A LIMIT THEOREM FOR QUADRATIC FORMS AND ITS APPLICATIONS

Wei Biao Wu and Xiaofeng Shao ()

Econometric Theory, 2007, vol. 23, issue 05, pages 930-951

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.

Date: 2007

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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:23:y:2007:i:05:p:930-951_07

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