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On the empirical measure of the Fourier coefficients with infinite variance data

Author

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  • Knight, Keith

Abstract

A result of Freedman and Lane concerning the behaviour of the empirical distribution of Fourier coefficients with infinite variance random variables is extended is extended to include arbitrary random variables in the domain of attraction of an infinite variance stable law. A probabilistic proof of this result is given which permits a more explicit representation of the limiting random probability measure.

Suggested Citation

  • Knight, Keith, 1991. "On the empirical measure of the Fourier coefficients with infinite variance data," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 109-117, August.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:2:p:109-117
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    Cited by:

    1. Fasen, Vicky & Fuchs, Florian, 2013. "On the limit behavior of the periodogram of high-frequency sampled stable CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 229-273.
    2. Bose, Arup & Guha, Suman & Hazra, Rajat Subhra & Saha, Koushik, 2011. "Circulant type matrices with heavy tailed entries," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1706-1716, November.
    3. Kokoszka, Piotr & Mikosch, Thomas, 2000. "The periodogram at the Fourier frequencies," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 49-79, March.

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