Browse > Article
http://dx.doi.org/10.5351/CSAM.2013.20.4.339

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

Lee, Oesook (Department of Statistics, Ewha Womans University)
Publication Information
Communications for Statistical Applications and Methods / v.20, no.4, 2013 , pp. 339-345 More about this Journal
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
Functional central limit theorem; Markov switching ARMA (p, q) process; ${\varphi}$-mixing;
Citations & Related Records
연도 인용수 순위
  • Reference
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.   DOI   ScienceOn
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.   DOI   ScienceOn
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.   DOI   ScienceOn
8 Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and business cycle, Econometrica, 57, 357-384.   DOI   ScienceOn
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.   DOI   ScienceOn
11 Ibragimov, I. A. (1962). Some limit theorems for stationary processes, Theory of Probability and Its Applications, 7, 349-382.   DOI
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.   DOI   ScienceOn
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.   DOI   ScienceOn