The most commonly used method for estimating the time domain parameters of an autoregressive process is to use the Yule-Walker equations. The Yule-Walker estimates of the parameters of an autoregressive process are known to often be highly biased. There is a Fourier transform relationship between the autocovariance sequence for an autoregressive process (the estimates of which are used in the Y...

The most commonly used method for estimating the time domain parameters of an autoregressive process is to use the Yule-Walker equations. The Yule-Walker estimates of the parameters of an autoregressive process of order p, or AR(p), are known to often be highly biased. This can lead to inappropriate order selection and very poor forecasting. There is a Fourier transform relationship between the...

AMS 2000 subject classifications: primary 62F12 62M10 secondary 62G08 62G20 Keywords: Autoregressive time series Local polynomial Oracle efficiency Yule–Walker estimator Moving average a b s t r a c t Time series often contain unknown trend functions and unobservable error terms. As is known, Yule–Walker estimators are asymptotically efficient for autoregressive time series. The focus of this a...

The processing of noise-corrupted signals is a common problem in signal processing applications. In most of the cases, it is assumed that the additive noise is white Gaussian and that the constant noise variance is either available or can be easily measured. However, this may not be the case in practical situations. We present a new approach to additive white Gaussian noise variance estimation....

The article considers the Yule-Walker estimator of the autoregressive coefficient based on the observed time series that contains an unknown trend function and an autoregressive error term. The trend function is estimated by means of B-splines and then subtracted from the observations. The Yule-Walker estimator is obtained from the residual sequence. Asymptotic properties of this estimator are ...

The eponym “Walker Circulation” refers to a concept used by atmospheric scientists and oceanographers in providing a physical explanation for the El Niño–Southern Oscillation phenomenon, whereas the eponym “Yule–Walker equations” refers to properties satisfied by the autocorrelations of an autoregressive process. But how many statisticians (or, for that matter, atmospheric scientists) are aware...

We present a novel formulation of nonstationary autoregressive (AR) models in terms of time-frequency (TF) shifts. The parameters of the proposed TFAR model are determined by “TF Yule-Walker equations” that involve the expected ambiguity function and can be solved efficiently due to their block-Toeplitz structure. For moderate model orders, we also propose approximate TF Yule-Walker equations t...

We present a novel formulation of nonstationary autoregressive (AR) models in terms of time-frequency (TF) shifts. The parameters of the proposed TFAR model are determined by "TF Yule-Walker equations" that involve the expected ambiguity function and can be solved efficiently due to their block-Toeplitz structure. For moderate model orders, we also propose approximate TF Yule-Walker equations t...

‎Recently a first-order Spatial Integer-valued Autoregressive‎ ‎SINAR(1,1) model was introduced to model spatial data that comes‎ ‎in counts citep{ghodsi2012}‎. ‎Some properties of this model‎ ‎have been established and the Yule-Walker estimator has been‎ ‎proposed for this model‎. ‎In this paper‎, ‎we introduce the...