Mixture autoregressive (MAR) models have the attractive property that the shape of the conditional distribution of a forecast depends on the recent history of the process. In particular, it may have a varying number of modes over time. We show that the distributions of the multi-step predictors in MAR models are also mixtures and specify them analytically. In the important case when the origina...

This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, the...

Normal mixture distributions are arguably the most important mixture models, and also the most technically challenging. The likelihood function of the normal mixture model is unbounded based on a set of random samples, unless an artificial bound is placed on its component variance parameter. Moreover, the model is not strongly identifiable so it is hard to differentiate between over dispersion ...

The skewness in physical distributions of equity index returns and the implied volatility skew in the risk neutral measure are subjects of extensive academic research. Much attention is now being focused on models that are able to capture time-varying conditional skewness and kurtosis. For this reason normal mixture GARCH(1,1) models have become very popular in financial econometrics. We introd...

In this paper, following the generalization of Delta Normal VaR to Delta Mixture Elliptic VaR in Sadefo-Kamdem [3], we give and explicit formula to estimate linear VaR and ES when the risk factors changes with the mixture of t-Student distributions. In particular, we give rise to Delta-Mixture-Student VaR and the Delta-Mixture-Elliptic ES.

In this paper, following the generalization of Delta Normal VaR to Delta Mixture Elliptic VaR in Sadefo-Kamdem [3], we give and explicit formula to estimate linear VaR and ES when the risk factors changes with the mixture of t-Student distributions. In particular, we give rise to Delta-Mixture-Student VaR and the Delta-Mixture-Elliptic ES.

In this study, a novel discrimination method for known and unknown target using High-Resolution Range Profile (HRRP), namely log-likelihood ratio score method, is proposed. The aim of this method is to minimize the error probability of discrimination by constructing the unknown target model when the data of unknown target is lack. The Gaussian Mixture Model (GMM) is introduced to model the stat...