Speaker：Dr CHANG Jinyuan (Southwestern University of Finance and Economics)

Time：15:30-17:00 March 24,2017(Friday)

Site：B253

Abstract: High frequency financial data are typically assumed to be an additive composite of a relatively slow-varying continuous-time stochastic process for the price and some measurement errors contaminating the observations. We propose new techniques for analyzing such noisy high frequency financial data, based on frequency domain methods which are extremely popular in simpler errors-in-variables problems for i.i.d. data. We propose to estimate the density function of the measurement error distribution by applying a deconvolution technique with appropriate localization, incorporating the slowly varying feature of the underlying stochastic process. Our analysis shows that the resulting density function estimator is consistent and minimax rate optimal. Estimators of moments of the error distributions and their properties are also investigated. With the estimated error density function, we further study a frequency domain estimator for integrated volatility of the stochastic price process. We show that our integrated volatility estimator achieves the optimal convergence rate when the financial data are contaminated with measurement errors. Numerical examples by simulations and a real data analysis are conducted to demonstrate and validate our analysis.