A Constrained Neural Network Kalman Filter for Price Estimation in High Frequency Financial Data

In this paper we present a neural network extended Kalman filter for modeling noisy financial time series. The neural network is employed to estimate the nonlinear dynamics of the extended Kalman filter. Conditions for the neural network weight matrix are provided to guarantee the stability of the filter. The extended Kalman filter presented is designed to filter three types of noise commonly observed in financial data: process noise, measurement noise, and arrival noise. The erratic arrival of data (arrival noise) results in the neural network predictions being iterated into the future. Constraining the neural network to have a fixed point at the origin produces better iterated predictions and more stable results. The performance of constrained and unconstrained neural networks within the extended Kalman filter is demonstrated on "Quote" tick data from the $/DM exchange rate (1993-1995).