Quantum-minimized BWGC/NGARCH approach to financial time series forecast

In this study, a novel approach to time series forecast is introduced in order to overcome the crucial problems of the overshoot phenomenon and the effect of volatility clustering at the same time. The prediction using grey model (GM) has encountered the overshoot phenomenon that results in big residual errors. To the contrary a method called cumulated 3-point least square polynomial model (C3LSP) may yield the underestimated output in the prediction. Thus we can utilize the predicted result from C3LSP to compensate the output of grey prediction so as for reducing the overshoot significantly. It is applicable to combine GM and C3LSP linearly and tune this combination optimally by back-propagation neural network (BPNN). This model denotes BPNN-weighted GM–C3LSP (BWGC). However, an effect of volatility clustering suggests a time series where successive disturbance, even if uncorrelated, are yet serially dependent. Consequently, this effect not only decreases the predictive accuracy but also deteriorates the localization for time series. Thus, incorporating a nonlinear generalized autoregressive conditional heteroscedasticity (NGARCH) into BWGC is proposed so that NGARCH is used to tackle the problem of volatility clustering effect during the time series forecast. For the purpose of simplicity, both BWGC and NGARCH models are composed linearly and then an algorithm called quantum-based minimization (QM) is particularly employed to regularize this composite model BWGC/NGARCH to best fit time series. As a result, the proposed approach can resolve the overshoot and volatility clustering effects simultaneously and outperforms the alternative models for time series forecasts.