Evaluating some Yule-Walker Methods with the Maximum-Likelihood Estimator for the Spectral ARMA Model

Authors

  • M.I.S. Bezerra
  • Y. Iano
  • M.H. Tarumoto

DOI:

https://doi.org/10.5540/tema.2008.09.02.0175

Abstract

The aim of this work is to compare some ARMA spectral separatede stimation methods based on the modified Yule-Walker equation and least squares method with the Maximum-Likelihood estimator, using the convergence curve of the relative mean error (RME), generated by Monte Carlo simulation.

References

[1] M.I.S. Bezerra, Precision of Yule-Walker Methods for the ARMA Spectral Model, in “Proceedings of the IASTED Conference on Circuits, Signals, and Systems”, pp. 54-59, IASTED, Clearwater Beach, 2004.

M.I.S. Bezerra, G. Stanghenhaus, Uma Compara¸c˜ao entre L-Estimadores de Regress˜ao, in “Anais do X Simp´osio Nacional de Probabilidade e Estat´ıstica”, p. 76, ABE, Caxamb´u, 1996.

G.E.P. Box, G.M. Jenkins, G.C. Reinsel, “Time Series Analysis: Forecasting and Control”, Third Edition, Prentice-Hall, Englewood Cliffs, 1994.

P.M.T. Broersen, Autoregressive Model Orders for Durbin’s MA and ARMA Estimators, IEEE Trans. on Signal Processing, 48, No. 8 (2000), 2454-2457.

J. A. Cadzow, High performance spectral estimation - a new ARMA method, IEEE Trans. on Acoustics, Speech and Signal Processing, ASSP-28, No. 5 (1980), 524-529.

P.A. Enqvist, A Convex Optimization Approach to ARMA(m,n) Model Design from Covariance and Cepstral Data, SIAM J. Control Optimization, 43, No. 3 (2004), 1011-1036.

B. Efron, R.J. Tibshirani, “An Introduction to the Bootstrap”, Chapman & Hall, New York, 1993.

B. Friedlander, B. Porat, The modified Yule-Walker method of ARMA spectral estimation, IEEE Trans. on Aerospace and Electronic Systems, AES-20, No. 2 (1984), 158-172.

S.M. Kay, “Modern Spectral Estimation Theory and pplications”, PrenticeHall, Englewood Cliffs, 1988.

S.L.Jr. Marple, “Digital Spectral Analysis”, Prentice-Hall, Englewood Cliffs, 1987.

D.N. Politis, Computer Intensive Methods in Statistical Analysis, IEEE Signal Processing Magazine, 15 (1998), 39-55.

P. Stoica, N. Sandgren, Smoothed Nonparanetric Spectral Estimation Via Cepstrum Thresholding, IEEE Signal Processing Magazine, 23, No. 6 (2006), 34-45.

C.W. Therrien, “Discrete Random Signals and Statistical Signal Processing”, Prentice-Hall, Englewood Cliffs, 1992.

A.M. Zoubir, B. Boashash, The Bootstrap and its Application in Signal Processing, IEEE Signal Processing Magazine, 15 (1998), 56-76.

Published

2008-06-01

How to Cite

Bezerra, M., Iano, Y., & Tarumoto, M. (2008). Evaluating some Yule-Walker Methods with the Maximum-Likelihood Estimator for the Spectral ARMA Model. Trends in Computational and Applied Mathematics, 9(2), 175–184. https://doi.org/10.5540/tema.2008.09.02.0175

Issue

Section

Original Article