Resolving the forecasting problems of overshoot and volatility clustering using ANFIS coupling nonlinear heteroscedasticity with quantum tuning

In this paper, an approach to resolving two crucial problems of the overshoot and volatility clustering effects in time-series forecast has been proposed. In time-series prediction, big residuals round the turning-point region of a data sequence due to the overshoot phenomenon. Volatility clustering effect suggests a time series with successive disturbances being serially dependent. Both effects degrade the efficiency and effectiveness of time-series prediction and give rise to large residual errors. To overcome the overshoot and volatility clustering problems, an adaptive neuro-fuzzy inference system (ANFIS) coupling a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH), which is adapted by quantum minimization (QM), is introduced to resolve the drawbacks of the predicted outputs with big residuals around the inflection points of a data sequence and time-varying conditional variance in residual errors. Besides, the trial of two distinct quantum amplitude amplification (QAA) techniques called by QM is also considered to show their different computational complexity. Two experiments on the financial time series were taken and a performance evaluation was made between the proposed one and several well-known alternative methods. Results show that our proposed method gains the best predictive accuracy to outperform the others. Goodness of fit of the proposed method was tested successfully by Ljung–Box Q-test. It followed that the proposed method in fact can reduce large residual errors significantly in time-series forecast because the overshoot and volatility clustering effects are simultaneously regulated to the trivial levels.