Recursive estimation of a drifted autoregressive parameter

Annals of Statistics

Volumn 28, Issue 3, 2000, Pages 860-870

  Belitser, Eduard ^a  

^a LEIDEN UNIVERSITY   (Netherlands)

Author keywords

Autoregressive model; Convergence rate; Recursive algorithm

Indexed keywords

EID: 0034366752     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015952001     Document Type: Article

References (13)

1. BROCKWELL, P. J. and DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed. Springer, New York.
2. DAHLHAUS, R. (1997). Fitting time series models to nonstationary processes. Ann. Statist. 25 1-37.
3. DE LA PEÑA, V. H. and GINÉ, E. (1999). Decoupling. From Dependence to Independence. Randomly Stopped processes. U-Statistics and Processes. Martingales and Beyond. Springer, New York.
4. DMITRIENKO, A. A., KONEV V. V. and PERGAMENSHCHIKOV, S. M. (1997). Sequential generalized least squares estimator for an autoregressive parameter. Sequential Anal. 16 25-46.
5. KUSHNER, H. J. and YIN, G. G. (1997). Stochastic Approximation Algorithms and Aplications. Springer, New York.
6. LEONOV, S. L. (1988). Recurrent estimation of autoregression parameters. Automat. Remote Control 49 633-642.
7. LJUNG, L. (1977). Analysis of recursive stochastic algorithms. IEEE Trans. Autom. Control 22 551-575.
8. LJUNG, L. (1987). System Identification - Theory for the User. Prentice Hall, Englewood Cliffs, NJ.
9. LJUNG, L. and SÖDERSTRÖM, T. (1983). Theory and Practice of Recursive Identification. MIT Press.
10. NEVELSON, M. B. and HASMINSKII, R. Z. (1973). Stochastic Approximation and Recursive Estimation. Amer. Math. Soc, Providence, RI.
11. POZNYAK, A. S. (1979). Convergence of stochastic approximation algorithms in parameter identification of dynamic systems. Automat. Remote Control 40 1254-1258.
12. VERULAVA, Y. S. (1981). Convergence of the stochastic approximation algorithm for estimating the autoregression parameter. Automat. Remote Control 42 943-947.
13. WILLIAMS, D. (1991). Probability with Martingales. Cambridge Univ. Press.