{'fraction_non_alphanumeric': 0.023106546854942234, 'fraction_numerical': 0.0, 'mean_word_length': 5.842105263157895, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
ON MARKOV-SWITCHING ARMA PROCESSES—STATIONARITY, EXISTENCE OF MOMENTS, AND GEOMETRIC ERGODICITY

The probabilistic properties of ℝd-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.