Why Yule-Walker should not be used for autoregressive modelling

Hoon, Michiel de; Hagen, T.H.J.J. van der; Schoonewelle, H.; Dam, H. van

doi:10.1016/0306-4549(95)00126-3

Cited by 86 publications

(50 citation statements)

References 2 publications

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“…The condition number κ of Toeplitz correlation matrix R with elements r(0)−r(p − 1) has been proposed to classify the sensitivity of an AR process to the YW bias [15]. It is defined as…”

Section: Ar Estimates With the Yw Methodsmentioning

confidence: 99%

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Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule–Walker Method

Broersen

2009

IEEE Trans. Instrum. Meas.

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Abstract-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 weak parts of the power spectral density. The distortion is shown to be influential in an example without strong spectral peaks. The true biased AR model, which is computed by applying the triangular bias to the true autocorrelation function, has an infinite order. A new objective measure is introduced to determine the smallest sample size for which the unbiased asymptotic theory can be considered as a fair approximation.

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Section: Ar Estimates With the Yw Methodsmentioning

confidence: 99%

“…The value of the last parameter of order p never causes this extra YW bias for an AR(p) process [15]. The importance of the bias can be related to the condition number of the Toeplitz autocorrelation matrix, which contains only the autocorrelations until order p − 1.…”

Section: Introductionmentioning

confidence: 99%

Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule–Walker Method

Broersen

2009

IEEE Trans. Instrum. Meas.

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“…Variations in the decay ratio and the frequency among five different models are within 0.03 and 0.01 Hz, respectively. De Hoon et al (13) reported that the Yule-Walker model gives a lower decay ratio than Burg's lattice-based model does when those are applied for less stable signals. The experimental results are consistent with the finding that the Yule-Walker model gives a lower decay ratio than Burg's lattice-based model does for high thermal power, which is less stable conditions.…”

Section: Effect Of Auto-regressive Modelmentioning

confidence: 99%

Stability Estimation of ABWR on the Basis of Noise Analysis

Furuya

Fukahori²,

Mizokami

et al. 2008

JPES

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In order to investigate the stability of a nuclear reactor core with an oxide mixture of uranium and plutonium (MOX) fuel installed, channel stability and regional stability tests were conducted with the SIRIUS-F facility. The SIRIUS-F facility was designed and constructed to provide a highly accurate simulation of thermal-hydraulic (channel) instabilities and coupled thermalhydraulics-neutronics instabilities of the Advanced Boiling Water Reactors (ABWRs). A real-time simulation was performed by modal point kinetics of reactor neutronics and fuel-rod thermal conduction on the basis of a measured void fraction in a reactor core section of the facility. A time series analysis was performed to calculate decay ratio and resonance frequency from a dominant pole of a transfer function by applying auto regressive (AR) methods to the time-series of the core inlet flow rate. Experiments were conducted with the SIRIUS-F facility, which simulates ABWR with MOX fuel installed. The variations in the decay ratio and resonance frequency among the five common AR methods are within 0.03 and 0.01 Hz, respectively. In this system, the appropriate decay ratio and resonance frequency can be estimated on the basis of the Yule-Walker method with the model order of 30.

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“…The advantages of the time-series approach to autocorrelation estimation have theoretically been derived [5, p. 144]. In addition, examples have been given where the Yule-Walker method of AR estimation gives poor results [15]. This paper describes estimators for the autocovariance and autocorrelation functions, with LP or with time-series models [2], [10].…”

Section: Introductionmentioning

confidence: 99%

The Quality of Lagged Products and Autoregressive Yule–Walker Models as Autocorrelation Estimates

Broersen

2009

IEEE Trans. Instrum. Meas.

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Abstract-The sample autocorrelation function is defined by the mean lagged products (LPs) of random observations. It is the inverse Fourier transform of the raw periodogram. Both contain the same information, and the quality of the full-length sample autocorrelation to represent random data is as poor as that of a raw periodogram. The autoregressive (AR) Yule-Walker method uses LP autocorrelation estimates to compute AR parameters as a parametric model for the autocorrelation. The order of the AR model can be taken as the full LP length, or it can be determined with an order selection criterion. However, the autocorrelation function can more accurately be estimated with a general parametric time-series method. This parametric estimate of the autocorrelation function always has better accuracy than the LP estimates. The LP autocorrelation function is as long as the observation window, but parametric estimates will eventually die out. They allow an objective answer to the question of how long the autocorrelation function really is.

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Why Yule-Walker should not be used for autoregressive modelling

Cited by 86 publications

References 2 publications

Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule–Walker Method

Finite-Sample Bias Propagation in Autoregressive Estimation With the Yule–Walker Method

Stability Estimation of ABWR on the Basis of Noise Analysis

The Quality of Lagged Products and Autoregressive Yule–Walker Models as Autocorrelation Estimates

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