On stability of nonlinear AR processes with Markov switching

被引：40
|
作者：
Yao, JF
Attali, JG
机构：
[1] Univ Paris 01, SAMOS, F-75634 Paris 13, France
[2] Univ Paris 06, Probabil Lab, F-75252 Paris, France
来源：
ADVANCES IN APPLIED PROBABILITY | 2000年 / 32卷 / 02期
关键词：
Markov switching; nonlinear AR; Lyapounov functions; stability;
D O I：
10.1017/S000186780000999X
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We investigate the stability problem for a nonlinear autoregressive model with Markov switching. First we give conditions for the existence and the uniqueness of a stationary ergodic solution. The existence of moments of such a solution is then examined and we establish a strong law of large numbers for a wide class of unbounded functions, as well as a central limit theorem under an irreducibility condition.
引用
收藏
页码：394 / 407
页数：14
相关论文
共 50 条
  • [1] A proof of consistency of the MLE for nonlinear Markov-switching AR processes
    Fermin, Lisandro
    Marcano, Jose
    Rodriguez, Luis-Angel
    STATISTICS & PROBABILITY LETTERS, 2022, 183
  • [2] Stability of the nonlinear filter for slowly switching Markov chains
    Chigansky, Pavel
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2006, 116 (08) : 1185 - 1194
  • [3] Stability of nonlinear discrete repetitive processes with Markovian switching
    Emelianova, Julia
    Pakshin, Pavel
    Galkowski, Krzysztof
    Rogers, Eric
    SYSTEMS & CONTROL LETTERS, 2015, 75 : 108 - 116
  • [4] Asymptotic properties of nonlinear autoregressive Markov processes with state-dependent switching
    Xi, Fubao
    Yin, G.
    JOURNAL OF MULTIVARIATE ANALYSIS, 2010, 101 (06) : 1378 - 1389
  • [5] On square-integrability of an AR process with Markov switching
    Yao, J
    STATISTICS & PROBABILITY LETTERS, 2001, 52 (03) : 265 - 270
  • [6] Local stability of Kolmogorov forward equations for finite state nonlinear Markov processes
    Budhiraja, Amarjit
    Dupuis, Paul
    Fischer, Markus
    Ramanan, Kavita
    ELECTRONIC JOURNAL OF PROBABILITY, 2015, 20 : 1 - 30
  • [7] Exponential ergodicity for Markov processes with random switching
    Cloez, Bertrand
    Hairer, Martin
    BERNOULLI, 2015, 21 (01) : 505 - 536
  • [8] Long time behaviour for population model by α-stable processes with Markov switching
    Tong, Jinying
    Zhang, Zihan
    Chen, Yeqin
    Zhang, Zhenzhong
    NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2023, 50
  • [9] Skewness and kurtosis of multivariate Markov-switching processes
    Fiorentini, Gabriele
    Planas, Christophe
    Rossi, Alessandro
    COMPUTATIONAL STATISTICS & DATA ANALYSIS, 2016, 100 : 153 - 159
  • [10] On geometric ergodicity of an AR-ARCH type process with Markov switching
    Lee, O
    Shin, DW
    JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2004, 41 (02) : 309 - 318
12345