Inference about realized volatility using infill subsampling

Kalnina, Ilze and Linton, Oliver (2007) Inference about realized volatility using infill subsampling. . Suntory and Toyota International Centres for Economics and Related Disciplines, London, UK.

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Abstract

We investigate the use of subsampling for conducting inference about the quadratic variation of a discretely observed diffusion process under an infill asymptotic scheme. We show that the usual subsampling method of Politis and Romano (1994) is inconsistent when applied to our inference question. Recently, a type of subsampling has been used to do an additive bias correction to obtain a consistent estimator of the quadratic variation of a diffusion process subject to measurement error, Zhang, Mykland, and Ait- Sahalia (2005). This subsampling scheme is also inconsistent when applied to the inference question above. This is due to a high correlation between estimators on different subsamples. We discuss an alternative approach that does not have this correlation problem; however, it has a vanishing bias only under smoothness assumptions on the volatility path. Finally, we propose a subsampling scheme that delivers consistent inference without any smoothness assumptions on the volatility path. This is a general method and can be potentially applied to conduct inference for quadratic variation in the presence of jumps and/or microstructure noise by subsampling appropriate consistent estimators.

Item Type:	Monograph (Discussion Paper)
Official URL:	http://sticerd.lse.ac.uk
Additional Information:	© 2007 the authors
Divisions:	Financial Markets Group Economics STICERD
Subjects:	H Social Sciences > HB Economic Theory
JEL classification:	C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General > C12 - Hypothesis Testing
Date Deposited:	21 Apr 2008 10:03
Last Modified:	13 Sep 2024 20:05
URI:	http://eprints.lse.ac.uk/id/eprint/4411

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