Asymptotic normality of quadratic forms of martingale differences

Liudas Giraitis, Masanobu Taniguchi, Murad S. Taqqu

研究成果: Article査読

3 被引用数 (Scopus)

抄録

We establish the asymptotic normality of a quadratic form Qn in martingale difference random variables ηt when the weight matrix A of the quadratic form has an asymptotically vanishing diagonal. Such a result has numerous potential applications in time series analysis. While for i.i.d. random variables ηt, asymptotic normality holds under condition | | A| | sp= o(| | A| |) , where | | A| | sp and ||A|| are the spectral and Euclidean norms of the matrix A, respectively, finding corresponding sufficient conditions in the case of martingale differences ηt has been an important open problem. We provide such sufficient conditions in this paper.

本文言語English
ページ(範囲)315-327
ページ数13
ジャーナルStatistical Inference for Stochastic Processes
20
3
DOI
出版ステータスPublished - 2017 10 1

ASJC Scopus subject areas

  • 統計学および確率

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