Quantum minimization for adapting ANFIS outputs to its nonlinear generalized autoregressive conditional heteroscedasticity

Abstract

Volatility clustering degrades the efficiency and effectiveness of time series prediction and gives rise to large residual errors. This is because volatility clustering suggests a time series where successive disturbances, even if uncorrelated, are yet serially dependent. Traditional time-series forecast model such as grey model (GM) or auto-regressive moving-average (ARMA) has often encountered the overshoot effect, thus leading to the deterioration of its predictive accuracy. To overcome the overshoot and volatility clustering problems at the same time, an adaptive neuro-fuzzy inference system (ANFIS) is combined with a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) model that is adapted by quantum minimization (QM) so as to tackle the problem of overshooting situation and time-varying conditional variance residual errors. The proposed method significantly reduces large residual errors in forecasts because the overshoot and volatility clustering effects are regulated to trivial levels. Two experiments using real financial and geographic data series, respectively, compare the proposed method and a number of well-known alternative methods. Results show that forecasting performance by the proposed method produces superior results, with good speed of computation. Goodness of fit of the proposed method is tested by Ljung-Box Q-test. It is concluded that the ANFIS/NGARCH composite model adapted by QM performs very well for improved predictive accuracy of irregular non-periodic short-term time series forecast and will be of interest to the science of statistical prediction of time series.