| The ARMA-GARCH model is often used to study the changes in the price of financial assets,when modeling the return rate of financial assets,it is generally assumed that the noise follows a Gaussian distribution.However,the Gaussian distribution is a hypothetical distribution under ideal conditions,and the real financial asset returns may have non-Gaussian characteristics such as positive or negative stage jumps.For this kind of financial data,the ARMA-GARCH model based on Gaussian distribution is insufficient in forecasting effect.Therefore,the ARMA-GARCH model with Gaussian-Poisson noise is considered to be constructed.Noting that Gaussian-Poisson noise usually has the characteristics of non-zero mean,so the ARMA-GARCH model with non-zero mean noise is investigated.In this paper,the asymptotic properties of ARMA-GARCH model with non-zero mean noise are studied,and some theoretical results are obtained.Firstly,under fourth-order moment conditions,the quasi-maximum likelihood estimator of the model is given,and the strong consistency of the estimator is proved.On this basis,the asymptotic normality of the estimator is investigated.Secondly,this paper takes Gaussian-Poisson noise as an example,and verifies the reliability of the theoretical results combines Bias,SD and MSE error evaluation indexes through numerical simulation.In addition,the model is used to analyze S&P 500 data,which reflects the applicability of the model.Finally,the ARMA-GARCH model based on GaussianPoisson noise is extended,and the historical filter distribution with compound Poisson jump is proposed,then the effectiveness of the estimation method is verified based on the historical filter distribution model with Gaussian compound Poisson jump. |
