Second order optimality for estimators in time series regression models

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator over(β, ^) proposed by Hannan [Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, pp. 17-37]. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of over(β, ^). Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that over(β, ^) has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of over(β, ^). Numerical studies are given to confirm the theoretical results.

    Original languageEnglish
    Pages (from-to)638-659
    Number of pages22
    JournalJournal of Multivariate Analysis
    Volume98
    Issue number3
    DOIs
    Publication statusPublished - 2007 Mar

    Fingerprint

    Time Series Models
    Time series
    Optimality
    Regression Model
    Estimator
    Time series analysis
    Second-order Asymptotics
    Asymptotic Properties
    Bandwidth
    Bandwidth Choice
    Parametric Estimation
    Estimation Theory
    Edgeworth Expansion
    Semiparametric Estimation
    Time Series Analysis
    Regression Coefficient
    Frequency Domain
    Numerical Study
    Rate of Convergence
    Regression

    Keywords

    • Efficient estimation
    • Second order asymptotics
    • Semiparametric estimation
    • Spectral regression

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Numerical Analysis
    • Statistics and Probability

    Cite this

    Second order optimality for estimators in time series regression models. / Tamaki, Kenichiro.

    In: Journal of Multivariate Analysis, Vol. 98, No. 3, 03.2007, p. 638-659.

    Research output: Contribution to journalArticle

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