Efficient detection of random coefficients in autoregressive models

Efficient inference for autoregressive coefficients in the presence of trends

AMS 2000 subject classifications: primary 62F12 62M10 secondary 62G08 62G20 Keywords: Autoregressive time series Local polynomial Oracle efficiency Yule–Walker estimator Moving average a b s t r a c t Time series often contain unknown trend functions and unobservable error terms. As is known, Yule–Walker estimators are asymptotically efficient for autoregressive time series. The focus of this a...

Quasi-likelihood Estimation in Stationary and Nonstationary Autoregressive Models with Random Coefficients

We propose a unified quasi-likelihood procedure for the estimation of the unknown parameters of a first-order random coefficient autoregressive, RCA, model that works both for stationary and nonstationary processes. For this procedure, the weak consistency and the asymptotic normality are established under minimal assumptions on the noise sequences. In an empirical study, we highlight the pract...

Autoregressive Gaussian Random Vectors of First Order

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.