A limit theorem for quadratic forms and its applications

Wei Biao Wu, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review


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 periodograrn 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.

Original languageEnglish (US)
Pages (from-to)930-951
Number of pages22
JournalEconometric Theory
Issue number5
StatePublished - Oct 2007

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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