.-T. Pang (1997) Asymptotic stability and generalized Gelfand spectral radius formula. Linear Algebra and Its Applications 252, 61–70.Google Scholar