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Recursive estimation of a drifted autoregressive parameter. (English) Zbl 1105.62373
Summary: Suppose the $$X_0,\dots, X_n$$ are observations of a one-dimensional stochastic dynamic process described by autoregression equations when the autoregressive parameter is drifted with time, i.e. it is some function of time: $$\theta_0,\dots, \theta_n$$, with $$\theta_k = \theta(k/n)$$. The function $$\theta(t)$$ is assumed to belong a priori to a predetermined nonparametric class of functions satisfying the Lipschitz smoothness condition. At each time point t those observations are accessible which have been obtained during the preceding time interval. A recursive algorithm is proposed to estimate $$\theta(t)$$. Under some conditions on the model, we derive the rate of convergence of the proposed estimator when the frequencyof observations n tends to infinity.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 65C60 Computational problems in statistics (MSC2010) 62G07 Density estimation
##### Keywords:
Autoregressive model; convergence rate; recursive algorithm
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##### References:
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