Identification of continuous-time linear filters when only discrete-time data is available
研究了如何从离散时间观测数据中推断连续时间线性滤波器，解决了因不同协方差结构对应相同离散表示而导致的识别问题，并应用于高频金融数据下的最优交易策略。
We study the inference of continuous-time linear filters from discrete-time observations of the underlying stochastic differential equation. This problem poses several identification issues related to the existence of infinite continuous-time specifications with different covariance structures having the same exact discrete-time representation. We derive mild restrictions on the drift dynamics, allowing to uniquely determine the drift linear projections and other relevant covariance structures of the stochastic differential equation. Our results are employed to identify, based on discrete-time data, the solution to an optimal stochastic control problem under partial information, thereby reconciling the continuous-time formulation of the problem with the statistical inference of the model parameters based on discrete-time information. We illustrate, through an empirical application using high-frequency financial data, how our identification scheme enhances the expected utility of intraday trading strategies.