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On Asymptotic Theory for ARCH (∞) Models
Author(s) -
Hafner Christian M.,
Preminger Arie
Publication year - 2017
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12239
Subject(s) - arch , mathematics , heteroscedasticity , estimator , asymptotic distribution , econometrics , autoregressive conditional heteroskedasticity , consistency (knowledge bases) , moment (physics) , volatility (finance) , statistics , discrete mathematics , structural engineering , physics , classical mechanics , engineering
Autoregressive conditional heteroskedasticity (ARCH)( ∞ ) models nest a wide range of ARCH and generalized ARCH models including models with long memory in volatility. Existing work assumes the existence of second moments. However, the fractionally integrated generalized ARCH model, one version of a long memory in volatility model, does not have finite second moments and rarely satisfies the moment conditions of the existing literature. This article weakens the moment assumptions of a general ARCH( ∞ ) class of models and develops the theory for consistency and asymptotic normality of the quasi‐maximum likelihood estimator.