Fuzzy weighted local approximation for financial time series modelling and forecasting

Abstract

The authors develop a fuzzy local approach to model and forecast time series. The method appears to be flexible, both in modeling nonlinearities and in coping with weak nonstationarities. They estimate local linear approximation (LLA) by a fuzzy weighted regression. They test the model on data from a simulated noisy chaotic map and on two real financial time series, namely FIAT daily stock returns and USD-LIT exchange return rates. The LLA produces very accurate forecasts and is able to identify the correct order of the chaotic map. Moreover, they find evidence that financial time series exhibit low stationarity over time and there is often nonlinear forecastability, although this is true especially when volatility is relatively low. Some of their results point to the fact that possibly better forecasts are obtained when small data sets are used. They argue that large financial datasets might be more difficult to model because of structural changes and other irregularities.