On the estimation of the autocorrelation function

Manuel Duarte Ortigueira

Discussiones Mathematicae Probability and Statistics (2010)

  • Volume: 30, Issue: 1, page 103-115
  • ISSN: 1509-9423

Abstract

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The autocorrelation function has a very important role in several application areas involving stochastic processes. In fact, it assumes the theoretical base for Spectral analysis, ARMA (and generalizations) modeling, detection, etc. However and as it is well known, the results obtained with the more current estimates of the autocorrelation function (biased or not) are frequently bad, even when we have access to a large number of points. On the other hand, in some applications, we need to perform fast correlations. The usual estimators do not allow a fast computation, even with the FFT. These facts motivated the search for alternative ways of computing the autocorrelation function. 9 estimators will be presented and a comparison in face to the exact theoretical autocorrelation is done. As we will see, the best is the AR modified Burg estimate.

How to cite

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Manuel Duarte Ortigueira. "On the estimation of the autocorrelation function." Discussiones Mathematicae Probability and Statistics 30.1 (2010): 103-115. <http://eudml.org/doc/277026>.

@article{ManuelDuarteOrtigueira2010,
abstract = {The autocorrelation function has a very important role in several application areas involving stochastic processes. In fact, it assumes the theoretical base for Spectral analysis, ARMA (and generalizations) modeling, detection, etc. However and as it is well known, the results obtained with the more current estimates of the autocorrelation function (biased or not) are frequently bad, even when we have access to a large number of points. On the other hand, in some applications, we need to perform fast correlations. The usual estimators do not allow a fast computation, even with the FFT. These facts motivated the search for alternative ways of computing the autocorrelation function. 9 estimators will be presented and a comparison in face to the exact theoretical autocorrelation is done. As we will see, the best is the AR modified Burg estimate.},
author = {Manuel Duarte Ortigueira},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {time-series autocorrelation; regression},
language = {eng},
number = {1},
pages = {103-115},
title = {On the estimation of the autocorrelation function},
url = {http://eudml.org/doc/277026},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Manuel Duarte Ortigueira
TI - On the estimation of the autocorrelation function
JO - Discussiones Mathematicae Probability and Statistics
PY - 2010
VL - 30
IS - 1
SP - 103
EP - 115
AB - The autocorrelation function has a very important role in several application areas involving stochastic processes. In fact, it assumes the theoretical base for Spectral analysis, ARMA (and generalizations) modeling, detection, etc. However and as it is well known, the results obtained with the more current estimates of the autocorrelation function (biased or not) are frequently bad, even when we have access to a large number of points. On the other hand, in some applications, we need to perform fast correlations. The usual estimators do not allow a fast computation, even with the FFT. These facts motivated the search for alternative ways of computing the autocorrelation function. 9 estimators will be presented and a comparison in face to the exact theoretical autocorrelation is done. As we will see, the best is the AR modified Burg estimate.
LA - eng
KW - time-series autocorrelation; regression
UR - http://eudml.org/doc/277026
ER -

References

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  12. [12] A. Papoulis and S.U. Pilai, Probability, Random Variables, and Stachastic Processes, McGraw-Hill Book Company 2002. 
  13. [13] M.C. Sullivan, Efficient Autocorrelation Estimation Using Relative Magnitudes, IEEE Transactions On Acoustics, Speech. And Signal Processing 37 (3) (1989). 
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