Functional Time Series Analysis and Its Application to Limit Order Books

Abstract

In this study, we use a vector functional auto-regressive model to analyze the supply and demand (S-D) curves of a Limit Order Book (LOB) simultaneously. The S-D curves are represented by a linear combination of multi-resolution B-spline basis functions. The corresponding coefficients of the basis functions are shown to follow a vector auto-regressive model, which can be applied to the prediction of future S-D curves. Numerical results indicate that the proposed method has satisfactory performance and the areas under the S-D curves are capable of improving the classification of market trends.