Estimation of flexible fuzzy GARCH models for conditional density estimation

In this work we introduce a new flexible fuzzy GARCH model for conditional density estimation. The model combines two different types of uncertainty, namely fuzziness or linguistic vagueness, and probabilistic uncertainty. The probabilistic uncertainty is modeled through a GARCH model while the fuzziness or linguistic vagueness is present in the antecedent and combination of the rule base system. The fuzzy GARCH model under study allows for a linguistic interpretation of the gradual changes in the output density, providing a simple understanding of the process. Such a system can capture different properties of data, such as fat tails, skewness and multimodality in one single model. This type of models can be useful in many fields such as macroeconomic analysis, quantitative finance and risk management. The relation to existing similar models is discussed, while the properties, interpretation and estimation of the proposed model are provided. The model performance is illustrated in simulated time series data exhibiting complex behavior and a real data application of volatility forecasting for the S&P 500 daily returns series

Nonlinear Combination of Financial Forecast with Genetic Algorithm

Complexity in the financial markets requires intelligent forecasting models for return volatility. In this paper, historical simulation, GARCH, GARCH with skewed student-t distribution and asymmetric normal mixture GRJ-GARCH models are combined with Extreme Value Theory Hill by using artificial neural networks with genetic algorithm as the combination platform. By employing daily closing values of the Istanbul Stock Exchange from 01/10/1996 to 11/07/2006, Kupiec and Christoffersen tests as the back-testing mechanisms are performed for forecast comparison of the models. Empirical findings show that the fat-tails are more properly captured by the combination of GARCH with skewed student-t distribution and Extreme Value Theory Hill. Modeling return volatility in the emerging markets needs “intelligent” combinations of Value-at-Risk models to capture the extreme movements in the markets rather than individual model forecast.Forecast combination; Artificial neural networks; GARCH models; Extreme value theory; Christoffersen test

Multivariate Gram-Charlier Densities

This paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate seminonparametric densities proposed in the financial econometrics as marginal distributions of the different formulations. Within this family, we focus on the specifications that guarantee positivity so obtaining a well-defined multivariate density. We compare different "positive" multivariate distributions of the family with the multivariate Edgeworth-Sargan, Normal and Student’s t in an in- and out-sample framework for financial returns data. Our results show that the proposed specifications provide a quite reasonably good performance being so of interest for applications involving the modelling and forecasting of heavy-tailed distributions.Multivariate distributions; Gram-Charlier and Edgeworth-Sargan densities; MGARCH models; financial data

Conditional Density Models Integrating Fuzzy and Probabilistic Representations of Uncertainty

__Abstract__ Conditional density estimation is an important problem in a variety of areas such as system identification, machine learning, artificial intelligence, empirical economics, macroeconomic analysis, quantitative finance and risk management. This work considers the general problem of conditional density estimation, i.e., estimating and predicting the density of a response variable as a function of covariates. The semi-parametric models proposed and developed in this work combine fuzzy and probabilistic representations of uncertainty, while making very few assumptions regarding the functional form of the response variable's density or changes of the functional form across the space of covariates. These models possess sufficient generalization power to approximate a non-standard density and the ability to describe the underlying process using simple linguistic descriptors despite the complexity and possible non-linearity of this process. These novel models are applied to real world quantitative finance and risk management problems by analyzing financial time-series data containing non-trivial statistical properties, such as fat tails, asymmetric distributions and changing variation over time