We propose a double mixed Poisson autoregression in which the intensity, scaled by a unit mean independent and identically distributed (iid) mixing process, has di¤erent regime speci…cations according to the state of a …nite unobserved iid chain. Under some contraction in mean conditions, we show that the proposed model is strictly stationary and ergodic with a …nite mean. Applications to various count time series models are given.
In this paper, we set up a generalized periodic asymmetric power GARCH (PAP-GARCH) model whose coefficients, power, and innovation distribution are periodic over time. We first study its properties, such as periodic ergodicity, finiteness of moments and tail behavior of the marginal distributions. Then, we develop an MCMC algorithm, based on the Griddy-Gibbs sampler, under various distributions of the innovation term (Gaussian, Student-t, mixed Gaussian-Student-t). To assess our estimation method we conduct volatility and Value-at-Risk forecasting. Our model is compared against other competing models via the Deviance Information Criterion (DIC). The proposed methodology is applied to simulated and real data.
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