Lagged-product autocorrelation estimates have a small triangular bias. However, using them to compute an autoregressive model with the Yule-Walker method can give a strongly distorted spectral model in finite samples. The distortion is shown for examples where the reflection coefficients are not very close to one in absolute value. It will disappear asymptotically. An objective measure is prese...

The INteger-valued AutoRegressive (INAR) processes were introduced in the literature by Al-Osh and Alzaid (1987) and McKenzie (1988) for modelling correlated series of counts. These processes have been considered as the discrete counter part of AR processes, but their highly nonlinear characteristics lead to some statistically challenging problems, namely in parameter estimation. Several estima...

We consider the problem of spectrum estimation of an AutoRegressive (AR) process in a sparse multipath environment. The presence of even a small number of delayed and attenuated replica of the source signal in the received signal may severely degrade the performance of classical AR spectrum estimation methods. Dwelling on the sparsity of the multipath reflections, we propose an approach which l...

The aims of this paper are estimate and forecast the Non-Accelerating Inflation Rate of Unemployment, or nairu, for Brazilian unemployment time series data. In doing so, we introduce a methodology for estimating mixed additive seasonal autoregressive (masar) models, by the Generalized Method of Moments (gmm). Furthermore, in order to cover a lack in econometric literature, an asymptotic theory ...

High-resolution spectrum estimation techniques have been extensively studied in recent publications. Knowledge of the noise variance is vital for spectrum estimation from noise-corrupted observations. This paper presents the use of noise compensation and data extrapolation for spectrum estimation. We assume that the observed data sequence can be represented by a set of autoregressive parameters...

Periodically correlated autoregressive nonstationary processes of finite order are considered. The corresponding Yule-Walker equations are applied to derive the generating functions of the covariance functions, what are called here the periodic covariance generating functions. We also provide closed formulas for the spectral densities by using the periodic covariance generating functions, which...

I n a number of applications involving the processing of noisy signals, it is desirable to know a priori the noise variance. We propose here a method of estimating the noise variance from the autoregressive (AR) signal corrupted by the additive white noise. This method first estimates the AR parameters from the highorder Yule-Wal ker equations and then uses these AR parameters to estimate ,the ...

This study presents alpha-stable autoregressive (AR) modeling of the dynamics Chua's circuit in presence heavy-tailed noise. The parameters AR time series are estimated using covariation-based Yule-Walker method, and distributed residuals calculated regression type method. Visual depictions model distributions presented. medians presented for noise with various stability index parameters. Thus,...

A new recursive eigendecomposition algorithm of Complex Hermitian Tœplitz matrices is studied. Based on Trench’s inversion of Tœplitz matrices from their autoregressive analysis, we have developed a fast recursive iterative algorithm that takes into account the rank-one modification of successive order Toeplitz matrices. To speed up the computational time and to increase numerical stability of ...

A noise-compensated long correlation matching (NCLCM) method is proposed for autoregressi~e ~AR) spectral estimation of the noisy AR signals. This method first computes the AR parameters from the high-order "(ule-Walker equations. Next, it employs these AR parameters and uses the low-order Yule-Walker equations to compensate the zeroth autocorrelation coefficient for the additive white noise. F...