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A LIMIT THEOREM FOR QUADRATIC FORMS AND ITS APPLICATIONS

Published online by Cambridge University Press:  14 May 2007

Wei Biao Wu  and
Xiaofeng Shao
Wei Biao Wu
Affiliation:
University of Chicago
Xiaofeng Shao
Affiliation:
University of Illinois at Urbana-Champaign
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Abstract

We consider quadratic forms of martingale differences and establish a central limit theorem under mild and easily verifiable conditions. By approximating Fourier transforms of stationary processes by martingales, our central limit theorem is applied to the smoothed periodogram estimate of spectral density functions. Our results go beyond earlier ones by allowing a variety of nonlinear time series and by avoiding strong mixing and/or summability conditions on joint cumulants.We thank the two reviewers for their detailed comments, which led to substantial improvements. The work is supported in part by NSF grant DMS-0478704.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 5 , October 2007 , pp. 930 - 951
Copyright
© 2007 Cambridge University Press

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