Forecasting the Return and Volatility of Financial Instruments with Fuzzy Inference Systems and ARMA-GARCH Models

A modification of the GARCH model based on fuzzy inference system (FIS) is applied to the problem of returns and volatility forecasting of financial instruments. The proposed modification allows for the skewness and multiple clusters of volatility. It also performs a fuzzy switching between clusters and dynamically adapts their structure. Such an approach gives the opportunity to account for different volatility behavior under diverse conditions. Furthermore, with FIS-type models it is possible to incorporate large number of affecting factors without explicitly adding them to the model. These models also allow for estimation and dynamic adjustments of the affecting degree of these factors. First, for a series of instrument returns an ARMA model is built, then its residuals are used to calibrate the FIS-GARCH model which is further used to forecast volatility. More than 35 samples are examined, all of which are daily quotes of Russian financial market instruments. The stock, bond and money markets were studied. Calculations showed that for some time series, especially for stock market instruments, the fuzzy approach offers a result that exceeds the original autoregressive — conditional heteroskedasticity model. For several time series fuzzy system helps improve the forecast accuracy (it is also supported by statistical criteria). However, in most cases forecast errors of models with fuzziness and without such are comparable. One may state that due to their features fuzzy systems have a potential in forecasting returns and volatility on stock markets.

fuzzy systems, forecasting, time series, financial markets, asset return, volatility