Title :
An approach to time series analysis and ARMA spectral estimation
Author :
Zhang, Xian-Da ; Takeda, Hiroshi
Author_Institution :
Changcheng Institute of Metrology and Measurement (CIMM), Beijing, China
fDate :
9/1/1987 12:00:00 AM
Abstract :
This paper presents an approach to time series analysis and ARMA spectral estimation from only the output data corrupted by noise. It is shown that the generalized (not well-known) modified Yule-Walker (MYW) equations hold when the residual is some correlated noise. To solve such equations, a new version of the generalized least squares (GLS) method is proposed, yielding AR parameter estimates with higher accuracy. This GLS method can also be used to enhance the estimation accuracy of AR parameters for short and noisy data in case of the MYW equation holding theoretically. Furthermore, a simple procedure for improving MA parameter estimates is studied. Our approach, as Cadzow´s singular value decomposition (SVD) method, has provided significantly higher performance spectral estimates for a low-order ARMA model than those obtained via usual techniques which are based upon direct solution of the MYW equations and which use a high-order model without considering an additive noise.
Keywords :
Additive noise; Equations; Least squares methods; Maximum likelihood detection; Parameter estimation; Singular value decomposition; Spectral analysis; Stochastic resonance; System identification; Time series analysis;
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
DOI :
10.1109/TASSP.1987.1165272