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Estimation of flexible fuzzy GARCH models for conditional density estimation

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  • Almeida e Santos Nogueira, R.J.
  • Basturk, N.
  • Kaymak, U.
  • Costa Sousa, J.M.

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.

Suggested Citation

  • Almeida e Santos Nogueira, R.J. & Basturk, N. & Kaymak, U. & Costa Sousa, J.M., 2013. "Estimation of flexible fuzzy GARCH models for conditional density estimation," ERIM Report Series Research in Management ERS-2013-013-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  • Handle: RePEc:ems:eureri:40785
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    References listed on IDEAS

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    Cited by:

    1. Roy Cerqueti & Massimiliano Giacalone & Raffaele Mattera, 2020. "Skewed non-Gaussian GARCH models for cryptocurrencies volatility modelling," Papers 2004.11674, arXiv.org.

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    More about this item

    Keywords

    Linguistic descriptions; Volatility forecasting; Conditional density estimation; Fuzzy GARCH models;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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