Efficient and Feasible Inference for the Components of Financial Variation Using Blocked Multipower Variation

44 Pages Posted: 21 Feb 2012

See all articles by Per A. Mykland

Per A. Mykland

University of Chicago - Department of Statistics

Neil Shephard

Harvard University

Kevin Sheppard

University of Oxford - Department of Economics; University of Oxford - Oxford-Man Institute of Quantitative Finance

Date Written: February 21, 2012

Abstract

High frequency financial data allows us to learn more about volatility, volatility of volatility and jumps. One of the key techniques developed in the literature in recent years has been bipower variation and its multipower extension, which estimates time-varying volatility robustly to jumps. We improve the scope and efficiency of multipower variation by the use of a more sophisticated exploitation of high frequency data. This suggests very significant improvements in the power of jump tests. It also yields efficient estimates of the integrated variance of the continuous part of a semimartingale. The paper also shows how to extend the theory to the case where there is microstructure in the observations and derive the first nonparametric high frequency estimator of the volatility of volatility. A fundamental device in the paper is a new type of result showing path-by-path (strong) approximation between multipower and the (unobserved) RV based on the continuous part of the process.

Keywords: bipower variation, jumps, market microstructure noise, multipower variation, non-parametric analysis, quadratic variation, semimartingale, volatility, volatility of volatility

JEL Classification: C01, C02, C13, C14, C22, D53, D81

Suggested Citation

Mykland, Per A. and Shephard, Neil and Sheppard, Kevin Keith, Efficient and Feasible Inference for the Components of Financial Variation Using Blocked Multipower Variation (February 21, 2012). Available at SSRN: https://ssrn.com/abstract=2008690 or http://dx.doi.org/10.2139/ssrn.2008690

Per A. Mykland

University of Chicago - Department of Statistics ( email )

Chicago, IL 60637-1514
United States
773-702-8044 (Phone)

Neil Shephard (Contact Author)

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

Kevin Keith Sheppard

University of Oxford - Department of Economics ( email )

Manor Road Building
Manor Road
Oxford, OX1 3BJ
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom
+44 1865 616 613 (Phone)

HOME PAGE: http://www.oxford-man.ox.ac.uk

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