Exact distribution and moments for the RLS estimate in a time-varying AR(1) process

Automatica

Volumn 32, Issue 3, 1996, Pages 429-433

  Lindoff, B ^a   Holst, J ^a  

^a LUND INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Forgetting factor; Quadratic forms; Recursive estimation; Weighted least squares

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; LEAST SQUARES APPROXIMATIONS; RECURSIVE FUNCTIONS; REGRESSION ANALYSIS; TIME VARYING SYSTEMS;

FORGETTING FACTOR; QUADRATIC FORMS; TIME VARYING AUTOREGRESSIVE PROCESS; WEIGHTED LEAST SQUARES;

PARAMETER ESTIMATION;

EID: 0030110333     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/0005-1098(95)00154-9     Document Type: Article

References (18)

1. Arvastson, L., H. Olsson and J. Holst (1995). Parameter distribution in exponential forgetting. Research Report 1995:11, Department of Mathematical Statistics, Lund Institute of Technology.
2. Bittanti, S. and M. Campi (1994). Bounded error identification of time-varying parameters by RLS techniques. IEEE Trans. Autom. Control, AC-39, 1106-1110.
3. Cryer, J., J. Nankervis and N. Savin (1989). Mirror-image and invariant distributions in ARMA models. Econometric Theory, 5, 36-52.
4. Gil-Pelaez, J. (1951). Note on the inversion theorem. Biometrika, 38, 481-482.
5. Guo, L. and L. Ljung (1994). Performance analysis of general tracking algorithms. In Proc. 33rd IEEE Conf. on Decision and Control, Lake Buena Vista, FL, pp. 2851-2855.
6. Guo, L., L. Ljung and P. Priouret (1993). Performance analysis of the forgetting factor RLS algorithm. Int. J. Adaptive Control and Sig. Process., 7, 525-537.
7. Gurland, J. (1948). Inversion formulae for the distribution of ratios. Ann. Math. Statist., 19, 228-237.
8. Lindoff, B. and J. Holst (1995a). Bias and covariance on the RLS-estimator with exponential forgetting in vector autoregressions. Research Report 1995:16, Department of Mathematical Statistics, Lund Institute of Technology.
9. Lindoff, B. and J. Holst, (1995b). Distribution of the RLS-estimator in a time-varying AR(1)-process. In Proc. 5th IFAC Symp. on Adaptive Systems in Control and Signal Processing, Budapest, pp. 135-140.
10. Ljung, L. and T. Söderström (1983). Theory and Practice of Recursive Identification. MIT Press, Cambridge, MA.
11. Magnus, J. (1986). The exact moments of a ratio of quadratic forms in normal variables. Annales d'Economie et de Statistique, 4, 95-109.
12. Mathai, A. and S. Provost (1992). Quadratic Forms in Random Variables. Marcel Dekker, New York.
13. Niedzwiecki, M. and L. Guo (1991). Nonasymptotic results for finite-memory WLS filters. IEEE Trans. Autom. Control, AC-36, 198-206.
14. Porat, B. (1985). Second-order equivalence of rectangular and exponential windows in least-squares estimation of Gaussian autoregressive processes. IEEE Trans. Acoust., Speech Sig. Process., ASSP-33, 1209-1212.
15. Sawa, T. (1978). The exact moment of the least squares estimator for the autoregressive model. J. Econometr., 8, 159-172.
16. Söderström, T. and P. Stoica (1988). System Identification. Prentice-Hall, New York.
17. Stoica, P. and A. Nehorai (1988). On the asymptotic distribution of exponentially weighted prediction error estimators. IEEE Trans. Acoust., Speech Sig. Process., ASSP-36, 136-139.
18. Tsui, A. and M. Ali (1994). Exact distributions, density functions and moments of the least squares estimator in a first-order autoregressive model. Comput. Statist. Data Anal., 17, 433-454.