A State Space Approach to Estimating
the Integrated Variance under the Existence of
Market Microstructure Noise

Daisuke Nagakura
Toshiaki Watanabe

February 2010


Abstract We call the realized variance (RV) calculated with observed prices contaminated by (market) microstructure noises (MNs) the noise-contaminated RV (NCRV), referring to the bias component in the NCRV associated with the MNs as the MN component. This paper develops a state space method for estimating the integrated variance (IV) and MN component. 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 identifiable parameters. We illustrate how to estimate these parameters. The proposed method also serves as a convenient way for estimating a general class of continuous-time stochastic volatility (SV) models under the existence of MN. We apply the proposed method to yen/dollar exchange rate data, where we find that most of the variation in NCRV is of the MN component.

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