Correction note of E. Kremer: “Random coefficient autoregressive loss reserving”. BlÄtter, Oktober 1993

Bayesian Analysis of Random Coefficient AutoRegressive Models

Random Coefficient AutoRegressive (RCAR) models are obtained by introducing random coefficients to an AR or more generally ARMA model. These models have second order properties similar to that of ARCH and GARCH models. In this article, a Bayesian approach to estimate the first order RCAR models is considered. A couple of Bayesian testing criteria for the unit-root hypothesis are proposed: one i...

Estimation in nonstationary random coefficient autoregressive models

We investigate the estimation of parameters in the random coefficient autoregressive model Xk = (φ+ bk)Xk−1 + ek, where (φ,ω 2, σ2) is the parameter of the process, Eb0 = ω2, Ee0 = σ 2. We consider a nonstationary RCA process satisfying E log |φ + b0| ≥ 0 and show that σ2 cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimat...

Estimation in Random Coefficient Autoregressive Models

We propose the quasi-maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions.

Near–Integrated Random Coefficient Autoregressive Time Series

We determine the limiting behavior of near–integrated first–order random coefficient autoregressive RCA(1) time series. It is shown that the asymptotics of the finite dimensional distributions crucially depends on how the critical value 1 is approached, which determines whether the process is near–stationary, has a unit–root or is mildly explosive. In a second part, we derive the limit distribu...

Autoregressive Gaussian Random Vectors of First Order