Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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ON STATIONARITY OF NONLINEAR AR PROCESSES WITH NONLINEAR ARCH ERRORS

  • Lee, Oe-Sook (Department of Statistics Ewha Womans University) ;
  • Kim, Min-Hee (Department of Statistics Ewha Womans University)
  • Published : 2002.04.01
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Abstract

We consider the nonlinear autoregressive model with nonlinear ARCH errors, and find sufficient conditions for the existence of a strictly stationary process. New results are obtained, and known results are shown to emerge as special oases.

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References

  1. Stat.and Prob.Letters v.31 The geometric ergodicity and existence of moments for a class of nonlinear time series model H.An;M.Chen;F.Huang https://doi.org/10.1016/S0167-7152(96)00033-8
  2. Stat.and Prob.Letters v.22 On Geometric ergodicity of nonlinear autoregressive models R.N.Bhattacharya;C.Lee https://doi.org/10.1016/0167-7152(94)00082-J
  3. J.Econometrics v.52 Arch modeling in finance T.Bollerslev;R.T.Chou;K.F.Kroner https://doi.org/10.1016/0304-4076(92)90064-X
  4. Stoch.Proc.and their Appl. v.85 Extremal behavior of the outoregressive process with ARCH(1) errors M.Borkovec https://doi.org/10.1016/S0304-4149(99)00073-3
  5. Econometrica v.50 Autoregressive conditional heteroscedasticity with estimates of the variance of the United Kingdom inflation R.F.Engle https://doi.org/10.2307/1912773
  6. Statistica Sinica v.4 Probabilistic properties of the β-ARCH models D.Guegan;J.Diebolt
  7. Stat.and Prob.Letters v.46 On probabilistic properties of nonlinear ARMA(p,q) models O.Lee https://doi.org/10.1016/S0167-7152(99)00096-6
  8. J.Appl.Econometrics v.11 On a double threshold autoregressive conditional heteroskedastic time series model C.W.Li;W.K.Li https://doi.org/10.1002/(SICI)1099-1255(199605)11:3<253::AID-JAE393>3.0.CO;2-8
  9. J.Appl.Prob. v.36 On the probabilistic properties of a double threshold ARMA conditional heteroskedastic model S.Ling https://doi.org/10.1239/jap/1032374627
  10. J.Stat.Plann.and Inference v.62 On a threshold autoregression with conditional heteroscedastic variances J.Liu;W.Li;C.W.Li https://doi.org/10.1016/S0378-3758(96)00196-6
  11. Stat.and Prob.Letters v.30 A note on geometric ergodicity of autoregressive conditional heteroscedastivity(ARCH) model Z.Lu https://doi.org/10.1016/S0167-7152(95)00233-2
  12. Markov Chains and Stochastic Stability S.P.Meyn;R.L.Tweedie
  13. J.Appl.Econometrics v.8 Threshold ARCH model and asymmetries in volatility R.Rabemanjara;J.M.Zakoian https://doi.org/10.1002/jae.3950080104
  14. Adv.Appl.Prob. v.22 Nonlinear time series and Markov chains D.Tjφstheim https://doi.org/10.2307/1427459
  15. Nonlinear Time Series: a Dynamical System approach H.Tong
  16. J.Appl.Prob. v.25A Invariant measure for Markov chains with no irreducibility assumptions R.L.Tweedie
  17. Biometrica v.84 On a multivariate conditional heteroscedastic model H.Wong;W.K.Li https://doi.org/10.1093/biomet/84.1.111
  18. J.Time Series 5 ARMA models with ARCH errors A.Weiss https://doi.org/10.1111/j.1467-9892.1984.tb00382.x