Asymptotic normality of quadratic forms of martingale differences

Liudas Giraitis, Masanobu Taniguchi, Murad S. Taqqu

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    We establish the asymptotic normality of a quadratic form (Formula presented.) in martingale difference random variables (Formula presented.) 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 (Formula presented.), asymptotic normality holds under condition (Formula presented.), where (Formula presented.) and ||A|| are the spectral and Euclidean norms of the matrix A, respectively, finding corresponding sufficient conditions in the case of martingale differences (Formula presented.) has been an important open problem. We provide such sufficient conditions in this paper.

    Original languageEnglish
    Pages (from-to)1-13
    Number of pages13
    JournalStatistical Inference for Stochastic Processes
    DOIs
    Publication statusAccepted/In press - 2016 Jul 18

    Fingerprint

    Martingale Difference
    Asymptotic Normality
    Quadratic form
    Quadratic equation solution
    Spectral Norm
    Euclidean norm
    I.i.d. Random Variables
    Sufficient Conditions
    Time Series Analysis
    Open Problems
    Random variable

    Keywords

    • Asymptotic normality
    • Martingale differences
    • Quadratic form

    ASJC Scopus subject areas

    • Statistics and Probability

    Cite this

    Asymptotic normality of quadratic forms of martingale differences. / Giraitis, Liudas; Taniguchi, Masanobu; Taqqu, Murad S.

    In: Statistical Inference for Stochastic Processes, 18.07.2016, p. 1-13.

    Research output: Contribution to journalArticle

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