Statistical Inference And Its Application Of Several Kinds Of Time Series Models

Time series analysis is a branch of econometrics,in which the volatility clustering model describing the rate of return on financial assets has attracted the attention of many scholars.Such models are very important for macroeconomic theory and financial theory,and play an important role in two aspects of the financial field:the pricing of derivative securities and risk management.For several kinds of time series models,this paper mainly studies the parameter estimation,testing and application of the model.More specifically,we completed the following four sections.Firstly,the ?t of the GARCH model is:?t=[?t-E(?t|Ft-1)]/(?),Where es is the "disturbance" or "innovation" of the return on asset at time t,and Ft-1 is the known information set at time t-1.In many cases,the assumption that ?t follows a normal distribution cannot satisfy the characteristic of non-normal distribution with peak and thick tail of financial data,for the GARCH model,assuming that the ?t,follows Laplace(1,1)distribution,the quasi-maximum exponential likelihood estimation and two properties are given,and consistency and asymptotic normality are proved.The simulation shows that the Laplace(1,1)distribution is superior to the normal distribution N(0,1).As for the GARCH model with ?t following the distribution of Laplace(1,1),an empirical analysis is carried out and applied to the analysis of monthly precipitation variation characteristics in Wuhan urban area.Secondly,with the increasing complexity of financial time series data,the GARCH model can no longer satisfy some research assumptions,and more models are needed to replace the GARCH model to predict the volatility of financial assets,one of which is the ARMA-GARCH model.For the ARMA-GARCH model,assuming that the ?t follows Laplace(1,1)distribution,the quasi-maximum exponential likelihood estimation and two properties are given,and the consistency and asymptotic normality are proved.The closing prices of the Shenzhen composite index on December 22,2016 to December 31,2018 was selected to demonstrate the applicability of the ARMA-GARCH model based on Laplace(1,1)distribution through empirical analysis.Thirdly,the ARMA-GARCH model cannot analyze the volatility of financial data with long-term memory.Therefore,for the ARFIMA-GARCH model,assuming that the ?t follows Laplace(1,1)distribution,and giving the self-weighted quasi-maximum exponential likelihood estimation and two properties,and proves two properties.Then,under the condition of ?t fol-lows Laplace(1,1)distribution,two portmanteau test statistics of ARFIMA-GARCH model are given.The closing price of the US NASDAQ composite index on September 27,2017 to Jan-uary 18,2019 was selected to illustrate the applicability of ARFIMA-GARCH model based on Laplace(1,1)distribution through empirical analysis.Finally,for financial data with asymmetric or multimodal distribution,especially financial data with large fluctuations,few dual-AR models are adopted.For the dual-AR model,assum-ing that the ?t follows Laplace(1,1)distribution,the self-weighted quasi-maximum exponential likelihood estimation and the consistency are given,and the consistency is proved.Then,un-der the condition that ?t follows Laplace(1,1)distribution,two portmanteau test statistics of the dual-AR model are given.The closing price of CSI300 index on December 1,2016 to March 16,2018 was selected to demonstrate the applicability of the dual-AR model based on Laplace(1,1)distribution through empirical analysis.