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

Journal article (2009)

Authors

P.M.T. Broersen

Department

Multi-Scale Physics () (TU Delft)

DOI: https://doi.org/doi:10.1109/TIM.2008.2009400

Time series analysis Parameter estimation Spectral estimation Autocorrelation bias Autoregressive (AR) model Triangular bias

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Published Date

07-04-2009

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Source:

IEEE Transactions on Instrumentation and Measurement, 58 (5), 2009

Faculty

Applied Sciences

Department

Multi-Scale Physics

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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