Parameter Estimation For Covariate-driven Random Coefficient Autoregressive Models

Time series analysis has always been an important branch of statistics,mainly include linear time series model and nonlinear time series model.The results of linear time series model is much more mature.But due to some of the practical data is not conform to the linear time series model,in recent decades,scholars both China and abroad pay more attention to the nonlinear time series model,and have achieved good results.Random coefficient autoregressive model is a kind of nonlinear time series,also the Logistic regression model has been widely used in our life.But few scholar focus on the random coefficient autoregressive model with the Logistic model.Based on this,this paper proposes a new random coefficient of regression model:The random error sequence {(?)t} obey the Laplace distribution(0,1),the regression coefficient ?tis a random variable which obeys the Logistic regression contains covariant Z,this is the innovation of this article.In this paper,the main work is to use the least squares algorithm based on conditional expectation,the maximum likelihood estimation and bayes estimation to estimate the first-order Logistic regression model parameter ?1,?2.However,involved in the Logistic regression model,the function is relatively complex,so when doing the parameter estimation consider using Taylor expansion approximation.The complex expressions into the form of polynomial,it is concluded that the approximate estimation expressions.And to explicit parameters that cannot be solved consider using Matlab numerical solution to get the numerical results.Finally,propose the numerical simulation and empirical analysis,and compare the advantages and disadvantages of different methods and give the final conclusions.