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Stability Of Regime Switching Error Correction Models Under Linear Cointegration

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  • Saikkonen, Pentti

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 Yrj Jahnsson Foundation is gratefully acknowledged. The author thanks Anders Rahbek for stimulating discussions on the topic of this paper and Helmut L tkepohl and an anonymous referee for useful comments.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 24 (2008)
Issue (Month): 01 (February)
Pages: 294-318

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Handle: RePEc:cup:etheor:v:24:y:2008:i:01:p:294-318_08

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Cited by:
  1. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, School of Economics and Management, University of Aarhus.
  2. Theis Lange, 2009. "First and second order non-linear cointegration models," CREATES Research Papers 2009-04, School of Economics and Management, University of Aarhus.
  3. Dennis Kristensen & Anders Rahbek, 2007. "Likelihood-Based Inference in Nonlinear Error-Correction Models," CREATES Research Papers 2007-38, School of Economics and Management, University of Aarhus.
  4. Kristensen, Dennis & Rahbek, Anders, 2010. "Likelihood-based inference for cointegration with nonlinear error-correction," Journal of Econometrics, Elsevier, vol. 158(1), pages 78-94, September.
  5. Timo Teräsvirta & Yukai Yang, 2014. "Linearity and Misspecification Tests for Vector Smooth Transition Regression Models," CREATES Research Papers 2014-04, School of Economics and Management, University of Aarhus.
  6. Nedeljkovic, Milan, 2008. "Testing for Smooth Transition Nonlinearity in Adjustments of Cointegrating Systems," The Warwick Economics Research Paper Series (TWERPS) 876, University of Warwick, Department of Economics.
  7. Marçal, Emerson Fernandes & Valls Pereira, Pedro L., 2012. "Evaluating the existence of structural change in the brazilian term structure of interest : evidence based on cointegration models with structural break," Textos para discussão 314, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).

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