A constrained neural network Kalman filter for price estimation in high frequency financial data

Area of Science:

• Quantitative Finance
• Machine Learning
• Time Series Analysis

Background:

• Financial time series data are often corrupted by various noise types, including process, measurement, and arrival noise.
• Traditional filtering methods may struggle with the nonlinear dynamics inherent in financial markets.
• Accurate modeling of financial data is crucial for robust trading and risk management.

Purpose of the Study:

• To develop and evaluate a neural network extended Kalman filter (NEKF) for improved modeling of noisy financial time series.
• To investigate the impact of neural network constraints on filter stability and prediction accuracy.
• To address the challenges posed by erratic data arrival (arrival noise) in financial data filtering.

Main Methods:

• Utilizing a neural network to estimate the nonlinear dynamics within an extended Kalman filter framework.
• Deriving conditions for the neural network weight matrix to ensure filter stability.
• Implementing a fixed-point constraint at the origin for the neural network to improve iterated predictions and stability.
• Testing the performance of constrained versus unconstrained NEKF on real-world $/DM exchange rate tick data.

Main Results:

• The proposed neural network extended Kalman filter effectively models noisy financial time series.
• Constraining the neural network with a fixed point at the origin significantly enhances prediction stability and accuracy, particularly for arrival noise.
• The filter demonstrated robust performance on high-frequency exchange rate data.

Conclusions:

• The neural network extended Kalman filter offers a powerful approach for filtering complex financial time series.
• Neural network constraints are vital for achieving stable and reliable filtering in the presence of financial data noise.
• This methodology provides a valuable tool for quantitative finance and algorithmic trading applications.