Asymptotic efficiency of conditional least squares estimators for ARCH models

Tomoyuki Amano; Masanobu Taniguchi

doi:10.1016/j.spl.2007.05.016

Asymptotic efficiency of conditional least squares estimators for ARCH models

Tomoyuki Amano, Masanobu Taniguchi^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	179-185
Number of pages	7
Journal	Statistics and Probability Letters
Volume	78
Issue number	2
DOIs	https://doi.org/10.1016/j.spl.2007.05.016
Publication status	Published - 2008 Feb 1
Externally published	Yes

Keywords

ARCH model
Asymptotic efficiency
Conditional least squares estimator
Local asymptotic normality

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1016/j.spl.2007.05.016

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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.",

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AU - Amano, Tomoyuki

AU - Taniguchi, Masanobu

PY - 2008/2/1

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N2 - 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.

AB - 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.

KW - ARCH model

KW - Asymptotic efficiency

KW - Conditional least squares estimator

KW - Local asymptotic normality

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DO - 10.1016/j.spl.2007.05.016

M3 - Article

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SN - 0167-7152

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EP - 185

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -

Asymptotic efficiency of conditional least squares estimators for ARCH models

Abstract

Keywords

ASJC Scopus subject areas

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