Forecasting price of financial market crash via a new nonlinear potential GARCH model

Abstract

Financial market crash is one of the most extreme manifestations of financial market instability. It is of great significance to study its underlying structure and its forecasting methods. From the perspective of Econophysics, in addition to the influence of factors such as fluctuation on the financial price crash, we consider that the financial price crash originates from the change of the underlying structure described by the nonlinear potential function in the financial system. So we first propose a new nonlinear potential GARCH model by introducing nonlinear potential function and combining with GARCH model. In order to only analyze the effects of potential functions and eliminate the effects of fluctuations on prices, we combine the realized volatility and propose the likelihood function estimations of the proposed model and the benchmark GARCH and ARCH models. Then, based on the 5-minute high-frequency data of CSI300 and WTI crude oil, the out of sample forecasting with rolling time window and the SPA test method with Bootstrap characteristics are calculated. Finally, Akaike information criterion and Bayesian information criterion are employed to test the Goodness of fit of three models for in-sample and out-of-sample. The dynamic forecasting performance of the proposed new nonlinear potential GARCH model is compared with that of the benchmark GARCH and ARCH models. The main empirical results show that the proposed new nonlinear potential GARCH model is better than the benchmark GARCH and ARCH models for forecasting the returns and prices in the financial price crash for the given data. In addition, the potential well of the underlying nonlinear potential function changes obviously in the financial price crash.