# On the estimation of the autocorrelation function

Discussiones Mathematicae Probability and Statistics (2010)

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

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topManuel 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 -

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