Statistical Methods in Finance 2017

Abstract

Estimation of Parameters of Continuous Processes from High-Frequency Data

by Vladimir Holy

When a time series is observed at high frequencies, more information can be utilized in estimating parameters of the process. However, high-frequency data are also contaminated by the market microstructure noise which causes significant bias in volatility estimation when not taken into account. This property is widely studied in literature concerning with non-parametric estimation of quadratic variation. We focus on impact of the noise on estimation of parametric processes. Traditional methods ignoring the noise give biased estimates even when the variance of the noise is relatively small. We show that the Wiener process observed at discrete equidistant times and contaminated by the independent white noise follows ARIMA(0, 1, 1) instead of ARIMA(0, 1, 0). Similarly, the discretized and contaminated Ornstein-Uhlenbeck process follows ARIMA(1, 0, 1) instead of ARIMA(1, 0, 0). To overcome this problem, we present estimators robust to the noise based on the method of moments and maximum likelihood.

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