Modelling the Dynamics of Cross-Sectional Price Functions: an Econometric Analysis of the Bid and Ask Curves of an Automated Exchange
Functional Signal plus Noise (FSN) time series models are introduced for the econometric analysis of the dynamics of a large cross-section of prices in which contemporaneous observations are functionally related. A semiparametric FSN model is developed in which a smooth, cubic spline signal function is used to approximate the price curve data. Estimation may then be performed using quasi-maximum likelihood methods based on the Kalman filter. The model is used to provide one of the first studies of the dynamics of the bid and ask curves of an electronic limit order book and enables the comprehensive measurement of the dynamic determinants of traders' execution costs. It is found that the differences between the bid and ask curves and their intercepts (i.e. the immediate price impacts of market orders) are well described by covariance stationary processes. The in-sample, 1-step ahead point predictions for these curves perform well and motivate the development of parametric FSN models that take into account the monotonicity of the price curves and can be used to form predictive distributions.