Fuzzy Gaussian GARCH and Fuzzy Gaussian EGARCH Models: Foreign Exchange Market Forecast

José Eduardo Medina Reyes; Agustín Ignacio Cabrera Llanos; Salvador Cruz Aké

doi:10.21919/remef.v18.3.855

Authors

José Eduardo Medina Reyes Queen Mary University of London
Agustín Ignacio Cabrera Llanos Instituto Politécnico Nacional
Salvador Cruz Aké Instituto Politécnico Nacional

DOI:

https://doi.org/10.21919/remef.v18.3.855

Keywords:

Fuzzy Logic, GARCH, FUZZY EGARCH

Abstract

This article discusses a comparison of the GARCH and EGARCH conditional variance methods, with respect to
the Fuzzy Gaussian GARCH and Fuzzy Gaussian EGARCH. The returns of four exchange rates were forecasted at
daily periodicity from January 2015 to November 2022 and out-of-sample, January 2019, and December 2022.
The results indicate that the Fuzzy GARCH and Fuzzy EGARCH models better estimate the volatility behaviour
of the exchange market series compared to traditional techniques. Therefore, the recommendation is to estimate
other high volatility variables to verify the efficiency of the fuzzy techniques, however, the main limitation is
that it is not possible to apply traditional econometric tests for fuzzy techniques because the parameters are not
estimated with the logarithm of maximum likelihood. The estimation of the parameters of GARCH and EGARCH
models with fuzzy theory is the originality proposal. In conclusion, fuzzy methodologies have less error in
forecasting the volatility of in-sample and out-of-sample exchange rates.

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