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AbstractThis paper wishes to propose a new model for count data and it is shortly called a Zero-Inflated Poisson - Probit (ZIP-P) model. The way of setting up for this new model is also based on the traditional model, the Zero-Inflated Poisson (ZIP) model. Note that this new model as well as the ZIP model has a wide range of practical applications and it can be easily applied and analyzed to the real data sets. More specifically, both of these models can be applied very well to count data sets where the frequency of zeros occupies a very high percentage. To achieve the goal of this study, we first recall the construction and general formula of the ZIP model. Then we present the most detailed way for building a new model includes the general formula and related equations necessary for estimating the parameters of the ZIP-P model. In addition, asymptotic results, numerical simulations and analysis of a real data set are also performed in this work. Moreover, we also clarify that this actual data set fits the ZIP-P model better than the other models considered. Finally, several lines of discussions and inferences are made in the study. [ABSTRACT FROM AUTHOR]

This paper proposes a hysteretic autoregressive model with GARCH specification and a skew Student'st-error distribution for financial time series. With an integrated hysteresis zone, this model allows both the conditional mean and conditional volatility switching in a regime to be delayed when the hysteresis variable lies in a hysteresis zone. We perform Bayesian estimation via an adaptive Markov Chain Monte Carlo sampling scheme. The proposed Bayesian method allows simultaneous inferences for all unknown parameters, including threshold values and a delay parameter. To implement model selection, we propose a numerical approximation of the marginal likelihoods to posterior odds. The proposed methodology is illustrated using simulation studies and two major Asia stock basis series. We conduct a model comparison for variant hysteresis and threshold GARCH models based on the posterior odds ratios, finding strong evidence of the hysteretic effect and some asymmetric heavy-tailness. Versus multi-regime threshold GARCH models, this new collection of models is more suitable to describe real data sets. Finally, we employ Bayesian forecasting methods in a Value-at-Risk study of the return series. [ABSTRACT FROM AUTHOR]