A Note on Method of Moments Estimation of Ornstein-Uhlenbeck Process Using Ultra-High-Frequency Data

Stock prices, foreign exchange rates and commodity prices are recorded with each transaction or bid/ask offer resulting in intraday ultra-high-frequency data. Such time series have a very fine time scale and several distinctive characteristics including irregularly spaced observations and the presence of the market microstructure noise. When time series also exhibit mean-reverting behavior, the Ornstein-Uhlenbeck process with continuous values and continuous time can be used to model them. We propose an estimator of the Ornstein-Uhlenbeck process for irregularly spaced observations contaminated by the independent white noise. The estimator is based on the method of moments and utilizes the sample mean, the sample variance and the autocovariance function approximated by the least squares method. The advantage of the method of moments is that it does not require the underlying distribution to be specified. In a simulation study, we compare the proposed method of moments estimator with the maximum likelihood estimator.