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Asymptotic efficiency of conditional least squares estimators for ARCH models

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  • Amano, Tomoyuki
  • Taniguchi, Masanobu

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.

Suggested Citation

  • Amano, Tomoyuki & Taniguchi, Masanobu, 2008. "Asymptotic efficiency of conditional least squares estimators for ARCH models," Statistics & Probability Letters, Elsevier, vol. 78(2), pages 179-185, February.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:2:p:179-185
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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Engle, Robert F. (ed.), 1995. "ARCH: Selected Readings," OUP Catalogue, Oxford University Press, number 9780198774327.
    3. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(4), pages 539-569, August.
    4. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
    5. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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