| Abstract: |
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. |