The Annals of Applied Probability

How misleading can sample ACFs of stable MAs be? (Very!)

Sidney Resnick, Gennady Samorodnitsky, and Fang Xue

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Abstract

For the stable moving average process $$X^t = \int_{-\infty}^{\infty} f(t + x)M(dx), t = 1, 2,\dots,$$ we find the weak limit of its sample autocorrelation function as the sample size n increases to $\infty$. It turns out that, as a rule, this limit is random! This shows how dangerous it is to rely on sample correlation as a model fitting tool in the heavy tailed case. We discuss for what functions f this limit is nonrandom for all (or only some--this can be the case, too!) lags.

Article information

Source
Ann. Appl. Probab., Volume 9, Number 3 (1999), 797-817.

Dates
First available in Project Euclid: 21 August 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1029962814

Digital Object Identifier
doi:10.1214/aoap/1029962814

Mathematical Reviews number (MathSciNet)
MR1722283

Zentralblatt MATH identifier
0959.62076

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60E07: Infinitely divisible distributions; stable distributions 60G70: Extreme value theory; extremal processes

Keywords
Heavy tails sample correlation acf stable process ARMA processes infinite variance moving average

Citation

Resnick, Sidney; Samorodnitsky, Gennady; Xue, Fang. How misleading can sample ACFs of stable MAs be? (Very!). Ann. Appl. Probab. 9 (1999), no. 3, 797--817. doi:10.1214/aoap/1029962814. https://projecteuclid.org/euclid.aoap/1029962814


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