Asymptotic Inferences For An RCA(1) Model

Time series analysis is general statistical method based on data from observations obtained time-sequentially. Many data in our world exist in the form of time series, thus the analytic technique is very popular in statistical works. During the past decades, there has been an increasing interest in nonlinear time series models. One of the examples is the random coefficient model.While we also note that the heavy-tailed random variables are very important and have appeared frequently in insurance, econometrics and other literatures. Therefore, deriving the asymptotics of the estimators with much weaker moment condition on the innovations raises our interest, and hence our interest of this paper is to show the limiting distribution of the conditional LSE in the RCA(1) model by allowing the second moment of the innovations to be possibly infinite. And, A number of simulation examples have been done to support the validity of methods in this Paper.On the other hand, The basic model in this paper is a RCA(1) model with a structural change in the RCA parameter at an unknown time τ0(=k0/T) 。 Then the limiting distributions of the conditional least squares estimators of parameter, and the consistency of the break-point estimator are all studied in the present paper. Then, A number of simulation examples have been done to support the validity of methods in this Paper.