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

Journal article (2009)

Authors

Department
Multi-Scale Physics (AS) (TU Delft)
Copyright: © 2009 IEEE
DOI: https://doi.org/doi:10.1109/TIM.2009.2021206
Identification Correlation Spectral estimation Autoregressive (AR) process Order selection Time-series model
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Published Date

09-10-2009

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Source:

IEEE Transactions on Instrumentation and Measurement, 58 (11), 2009

ISSN:

0018-9456

Faculty

Applied Sciences

Department

Multi-Scale Physics

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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