Schick, Anton \(\sqrt{n}\)-consistent estimation in a random coefficient autoregressive model. (English) Zbl 0884.62099 Aust. J. Stat. 38, No. 2, 155-160 (1996). Summary: This paper deals with \(\sqrt{n}\)-consistent estimation of the parameter \(\mu\) in the RCAR(1) model defined by the difference equation \[ X_j= (\mu+U_j) X_{j-1}+ \varepsilon_j \qquad (j\in \mathbb{Z}), \] where \(\{\varepsilon_j: j\in\mathbb{Z}\}\) and \(\{U_j: j\in \mathbb{Z}\}\) are two independent sets of i.i.d. random variables with zero means, positive finite variances and \(E[(\mu+ U_1)^2]<1\). A class of asymptotically normal estimators of \(\mu\) indexed by a family of bounded measurable functions is introduced. Then an estimator is constructed which is asymptotically equivalent to the best estimator in that class. This estimator, asymptotically equivalent to the quasi-maximum likelihood estimator derived by D. F. Nicholls and B. G. Quinn [Random coefficient autoregressive models: an introduction. Lecture Notes Stat. 11 (1982; Zbl 0497.62081)], is much simpler to calculate and is asymptotically normal without the additional moment conditions those authors impose. Cited in 1 ReviewCited in 20 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F12 Asymptotic properties of parametric estimators Keywords:stationary; ergodic; quasi-maximum likelihood estimator Citations:Zbl 0497.62081 PDFBibTeX XMLCite \textit{A. Schick}, Aust. J. Stat. 38, No. 2, 155--160 (1996; Zbl 0884.62099) Full Text: DOI