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August 1999 How misleading can sample ACFs of stable MAs be? (Very!)
Sidney Resnick, Gennady Samorodnitsky, Fang Xue
Ann. Appl. Probab. 9(3): 797-817 (August 1999). DOI: 10.1214/aoap/1029962814


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.


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Sidney Resnick. Gennady Samorodnitsky. Fang Xue. "How misleading can sample ACFs of stable MAs be? (Very!)." Ann. Appl. Probab. 9 (3) 797 - 817, August 1999.


Published: August 1999
First available in Project Euclid: 21 August 2002

zbMATH: 0959.62076
MathSciNet: MR1722283
Digital Object Identifier: 10.1214/aoap/1029962814

Primary: 62M10
Secondary: 60E07 , 60G70

Keywords: acf , ARMA processes , heavy tails , infinite variance , moving average , sample correlation , Stable process

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.9 • No. 3 • August 1999
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