| Random coefficient autoregressive models are models used to study the stochastic perturbations of dynamic systems,and play a crucial role in modeling continuous time series data.Existing about the construction of random coefficient autoregression model,it is mostly to assume that the random coefficient {αt} obey an independent and distributed sequence of random variables.However,in practical problems,random coefficients may be affected by some known or observable variables,which makes it impossible for independent and identically distributed random variable sequences to give a dynamic description of random coefficients.At the same time,in real life,time series data may be very active within an observation period with a certain probability,or may remain or disappear with a certain probability,causing more random events after a period of time.In order to better apply the random coefficient autoregressive model to practical data,this paper establishes a mixed time series autoregressive model with random coefficients driven by covariates.Considering the important position of exponential distribution functions in various distributions due to their memoryless nature.This article combines exponential distribution functions with random coefficient autoregressive models to discuss the random coefficients of time series autoregressive models in the form of exponential distribution functions of different dimensions,driven by different numbers of covariates.We have established a mixed RCAR(1)model with random coefficients in the form of a one-dimensional exponential distribution function and driven by one covariate,as well as a mixed RCAR(1)model with random coefficients in the form of a two-dimensional exponential distribution function and driven by two covariates.The main work of this paper is to analyze the attribute characteristics of a class of mixed random coefficient autoregressive models driven by covariates proposed in this paper.Aiming at three different assumptions of the Error term,the unknown parameters in a class of mixed random coefficient autoregressive models driven by covariates proposed.In this paper are estimated using conditional maximum likelihood method and maximum a posteriori estimation method,and some numerical results of the two estimates are obtained,through numerical simulation.Finally,the model was applied to a real dataset,and empirical analysis was conducted using the Shanghai and Shenzhen 300 index data.The fitting effect was compared with the classic RCA(1)model,and the results showed that the mixed random coefficient autoregressive model proposed in this paper had better estimation performance. |
