Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

A Functional Central Limit Theorem for an ARMA(p, q) Process with Markov Switching

  • Lee, Oesook (Department of Statistics, Ewha Womans University)
  • Received : 2013.06.12
  • Accepted : 2013.07.08
  • Published : 2013.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we give a tractable sufficient condition for functional central limit theorem to hold in Markov switching ARMA (p, q) model.

Keywords

References

  1. Ango Nze, P. and Doukhan, P. (2004). Weak dependence: Models and applications to econometrics, Econometric Theory, 20, 995-1045.
  2. Billingsley, P. (1968). Convergence of Probability Measures, Wiley, New York.
  3. Davidson, J. (2002). Establishing conditions for functional central limit theorem in nonlinear and semiparametric time series processes, Journal of Econometrics, 106, 243-269. https://doi.org/10.1016/S0304-4076(01)00100-2
  4. Dedecker, J., Doukhan, P., Lang, G., Leon, J. R., Louhichi, S. and Prieur, C. (2007). Weak dependence, Examples and Applications In Springer Lecture Notes in Statistics, 190.
  5. De Jong, R. M. and Davidson, J. (2000). The functional central limit theorem and weak convergence to stochastic integrals I: weakly dependent processes, Econometric Theory, 16, 643-666. https://doi.org/10.1017/S0266466600165028
  6. Doukhan, P. and Wintenberger, O. (2007). An invariance principle for weakly dependent stationary general models, Probability and Mathematical Statistics, 27, 45-73.
  7. Francq, C. and Zakoian, J. M. (2001). Stationarity of multivariate Markov-switching ARMA models, Journal of Econometrics, 102, 339-364. https://doi.org/10.1016/S0304-4076(01)00057-4
  8. Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and business cycle, Econometrica, 57, 357-384. https://doi.org/10.2307/1912559
  9. Hamilton, J. D. and Raj, B.(eds) (2002). Advances in Markov-switching Models-Applications in Business Cycle Research and Finance, Physica-Verlag, Heidelberg.
  10. Harrndorf, N. (1984). A functional central limit theorem for weakly dependent sequences of random variables, The Annals of Probability, 12, 141-153. https://doi.org/10.1214/aop/1176993379
  11. Ibragimov, I. A. (1962). Some limit theorems for stationary processes, Theory of Probability and Its Applications, 7, 349-382. https://doi.org/10.1137/1107036
  12. Krolzig, H. M. (1997). Markov-Switching Vector Autoregressions: Lecture Notes in Economics and Mathematical Systems, 454, Springer, Berlin.
  13. Lee, O. (2005). Probabilistic properties of a nonlinear ARMA process with Markov switching, Communications in Statistics: Theory and Methods, 34, 193-204. https://doi.org/10.1081/STA-200045822
  14. Stelzer, R. (2009). On Markov-switching ARMA processes-stationarity, existence of moments and geometric ergodicity, Econometric Theory, 29, 43-62.
  15. Yang, M. (2000). Some properties of vector autoregressive processes with Markov switching coefficients, Econometric Theory, 16, 23-43.
  16. Yao, J. and Attali, J. G. (2000). On stability of nonlinear AR processes with Markov switching, Advances in Applied Probability, 32, 394-407. https://doi.org/10.1239/aap/1013540170