For { t y } a discrete time, second-order stationary process, the Levinson-Durbin recursion is used to determine the coefficients , jk α j=1, … , k, of the best linear predictor of 1 + k y , , ˆ 1 1 1 y y y kk k k k α α − − − = + L best in the sense of minimizing the mean square error. The coefficients jk α determine a Levinson-Durbin sequence. A generalized Levinson-Durbin sequence, a special ...

This paper presents an iterative autoregressive system parameter estimation algorithm in the presence of white observation noise. The algorithm is based on the parameter estimation bias correction approach. We use high order Yule–Walker equations, sequentially estimate the noise variance, and exploit these estimated variances for the bias correction. The improved performance of the proposed alg...

In this study, Doppler signals recorded from ophthalmic artery of 75 subjects were processed by PC-computer using classical and model-based methods. The classical method (fast Fourier transform) and three model-based methods (Burg autoregressive, moving average, least-squares modified Yule-Walker autoregressive moving average methods) were selected for processing ophthalmic arterial Doppler sig...

Doppler ultrasound is known as a reliable technique, which demonstrates the flow characteristics and resistance of arteries in various vascular disease. In this study, internal carotid arterial Doppler signals recorded from 105 subjects were processed by PC-computer using classical, model-based, and eigenvector methods. The classical method (fast Fourier transform), two model-based methods (Bur...

Recently a method of estimating the parameters of an AR(p) random process based on measurements corrupted by additive white noise was described. The method involves solving a matrix pencil, called the Noise-Compensated Yule-Walker (NCYW) equations, for the AR parameters and the variance of the measurement noise. In this correspondence we give a necessary and sufficient condition for there to ex...

The Yule–Walker (YW) method for autoregressive (AR) estimation uses lagged-product (LP) autocorrelation estimates to compute an AR parametric spectral model. The LP estimates only have a small triangular bias in the estimated autocorrelation function and are asymptotically unbiased. However, using them in finite samples with the YW method for AR estimation can give a strong distortion in the we...

Zadrozny (1990) proposed and illustrated a nonlinear Kalman-filtering (KF) method for estimating a vector autoregressive moving-average (VARMA) model with mixed-frequency and partly temporallyaggregated data. The present paper proposes an optimal three-step linear instrumental variable method for estimating a VAR model with mixed-frequency data. The method compensates for missing data arising f...

This article studies estimation of a stationary autocovariance structure in the presence an unknown number mean shifts. Here, Yule–Walker moment estimator for autoregressive parameters dependent time series contaminated by shift changepoints is proposed and studied. The based on first order differences proven consistent asymptotically normal when m length N satisfy $$m/N \rightarrow 0$$ as $$N ...

This review provides an introduction to the use of parametric modelling techniques for time series analysis, and in particular the application of autoregressive modelling to the analysis of physiological signals such as the human electroencephalogram. The concept of signal stationarity is considered and, in the light of this, both adaptive models, and non-adaptive models employing fixed or adap...