Generalized AIC method based on higher-order moments and entropy of financial time series

In this paper, a generalized method of traditional Akaike information criterion is proposed as a new measurement to compare and evaluate the volatility behaviors of time series in stock market. This new method is modified by extending variance to high-order statistics such as skewness, kurtosis, and permutation entropy, so as to demonstrate the different aspects of volatility behaviors of time series compared to low-order method. Furthermore, a new model of creating an AIC plane is proposed in order to derive more accurate results. Numerical simulations are conducted over synthetic data to provide comparative study. In addition, further reports about the results of distinguishing behaviors in stock market composite index of America, China and Hong Kong by using generalized AIC method and AIC plane are utilized to reflect the feasibility. Our results can effectively differentiate multiscale volatility details of time series from three areas.