Dynamic Density Estimation of Market Microstructure Variables
via Auxiliary Particle Filtering

Abstract

In this article, we introduce a new density estimation approach to sequentially model the distribution of market microstructure variables on a continuous basis. We employ a nonlinear state space model as our basic framework, where the market microstructure variables follow a distribution with unknown parameters that are identified as the states in the model. Instead of specifying a parametric family for the posterior distribution of the states given the observed microstructure variables, we use a discrete approximation approach. Combining an (auxiliary) particle filtering approach with an efficient change point detection methodology, we efficiently update the posterior distribution of the “states” with newly arrived observations of the relevant microstructure variables, which are detected to indicate a departure from the previous distributional regime. The methodology offers a potential solution to the challenge of updating the distribution of market variables of interest using only relevant data arriving at high frequencies while filtering out noise that is unlikely to indicate departures from previously estimated regimes. The method is validated using simulated data and real bid–ask spread data, and excellent performance is found.