Jackknifed whittle estimators

Masanobu Taniguchi, Kenichiro Tamaki, Thomas J. DiCiccio, Anna Clara Monti

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    The Whittle estimator (Whittle (1962)) is widely used in time series analysis. Although it is asymptotically Gaussian and efficient, this estimator suffers from large bias, especially when the underlying process has nearly unit roots. In this paper, we apply the jackknife technique to the Whittle likelihood in the frequency domain, and we derive the asymptotic properties of the jackknifed Whittle estimator. In particular, the second-order bias of the jackknifed estimator is shown to vanish for non-Gaussian stationary processes when the unknown parameter is innovation-free. The effectiveness of the jackknife technique for reducing the bias of the Whittle estimator is demonstrated in numerical studies. Since the Whittle estimator is applicable in many fields, including the natural sciences, signal processing, and econometrics, the bias-reduced jackknifed Whittle estimator can have widespread use.

    Original languageEnglish
    Pages (from-to)1287-1304
    Number of pages18
    JournalStatistica Sinica
    Volume22
    Issue number3
    DOIs
    Publication statusPublished - 2012 Jul

    Fingerprint

    Estimator
    Jackknife
    Whittle Likelihood
    Unit Root
    Time Series Analysis
    Stationary Process
    Econometrics
    Unknown Parameters
    Asymptotic Properties
    Frequency Domain
    Signal Processing
    Numerical Study
    Vanish

    Keywords

    • Asymptotic efficiency
    • Innovation-free
    • Jackknife
    • Secondorder bias
    • Spectral density
    • Stationary process
    • Whittle estimator

    ASJC Scopus subject areas

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

    Cite this

    Jackknifed whittle estimators. / Taniguchi, Masanobu; Tamaki, Kenichiro; DiCiccio, Thomas J.; Monti, Anna Clara.

    In: Statistica Sinica, Vol. 22, No. 3, 07.2012, p. 1287-1304.

    Research output: Contribution to journalArticle

    Taniguchi, M, Tamaki, K, DiCiccio, TJ & Monti, AC 2012, 'Jackknifed whittle estimators', Statistica Sinica, vol. 22, no. 3, pp. 1287-1304. https://doi.org/10.5705/ss.2011.113
    Taniguchi, Masanobu ; Tamaki, Kenichiro ; DiCiccio, Thomas J. ; Monti, Anna Clara. / Jackknifed whittle estimators. In: Statistica Sinica. 2012 ; Vol. 22, No. 3. pp. 1287-1304.
    @article{d13204e1205d46e49c16dad2e5da681d,
    title = "Jackknifed whittle estimators",
    abstract = "The Whittle estimator (Whittle (1962)) is widely used in time series analysis. Although it is asymptotically Gaussian and efficient, this estimator suffers from large bias, especially when the underlying process has nearly unit roots. In this paper, we apply the jackknife technique to the Whittle likelihood in the frequency domain, and we derive the asymptotic properties of the jackknifed Whittle estimator. In particular, the second-order bias of the jackknifed estimator is shown to vanish for non-Gaussian stationary processes when the unknown parameter is innovation-free. The effectiveness of the jackknife technique for reducing the bias of the Whittle estimator is demonstrated in numerical studies. Since the Whittle estimator is applicable in many fields, including the natural sciences, signal processing, and econometrics, the bias-reduced jackknifed Whittle estimator can have widespread use.",
    keywords = "Asymptotic efficiency, Innovation-free, Jackknife, Secondorder bias, Spectral density, Stationary process, Whittle estimator",
    author = "Masanobu Taniguchi and Kenichiro Tamaki and DiCiccio, {Thomas J.} and Monti, {Anna Clara}",
    year = "2012",
    month = "7",
    doi = "10.5705/ss.2011.113",
    language = "English",
    volume = "22",
    pages = "1287--1304",
    journal = "Statistica Sinica",
    issn = "1017-0405",
    publisher = "Institute of Statistical Science",
    number = "3",

    }

    TY - JOUR

    T1 - Jackknifed whittle estimators

    AU - Taniguchi, Masanobu

    AU - Tamaki, Kenichiro

    AU - DiCiccio, Thomas J.

    AU - Monti, Anna Clara

    PY - 2012/7

    Y1 - 2012/7

    N2 - The Whittle estimator (Whittle (1962)) is widely used in time series analysis. Although it is asymptotically Gaussian and efficient, this estimator suffers from large bias, especially when the underlying process has nearly unit roots. In this paper, we apply the jackknife technique to the Whittle likelihood in the frequency domain, and we derive the asymptotic properties of the jackknifed Whittle estimator. In particular, the second-order bias of the jackknifed estimator is shown to vanish for non-Gaussian stationary processes when the unknown parameter is innovation-free. The effectiveness of the jackknife technique for reducing the bias of the Whittle estimator is demonstrated in numerical studies. Since the Whittle estimator is applicable in many fields, including the natural sciences, signal processing, and econometrics, the bias-reduced jackknifed Whittle estimator can have widespread use.

    AB - The Whittle estimator (Whittle (1962)) is widely used in time series analysis. Although it is asymptotically Gaussian and efficient, this estimator suffers from large bias, especially when the underlying process has nearly unit roots. In this paper, we apply the jackknife technique to the Whittle likelihood in the frequency domain, and we derive the asymptotic properties of the jackknifed Whittle estimator. In particular, the second-order bias of the jackknifed estimator is shown to vanish for non-Gaussian stationary processes when the unknown parameter is innovation-free. The effectiveness of the jackknife technique for reducing the bias of the Whittle estimator is demonstrated in numerical studies. Since the Whittle estimator is applicable in many fields, including the natural sciences, signal processing, and econometrics, the bias-reduced jackknifed Whittle estimator can have widespread use.

    KW - Asymptotic efficiency

    KW - Innovation-free

    KW - Jackknife

    KW - Secondorder bias

    KW - Spectral density

    KW - Stationary process

    KW - Whittle estimator

    UR - http://www.scopus.com/inward/record.url?scp=84865017527&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84865017527&partnerID=8YFLogxK

    U2 - 10.5705/ss.2011.113

    DO - 10.5705/ss.2011.113

    M3 - Article

    VL - 22

    SP - 1287

    EP - 1304

    JO - Statistica Sinica

    JF - Statistica Sinica

    SN - 1017-0405

    IS - 3

    ER -