Local Whittle likelihood estimators and tests for non-Gaussian stationary processes

Tomohito Naito, Kohei Asai, Tomoyuki Amano, Masanobu Taniguchi

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    In this paper, we propose a local Whittle likelihood estimator for spectral densities of non-Gaussian processes and a local Whittle likelihood ratio test statistic for the problem of testing whether the spectral density of a non-Gaussian stationary process belongs to a parametric family or not. Introducing a local Whittle likelihood of a spectral density fθ (λ) around λ, we propose a local estimator θ̂=θ̂(λ) of θ which maximizes the local Whittle likelihood around λ, and use fθ̂(λ)(λ) as an estimator of the true spectral density. For the testing problem, we use a local Whittle likelihood ratio test statistic based on the local Whittle likelihood estimator. The asymptotics of these statistics are elucidated. It is shown that their asymptotic distributions do not depend on non-Gaussianity of the processes. Because our models include nonlinear stationary time series models, we can apply the results to stationary GARCH processes. Advantage of the proposed estimator is demonstrated by a few simulated numerical examples.

    Original languageEnglish
    Pages (from-to)163-174
    Number of pages12
    JournalStatistical Inference for Stochastic Processes
    Volume13
    Issue number3
    DOIs
    Publication statusPublished - 2010

    Fingerprint

    Whittle Likelihood
    Local Likelihood
    Stationary Process
    Spectral Density
    Estimator
    Likelihood Ratio Test Statistic
    Stationary Time Series
    Nonlinear Time Series
    Testing
    Generalized Autoregressive Conditional Heteroscedasticity
    Time Series Models
    Asymptotic distribution
    Maximise
    Statistics
    Numerical Examples

    Keywords

    • Local likelihood ratio test
    • Local Whittle likelihood estimator
    • Non-Gaussian linear process
    • Spectral density

    ASJC Scopus subject areas

    • Statistics and Probability

    Cite this

    Local Whittle likelihood estimators and tests for non-Gaussian stationary processes. / Naito, Tomohito; Asai, Kohei; Amano, Tomoyuki; Taniguchi, Masanobu.

    In: Statistical Inference for Stochastic Processes, Vol. 13, No. 3, 2010, p. 163-174.

    Research output: Contribution to journalArticle

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