Kernel Adaptive Filtering Approaches for Financial Time-Series Prediction

  • Sergio Garcia-Vega

Student thesis: Phd


Financial time-series are continuously generated by multiple sources, such as banks and corporations. These time-series are ordered sequences of data records that become available over time, imposing an order that must be considered when training models and making predictions. In addition, financial data represent, and are part of, highly complex systems that depend on and are generated by various factors such as financial policies and national economic growths. Thus, unlike traditional regression, predicting financial time-series requires consideration of both their sequential and interdependent nature. This thesis aims to address three related weaknesses of data-centralized and off-line machine learning methods: 1) Sequence Learning. Traditional approaches, developed to optimize per- formance on static data sets, restrict their flexibility to solve sequence pre- diction tasks in real-world applications. This means that, as traditional approaches are trained off-line, the profitable conditions of the trained models may disappear when they are tested in on-line environments; 2) Higher Order Statistics. The goal of dynamic modelling is to identify the dynamical system that produced a given input-output mapping. The mean square error (MSE), which is a second-order statistical measure, have been traditionally used as cost function when training adaptive systems. However, financial markets are complex and chaotic systems, meaning that second-order measures may be poor descriptors of optimality; 3) Distributed Learning. The movement of stock markets may affect the behaviour of stocks in other regions or countries. Traditional approaches do not directly consider inter-dependencies of the financial system, discarding interconnections and correlations that may represent important internal forces of the market. To address these issues, this work proposes a variety of kernel adaptive filtering approaches, which are data-driven methods for sequence learning that combine the convex optimization of linear adaptive filters and the universal approximation property of neural networks (NNs). The proposed approaches consider interconnections between stock markets, which reduces volatility and maximises returns while the robustness and simplicity of kernel adaptive filters are maintained. In particular, this thesis proposes: (1) a kernel adaptive filtering approach to support sequence prediction tasks in financial time-series; (2) an entropy-based cost function for kernel adaptive filtering to capture higher-order statistics of financial time-series; (3) a kernel adaptive filtering approach that captures internal forces of the market to improve profitability in real-time applications. The results show relatively low MSE values and higher Sharpe ratio when compared with recurrent NNs and autoregressive-based models. The proposed approaches, unlike NNs, do not need the whole training set to start learning the model, meaning that predictions are generated while the model is sequentially updated at the same time. In addition, when compared with kernel adaptive filtering methods, there is an improvement between 0.5% and 54% in terms of MSE, showing high tolerance to noisy and non-stationary conditions. The results of this thesis are in line with previous studies, suggesting that the United States market is more influenced by the European and not vice versa.
Date of Award31 Dec 2021
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorJohn Keane (Supervisor) & Xiaojun Zeng (Supervisor)


  • Financial time-series
  • Kernel adaptive filtering
  • Interdependence between markets
  • Sequential learning
  • Kernel least-mean-square
  • Sequence prediction
  • Learning from data streams
  • Stock returns prediction

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