Open Access
June 2002 Asymptotic nonequivalence of GARCH models and diffusions
Yazhen Wang
Ann. Statist. 30(3): 754-783 (June 2002). DOI: 10.1214/aos/1028674841


This paper investigates the statistical relationship of the GARCH model and its diffusion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's deficiency distance. To our surprise, we are able to show that the GARCH model and its diffusion limit are asymptotically equivalent only under deterministic volatility. With stochastic volatility, due to the difference between the structure with respect to noise propagation in their conditional variances, their likelihood processes asymptotically behave quite differently, and thus they are not asymptotically equivalent. This stochastic nonequivalence discredits a general belief that the two types of models are asymptotically equivalent in all respects and warns against the common financial practice that applies statistical inferences derived under the GARCH model to its diffusion limit.


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Yazhen Wang. "Asymptotic nonequivalence of GARCH models and diffusions." Ann. Statist. 30 (3) 754 - 783, June 2002.


Published: June 2002
First available in Project Euclid: 6 August 2002

zbMATH: 1029.62006
MathSciNet: MR1922541
Digital Object Identifier: 10.1214/aos/1028674841

Primary: 62B15
Secondary: 62M99 , 90A09 , 90A16 , 90A20

Keywords: ARCH , Black-Scholes , Comparison of experiments , conditional variance , deficiency distance , financial modeling , likelihood process , Stochastic differential equation , stochastic volatility

Rights: Copyright © 2002 Institute of Mathematical Statistics

Vol.30 • No. 3 • June 2002
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