Empirical Study Based on ARMA-GARCH Tempered Stable Lévy Processes: Evidence from Chinese Financial Markets

Abstract

This paper develops the ARMA-GARCH model and obtain the historical filtered noise sequence based on time series analysis of Shanghai Composite Index (SHI). Then, it estimates the parameters of noise using method of moments estimation and simulates TS measure applying sequence representation method. Further, it fits the noise distribution and tailed distribution employing normal distribution and α - stable distribution, classical tempered stable (CTS) distribution and rapidly decreasing tempered stable (RDTS) distribution, respectively. The empirical results are as follows. Firstly, the random residual noise sequence presents leptokurtic, skewed and heavy-tailed characteristics in Chinese financial markets. Secondly, tempered stable (TS) distribution fits tailed distribution well under the method of moments estimation and exhibits the characteristics of rapidly decreasing jump. Thirdly, the probability of extreme events is 5 times in TS process than that of the normal process, which is in line with markets and be closed to the annual average frequency of Chinese financial markets' turmoils.