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Asymptotic normality of quadratic forms of martingale differences

Giraitis, Liudas, Taniguchi, Masanobu and Taqqu, Murad S. (2016) Asymptotic normality of quadratic forms of martingale differences. Statistical Inference for Stochastic Processes. ISSN 1387-0874

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Identification Number: 10.1007/s11203-016-9143-3


We establish the asymptotic normality of a quadratic form QnQn in martingale difference random variables ηtηt 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 ηtηt, asymptotic normality holds under condition ||A||sp=o(||A||)||A||sp=o(||A||), where ||A||sp||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 ηtηt has been an important open problem. We provide such sufficient conditions in this paper.

Item Type: Article
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Additional Information: © 2016 The Authors © CC BY 4.0
Divisions: Economics
Subjects: Q Science > QA Mathematics
Date Deposited: 08 Aug 2016 12:53
Last Modified: 16 May 2024 02:18

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