Tracking Order Book Price Densities with Kalman Filters

Abstract

Since Kalman Filter was first developed by Kalman (1960), it has been widely used in engineering, statistics and econometrics. Filtering is different from forecasting as forecasting is made for predicting the future while filtering aims the estimation of unobservable parameters in the same period. For techniques as Kalman filters, on one hand, it can help to filter away the “noisy order”, revealing the true state of limit order book. On the other hand, it can be also use for prediction of state for next time step. In this paper, we estimate the limit order book using gamma distribution. Then each order book snapshot can be described using four parameters. After that, the basic filter is introduced with applications to disclose the pattern in limit order book.