Methods for estimating integrated variance: Jump robustness issues in high frequency time series

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Abstract

Integrated variance is a volatility measure of a process in continuous time, which is applicable in financial mathematics as a means to optimize a portfolio, project dynamics of a price of a financial asset. The consistency of an estimator for integrated variance of a random process is at the core of this article. A fundamental diffusion process is extended by adding a jump component as a means of improving the descriptive function of the process. It is activity of jumps that is a factor subject to which is the consistency of the estimator for integrated variance. Due to this fact, consistency is defined as an extent to which the estimator at hand is jump robust. Two main methods for estimating integrated variance are considered and the capacity of corresponding estimators to withstand the effect of jumps while converging is briefly analyzed. The arguments indicating a necessity for further research of the effect of jumps with reference to works of the authors who have established a ground for analysis of integrated variance and those works containing main asymptotic results for consistency of integrated variance estimators are elaborated. Based on this, avenue for further research and development of asymptotic theory for consistency of an estimator for integrated variance is identified.

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About the authors

Z. O. Kosimov

Lomonosov Moscow State University

Author for correspondence.
Email: zohirsho1@gmail.com
Russian Federation, Moscow

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2. Fig. 1. A jump process with infinite activity and finite variation (gamma variation)

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3. Fig. 2. A jump-like process with infinite activity and infinite variation (normal inverse Gaussian process)

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