Open Access
January 1998 Central limit theorems for quadratic forms with time-domain conditions
Liudas Giraitis, Murad S. Taqqu
Ann. Probab. 26(1): 377-398 (January 1998). DOI: 10.1214/aop/1022855425


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.


Download Citation

Liudas Giraitis. Murad S. Taqqu. "Central limit theorems for quadratic forms with time-domain conditions." Ann. Probab. 26 (1) 377 - 398, January 1998.


Published: January 1998
First available in Project Euclid: 31 May 2002

zbMATH: 0943.60018
MathSciNet: MR1617055
Digital Object Identifier: 10.1214/aop/1022855425

Primary: 60F05 , 62M10

Keywords: Appell polynomials , central limit theorem , long-range dependence , Quadratic forms , time series

Rights: Copyright © 1998 Institute of Mathematical Statistics

Vol.26 • No. 1 • January 1998
Back to Top