Spectral Analysis of Quadratic Variation in the Presence of Market Microstructure Noise

We analyze the ex-post variation of equity prices in the frequency domain. A realized periodogram-based estimator is proposed, which consistently estimates the quadratic variation of the log equilibrium price process. For prices which are contaminated by market microstructure noise, the proposed estimator behaves like a filter: it removes the noise by filtering out high frequency periodograms. In other words, the proposed estimator converts high frequency data into low frequency periodograms. We show, through a simulation study and an application to the General Electric transaction prices, that the proposed estimator is insensitive to the choice of sampling frequency and it is competitive with other existing volatility measures.