Abstract
We propose a double mixed Poisson autoregression in which the intensity, scaled by a unit mean independent and identically distributed (i.i.d.) mixing process, has different regime specifications according to the state of a finite unobserved i.i.d. chain. Under some contraction in mean conditions, we show that the proposed model is strictly stationary and ergodic with a finite mean. Applications to various count time series models are given.
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