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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
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