Flexible modeling of conditional distributions using smooth mixtures of asymmetric student t densities

Abstract

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A multi-covariate semi-parametric conditional volatility model using probabilistic fuzzy systems

“…The covariates used in this work follows the choices of previous studies [7], [6], as these predictors appear to contain valuable information that improves the outof-sample performance for VaR estimation. In this work we use a nine variable model.…”

“…Therefore, more flexible modelling approaches are needed. Flexible parametric models, based on regression density estimation using adaptive mixture of Gaussian [6] or student- [7] distributions, where the mixture probabilities of the components changes smoothly as a function of the covariates, have been use to analyze the distribution of daily returns. Semi-parametric approaches using fuzzy systems fuzzy stochastic approach [8], a fuzzy measure model for pricing options [9] and using fuzzy set theory [10] have also been used for VaR estimation.…”

Probabilistic fuzzy systems for seasonality analysis and multiple horizon forecasts

“…The probabilistic fuzzy models we consider approximate the distribution of returns at time t+1 and t+30 conditional on multi-covariates at time t. The covariates used in this work follows the choices of previous studies [8], [7], [15], as these predictors appear to contain valuable information that improves the out-of-sample performance for VaR estimation for one day ahead forecasts. The information contained in these predictors capture the well-known autoregressive structure in returns through past returns information and variation of returns in different functional forms and with different discount parameters for past information.…”

“…These parametric models are criticised since the underlying data distribution may be different from the one specified in these models. Therefore flexible parametric models, based on regression density estimation using adaptive mixture of Gaussian [7] or student-t [8] distributions, where the mixture probabilities of the components changes smoothly as a function of the covariates, have been use to analyze the distribution of daily returns. Semi-parametric approaches using fuzzy systems fuzzy stochastic approach [9], a fuzzy measure model for pricing options [10] and using fuzzy set theory [11] have also been used for VaR estimation.…”

Generalized smooth finite mixtures

“…The mixture components in the SAGM model are Gaussian with the mean and the log variance being functions of covariates, so SAGM is a model for a continuous response variable. Li et al (2010) extend the SAGM model by having skewed student-t components in the mixture. The scope of our model and inference methodology is much larger * Corresponding author.…”