Discussion Paper Series 2009-E-11

A State Space Approach to Estimating the Integrated Variance and Microstructure Noise Component

Daisuke Nagakura, Toshiaki Watanabe

We call the realized variance (RV) calculated with observed prices contaminated by microstructure noises (MNs) the noise-contaminated RV (NCRV) and refer to the component in the NCRV associated with the MNs as the MN component. This paper develops a method for estimating the integrated variance (IV) and MN component simultaneously, extending the state space method proposed by Barndorff-Nielsen and Shephard (2002). Our extension is based on the result obtained in Meddahi (2003), namely, when the true log-price process follows a general class of continuous-time stochastic volatility (SV) models, the IV follows an ARMA process. We represent the NCRV by a state space form and show that the state space form parameters are not identifiable; however, they can be expressed as functions of fewer identifiable parameters. We illustrate how to estimate these parameters. The proposed method is applied to yen/dollar exchange rate data. We find that the magnitude of the MN component is, on average, about 21%-48 % of the NCRV, depending on the sampling frequency.

Keywords: Realized Variance; Integrated Variance; Microstructure Noise

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

Copyright © 2009 Bank of Japan All Rights Reserved.

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