Recursive estimation of a drifted autoregressive parameter
Belitser, Eduard
Ann. Statist., Tome 28 (2000) no. 3, p. 860-870 / Harvested from Project Euclid
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.
Publié le : 2000-05-14
Classification:  Autoregressive model,  convergence rate,  recursive algorithm,  62M10,  62G20,  60F99
@article{1015952001,
     author = {Belitser, Eduard},
     title = {Recursive estimation of a drifted autoregressive
			 parameter},
     journal = {Ann. Statist.},
     volume = {28},
     number = {3},
     year = {2000},
     pages = { 860-870},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1015952001}
}
Belitser, Eduard. Recursive estimation of a drifted autoregressive
			 parameter. Ann. Statist., Tome 28 (2000) no. 3, pp.  860-870. http://gdmltest.u-ga.fr/item/1015952001/