The Annals of Probability

Central limit theorems for quadratic forms with time-domain conditions

Liudas Giraitis and Murad S. Taqqu

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Abstract

We establish the central limit theorem for quadratic forms $\Sigma_{t, s=1}^N b(t - s)P_{m, n} (X_t, X_s)$ of the bivariate Appell polynomials $P_{m, n} (X_t, X_x))$ under time-domain conditions. These conditions relate the weights $b(t)$ and the covariances of the sequences $(P_{m, n} (X_t, X_s))$ and $(X_t)$. The time-domain approach, together with the spectral domain approach developed earlier, yields a general set of conditions for central limit theorems.

Article information

Source
Ann. Probab., Volume 26, Number 1 (1998), 377-398.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022855425

Digital Object Identifier
doi:10.1214/aop/1022855425

Mathematical Reviews number (MathSciNet)
MR1617055

Zentralblatt MATH identifier
0943.60018

Subjects
Primary: 60F05: Central limit and other weak theorems 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Appell polynomials central limit theorem long-range dependence quadratic forms time series

Citation

Giraitis, Liudas; Taqqu, Murad S. Central limit theorems for quadratic forms with time-domain conditions. Ann. Probab. 26 (1998), no. 1, 377--398. doi:10.1214/aop/1022855425. https://projecteuclid.org/euclid.aop/1022855425


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