This paper discusses the modeling of financial volatility under the condition of non-normal distribution. In order to solve the problem that the traditional central moment cannot estimate the thick-tailed distribution, the L-moment which is widely used in the hydrological field is introduced, and the autoregressive conditional moment model is used for static and dynamic fitting based on the generalized Pareto distribution. In order to solve the dimension disaster of multidimensional conditional skewness and kurtosis modeling, the multidimensional skewness and kurtosis model based on distribution is established, and the high-order moment model is deduced. Finally, the problems existing in the traditional investment portfolio are discussed, and on this basis, the high-order moment portfolio is further studied. The results show that the key lies in the selection of the model and the assumption of asset probability distribution. Financial risk analysis can be effective only with a large sample. High-frequency data contain more information and can provide rich data resources. The conditional generalized extreme value distribution can well describe the time-varying characteristics of scale parameters and shape parameters and capture the conditional heteroscedasticity in the high-frequency extreme value time series. Better describe the persistence and aggregation of the extreme value of high frequency data as well as the peak and thick tail characteristics of its distribution.
Inverse parametric uncertainty identification using polynomial chaos and high-order moment matching benchmarked on a wet friction clutch
