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span class="fontstyle0">This paper develops the comparison of the volatility prediction of the traditional models (ARIMA, EGARCH, and PARCH), with respect to the Hybrid Fuzzy Time Series and Fuzzy ARIMA Model of Tseng’s and Tanaka’s methodology (FTS-Fuzzy ARIMA Tseng and FTS-Fuzzy ARIMA Tanaka). For this purpose, it applies to the time series of the foreign exchange market to forecast the foreign currency exchange rate of Mexican Pesos against American Dollar, the growth rate of the time series data in a daily format from January 2008 to December 2017, to perform the sample test is used January 2018. The main result is that the models based on fuzzy theory generate a better estimate of the volatility of the foreign exchange rate. <br /
This article compares the results obtained when forecasting the Stock Market Index applying a proposed Fuzzy Nonlinear Autoregressive Neural Network with those obtained using the Autoregressive Neural Network. For this purpose, the methodology is applied to four stock indices, IPC, IBEX 35, S&P 500 and the Nikkei 225 using daily data from January 2015 to December 2018, the first five financial days of January 2019 are added to carry out a forecast outside the sample, A Nonlinear Autoregressive Neural Network with three lags and Bayesian learning algorithms and the Fuzzy Nonlinear Autoregressive Neural Networks with three lags and a Backpropagation algorithm were used to calculate a forecast. The results have shown that the models proposed generate better forecast considering in-sample and out-sample tests than the Nonlinear Autoregressive Neural Network. It was shown that the neural networks can learn from the dynamics of the time series, and if fuzzy theory is added, they can also learn from the uncertainty around financial variables. This indicates that method proposed yields better results than the traditional network method.
This research presents the comparison of the techniques modified using fuzzy logic called FTS-Fuzzy ARIMA, Fuzzy AR, Fuzzy GARCH, Fuzzy EGARCH, Fuzzy Triangular NARNET, and Fuzzy Trapezoidal NARNET, with respect to the volatility prediction techniques ARIMA, GARCH, EGARCH, and Nonlinear Autoregressive Neural Network, For this purpose, it applies to the time series of the foreign exchange market to forecast the foreign currency exchange rate, MX pesos against the US Dollar. In this work, the growth rate of the data from the time series is used in a daily format from January 2008 to December 2017; to perform the sample test is used in January 2018. We found that the models based on fuzzy theory have better estimates of volatility in financial time series. This allows developing new prediction methods based on the structure of fuzzy logic, it is also essential to establish an analysis of a greater number of data to try to discriminate if the effect of the error effect decreases.