• Lee, Oe-Sook ;
  • Shin, Dong-Wan
  • Published : 2004.03.01


We consider a nonlinear AR-ARCH type process subject to Markov-switching and give sufficient conditions for geometric ergodicity of the process. Existence of moments is also obtained.


Markov chain;ARCH type model;Markov switching;irreducibility;geometric ergodicity;moment


  1. J. Econometrics v.52 Arch modeling in finance T. Bollerslev;R.T.Chou;K.F.Kroner
  2. Probabilistic properties of a nonlinear ARMA processes with Markov switching O.Lee
  3. Irreducibility of ARMA(p,q) process with Markov switching O.Lee
  4. J. Appl. Econometrics v.11 On a double threshold autoregressive conditional heteroscedastic time series model C.W.Li;W.K.Li<253::AID-JAE393>3.0.CO;2-8
  5. J. Econometrics v.106 Stationarity and existence of moments of a family of GARCH processes S.Ling;M.McAleer
  6. J. Time Ser. Anal. v.15 Statistical analysis of economic time series via Markov switching models R.McCulloch;R.Tsay
  7. J. Appl. Probab. v.25A Invariant Measures for Markov chains with no irreducibility assumptions R.L.Tweedie
  8. Statist. Probab. Lett. v.22 On geometric ergodicity of nonlinear autoregressive models R.N.Bhattacharya;C.Lee
  9. Statist. Probab. Lett. v.52 no.3 On square integrability of an AR precess with Markov switching J.F.Yao
  10. J. Econometrics v.102 Stationarity of multivariate Markov switching ARMA models C.Francq;J-M.Zakoian
  11. J. Econometrics v.70 Specification testing in Markov switchin time series models. J.D.Hamilton
  12. J. Statist. Plann. Inference v.62 On a threshold autoregression with conditional heteroscedastic variances J.Liu;W.Li;C.W.Li
  13. Econometrica v.50 Autoregressive conditional heteroscedasticity with estimates of the variance of the United Kingdom inflation R.F.Engle
  14. Ann. Prob. v.20 Strict stationarity of generalized autoregressive processes P.Bougerol;N.Picard
  15. J. Time Ser. Anal. v.22 no.1 Autocovariance structure of Markov regime switching models and model selection J.Zhang;R.Stine
  16. Ann. Prob. v.2 no.2 A Lyapounov bound for solutions of the Poisson equation P.W.Glynn;S.P.Meyn
  17. Econometrica v.57 no.2 A new approach to the economic analysis of nonstationary time series and business cycle J.D.Hamilton
  18. Adv. Appl. Probab. v.22 Nonlinerar time series and Markov chains D.Tjostheim
  19. Econometric Theory v.16 Some properties of vector auroregressive with Markov-switching coefficients M.Yang
  20. J. Time Ser. Anal. v.22 no.2 Conditional heteroskedasticity driven by hidden Markov chains C.Francq;M.Roussignol;J-M.Zakoian
  21. J. Appl. Probab. v.36 On the probabilistic properties of a double threshold ARMA conditional heteroskedastic model S.Ling
  22. Econometric theory v.11 Nonparametric estimation and identification of nonlinear ARCH time series E.Masry;D.Tjostheim
  23. Nonlinear Time Series: A dynamical system approach H.Tong
  24. Bull. Korean Math. Soc. v.38 no.3 Strict stationarity and functional central limit theorem for ARCH/GARCH models O.Lee;J.Kim
  25. On strict stationarity of nonlinear ARMA processed with nonlinear GARCH innovations O.Lee
  26. Adv. Appl. Probab. v.32 On stationarity of nonlinear AR processes with Markov switching J.F.Yao;J.G.Attail
  27. Markov Chains and Stochastic Stability S.P.Meyn;R.L.Tweedie

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