ARMA Model Order Estimation Based on the Eigenvalues of the Covariance Matrix

IEEE Transactions on Signal Processing

Volumn 41, Issue 10, 1993, Pages 3003-3009

  Wilkes, D Mitchell ^b   Cadzow, James A ^b  

^a TENNESSEE STATE UNIVERSITY   (United States)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; REGRESSION ANALYSIS;

AKAIKE INFORMATION CRITERION; AUTOREGRESSIVE MOVING AVERAGE MODEL; COVARIANCE MATRIX; FINAL PREDICTION ERROR; MINIMUM DESCRIPTION LENGTH;

SIGNAL PROCESSING;

EID: 0027680559     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.277805     Document Type: Article

References (24)

1. L. Ljung, System Identification—Theory for the User. Englewood Cliffs, NJ: Prentice-Hall, 1987.
2. H. Akaike, “Fitting autoregressive models for prediction,” Ann. Inst. of Stat. Math., vol. 21, pp. 243-347, 1969.
3. H. Akaike, “Information theory and extension of the maximum likelihood principle,” 2nd Int. Symp. Inform. Theory, vol. Tsahkadsor, Armenian, USSR, 1971.
4. H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Automat. Contr., vol. AC-19, pp. 716–723, 1974.
5. H. Akaike, “On model structure testing in system identification,” Int. J. of Contr., vol. 26, pp. 1–18, 1977.
6. E. J. Hannan, “The estimation of the order of an ARMA process,” Ann. Stat., vol. 8, pp. 1071–1081, 1980.
7. T. Soderstrom and P. Stoica, System Identification. Englewood Cliffs, NJ; Prentice-Hall, 1989.
8. G. Schwarz, “Estimation of the dimension of a model,” Ann. Stat., vol. 6, pp. 461–464, 1978.
9. J. Rissanen, “Modeling by shortest data description,” Automatica, vol. 14, pp. 465–471, 1978.
10. J. Rissanen, “Consistent order estimates of autoregressive processes by shortest description of data,” Analysis and Optimization of Stochastic Systems. New York: Academic, 1980, pp. 451–461.
11. J. Rissanen, “A universal prior for integers and estimation by minimum description length,” Ann. Stat., vol. 11, pp. 416–431, 1983.
12. E. J. Hannan and B. G. Quinn, “The determination of the order of an autoregression,” J. Roy. Stat. Soc., Series B, vol. 41, pp. 190–195, 1979.
13. M. Wax and T. Kailath, “Detection of signals by information theoretic criteria,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-33, pp. 387–392, 1985.
14. J. A. Cadzow and O. M. Solomon, “Algebraic approach to system identification,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, no. 3, pp. 492–496, June 1988.
15. J. A. Cadzow and D. M. Wilkes, “Enhanced rational signal modeling,” to appear in IEEE Trans. Signal Processing.
16. D. M. Wilkes, “The RISE algorithm for recursive eigenspace decomposition,” IEEE Trans. Signal Processing, vol. 40, pp. 703–707, Mar., 1992.
17. D. M. Wilkes, “A reverse formulation of the RISE algorithm,” IEEE Trans. Signal Processing, vol. 40, pp. 2105–2108, Aug. 1992.
18. D. M. Wilkes, “The fitting of time-series models,” Revue de L’institut International De Statistique (Review of the International Statistical Institute), vol. 28, pp. 233–243, 1960.
19. M. J. Korenberg and L. D. Paarmann, “Orthogonal approaches to time-series analysis and system identification,” IEEE Signal Processing Mag., vol. 8, pp. 29-43, July, 1991.
20. D. Q. Mayne and F. Firoozan, “Linear identification of ARMA processes,” Automatica, vol. 18, pp. 461–466, 1982.
21. G. Liang and D. M. Wilkes, “The recursive linear identification method for ARMA model estimation,” in Proc. IEEE Southeastcon ‘92, pp. 677–682, Apr., 1992.
22. G. Liang, “ARMA model order estimation and parameter estimation based on recursive techniques,” Ph.D. dissertation, Vanderbilt University, TN, Mar., 1992.
23. L. Ljung, System Identification Toolbox-User‘s Guide. Natick, MA: The Math Works, Inc., 1988.
24. J. M. Beguin, C. C. Govrieroux, and A. Monfort, “Identification of a mixed autoregressive-moving average process: The corner method,” in O. D. Anderson, Ed., Time Series. Amsterdam: North-Holland, 1980, pp. 423–436.