Journal of the Korean Statistical Society

  • 제30권1호
  • /
  • Pages.115-125
  • /
  • 2001
  • /
  • 1226-3192(pISSN)
  • /
  • 2005-2863(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

On Stationarity of TARMA(p,q) Process

  • Lee, Oesook (Department of Statistics, Ewha Womans University) ;
  • Lee, Mihyun (Department of Statistics, Ewha Womans University)
  • 발행 : 2001.03.01
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초록

We consider the threshold autoregressive moving average(TARMA) process and find a sufficient condition for strict stationarity of the proces. Given region for stationarity of TARMA(p,q) model is the same as that of TAR(p) model given by Chan and Tong(1985), which shows that the moving average part of TARMA(p,q) process does not affect the stationarity of the process. We find also a sufficient condition for the existence of kth moments(k$\geq$1) of the process with respect to the stationary distribution.

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참고문헌

  1. Statistics and Probability Letters v.22 On geometric ergodicity of nonlinear autoregressive models Bhattacharya, R. N.;Lee, C.
  2. Journal of Time Series Analysis v.2 On the existence of stationary threshold autoregressive moving-average processes Brockwell, P. J.;Liu, J.;tweedie, R. L.
  3. Advances in Applied Probability v.17 On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations Chan, K. S.;Tong, H.
  4. Journal of Applied Econometrics v.11 On a double threshold autoregressive conditional heteroskedastic time series model Li, C. W.;Li, W. K.
  5. Journal of Applied Probability v.36 On the probabilistic properties of a double threshold ARMA conditional heteroskedastic model Ling, S.
  6. Journal of Applied Probability v.29 On strict stationarity and ergodicity of a nonlinear ARMA model Liu, J.;Susko (Ed.)
  7. Markov Chains and Stochastic Stability Meyn, S. P.;Tweedie, R. L.
  8. Journal of Applied Probability v.21 A threshold AR(1) model Petrucelli, J. D.;Woolford, S. W.
  9. Advances in Applied Probability v.22 Nonlinear time series and Markov chains Tjostheim, D.
  10. Pattern Recognition and Signal Processing. (Ed.) On a threshold model Tong, H.;C. H. Chen.
  11. Nonlinear Time Series;a Dynamical System approach Tong, H.
  12. In Papers in Probability, Statistics and Analysis. (Ed.) Criteria for rates od convergence of Markov chains with application to queueing theory Tweedia, R. L.;J. F. C. Kingman;G. E. H. Reuter.
  13. Journal of Applied Probability v.25A Invariant measure for Markov chains with no irreducibility assumptions Tweedie, R. L.