Abstract: Sufficient and necessary conditions for the existence of a unique second order stationary solution of conditional heteroskedastic autoregressive moving-average (CHARMA) models proposed by Tsay (1987) are derived. The solution is strictly stationary and ergodic, and has a causal representation. When the CHARMA model reduces to some special cases, it is shown that the conditions are equivalent to those already known in the literature. Based on Tweedie's (1988) result, sufficient conditions for the existence of finite-order moments of CHARMA models are also derived.
Key words and phrases: ARCH model, CHARMA model, ergodicity, existence of finite-order moments, Markov chain, stationarity.