Minimum α-divergence estimation for arch models

S. Ajay Chandra*, Masanobu Taniguchi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


This paper considers a minimum α-divergence estimation for a class of ARCH(p) models. For these models with unknown volatility parameters, the exact form of the innovation density is supposed to be unknown in detail but is thought to be close to members of some parametric family. To approximate such a density, we first construct an estimator for the unknown volatility parameters using the conditional least squares estimator given by Tjøstheim [Stochastic processes and their applications (1986) Vol. 21, pp. 251-273]. Then, a nonparametric kernel density estimator is constructed for the innovation density based on the estimated residuals. Using techniques of the minimum Hellinger distance estimation for stochastic models and residual empirical process from an ARCH(p) model given by Beran [Annals of Statistics (1977) Vol. 5, pp. 445-463] and Lee and Taniguchi [Statistica Sinica (2005) Vol. 15, pp. 215-234] respectively, it is shown that the proposed estimator is consistent and asymptotically normal. Moreover, a robustness measure for the score of the estimator is introduced. The asymptotic efficiency and robustness of the estimator are illustrated by simulations. The proposed estimator is also applied to daily stock returns of Dell Corporation.

Original languageEnglish
Pages (from-to)19-39
Number of pages21
JournalJournal of Time Series Analysis
Issue number1
Publication statusPublished - 2006 Jan
Externally publishedYes


  • ARCH model
  • Asymptotic efficiency
  • Conditional least squares estimator
  • Kernel density estimator
  • Residual empirical process
  • Robustness
  • α-divergence

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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