Asymptotic theory for ARCH-SM models: Lan and residual empirical processes

Sangyeol Lee*, Masanobu Taniguchi


研究成果: Article査読

26 被引用数 (Scopus)


In this paper, we have two asymptotic objectives: the LAN and the residual empirical process for a class of ARCH(∞)-SM (stochastic mean) models, which covers finite-order ARCH and GARCH models. First, we establish the LAN for the ARCH(∞)-SM model and, based on it, construct an asymptotically optimal test when the parameter vector contains a nuisance parameter. Also, we discuss asymptotically efficient estimators for unknown parameters when the innovation density is known and when it is unknown. For the residual empirical process, we investigate its asymptotic behavior in ARCH(q)-SM models. We show that, unlike the usual autoregressive model, the limiting distribution in this case depends upon the estimator of the regression parameter as well as those of the ARCH parameters.

ジャーナルStatistica Sinica
出版ステータスPublished - 2005 1月 1

ASJC Scopus subject areas

  • 統計学および確率
  • 統計学、確率および不確実性


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