Asymptotic normality for quadratic forms of martingale differences
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Published version
Date
2016
Authors
Taqqu, Murad
Giraitis, Liudas
Taniguchi, Masanobu
Version
Published version
OA Version
Citation
M. Taqqu, Liudas Giraitis, Masanobu Taniguchi. "Asymptotic normality for quadratic forms of martingale differences." Statistical Inference for Stochastic Processes, https://doi.org/10.1007/s11203-016-9143-3
Abstract
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.
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© The Author(s) 2016. Open Access.
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