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Abstract In this paper we will consider the periodic AGARCH( p , q ) (Periodic Asymmetric Generalized Autoregressive Conditional Heteroscedastic) process, denoted PAGARCH( p , q ). These processes are similar to the standard AGARCH processes but now include seasonally varying coefficients. We examine the probabilistic structure of a PAGARCH-type stochastic difference equation with periodically varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions basing on the top Lyapunov exponent. Furthermore, we examine the necessary and sufficient conditions ensuring the existence of a unique causal periodically correlated (PC) solution to our processes.
Ines Lescheb (Thu,) studied this question.