ON MARKOV-SWITCHING ARMA PROCESSES—STATIONARITY, EXISTENCE OF MOMENTS, AND GEOMETRIC ERGODICITY
研究了取值于ℝ^d的马尔可夫切换自回归移动平均过程的概率性质，给出了平稳性和遍历性条件，并引入了一个易于检验的充分平稳性条件，还证明了矩的存在性、几何遍历性和强混合性。
The probabilistic properties of ℝ d -valued Markov-switching autoregressive moving average (ARMA) processes with a general state space parameter chain are analyzed. Stationarity and ergodicity conditions are given, and an easy-to-check general sufficient stationarity condition based on a tailor-made norm is introduced. Moreover, it is shown that causality of all individual regimes is neither a necessary nor a sufficient criterion for strict negativity of the associated Lyapunov exponent. Finiteness of moments is also considered and geometric ergodicity and strong mixing are proven. The easily verifiable sufficient stationarity condition is extended to ensure these properties.