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.
This paper considers a non-Markovian priority retrial queue which serves two types of customers. Customers in the regular queue have priority over the customers in the orbit. This means that the customer in orbit can only start retrying when the regular queue becomes empty. If another customer arrives during a retrial time, this customer is served and the retrial has to start over when the regular queue becomes empty again. In this study, a particular interest is devoted to the stochastic monotonicity approach based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary joint distribution of the embedded Markov chain of the considered system.
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