Asymptotic efficiency of conditional least squares estimators for ARCH models

Tomoyuki Amano, Masanobu Taniguchi

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    4 Citations (Scopus)

    Abstract

    The conditional least squares (CL) estimators proposed by Tjostheim [1986. Estimation in nonlinear time series models. Stochastic Process. Appl. 21, 251-273] are important and fundamental. The CL estimator applied to the square-transformed ARCH model has an explicit form, which does not depend on the distribution of the innovation. Since the CLs are not asymptotically efficient in general, we give a necessary and sufficient condition that CL is asymptotically efficient based on the LAN approach. Next, a measure of efficiency for CL is introduced. Numerical evaluations of the measure of efficiency for various nonlinear time series models are given. They elucidate some interesting features of CL.

    Original languageEnglish
    Pages (from-to)179-185
    Number of pages7
    JournalStatistics and Probability Letters
    Volume78
    Issue number2
    DOIs
    Publication statusPublished - 2008 Feb 1

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    Keywords

    • ARCH model
    • Asymptotic efficiency
    • Conditional least squares estimator
    • Local asymptotic normality

    ASJC Scopus subject areas

    • Statistics, Probability and Uncertainty
    • Statistics and Probability

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