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Inference about realized volatility using infill subsampling

Ilze Kalnina and Oliver Linton ()

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Realised Volatility; Semimartingale; Subsampling; Infill Asymptotic Scheme (search for similar items in EconPapers)
JEL-codes: C12 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2007-09
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Citations: View citations in EconPapers (6) Track citations by RSS feed

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http://eprints.lse.ac.uk/4411/ Open access version. (application/pdf)

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Working Paper: Inference about Realized Volatility using Infill Subsampling (2007) Downloads
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