Adaptive Regression Methods with Application to Streaming Financial Data

Abstract

This thesis is concerned with the analysis of adaptive incremental regression algorithms for data streams. The development of these algorithms is motivated by issues pertaining to financial data streams, data which are very noisy, non-stationary and exhibit high degrees of dependence. These incremental regression techniques are subsequently used to develop efficient and adaptive algorithms for portfolio allocation. We develop a number of temporally incremental regression algorithms that have the following attributes; efficiency: the algorithms are iterative, robustness: the algorithms have a built-in safeguard for outliers and/or use regularisation techniques to alleviate for estimation error, and adaptiveness: the algorithms estimation is adaptive to the underlying streaming data. These algorithms make use of known regression techniques: EWRLS (Exponentially Weighted Recursive Least Squares), TSVD (Truncated Singular Value Decomposition) and FLS (Flexible Least Squares). We focus more of our attention on a proposed robust version of EWRLS algorithm, denoted R-EWRLS, and assess its robustness using a purpose built simulation engine. This simulation engine is able to generate correlated data streams whose drift and correlation change over time and can be subjected to randomly generated outliers whose magnitudes and directions vary. The R-EWRLS algorithm is developed further to allow for a self-tuned forgetting factor in the formulation. The forgetting factor is an important tool to account for non-stationarity in the data through an exponential decay profile which assigns more weight to the more recent data. The new algorithm is assessed against the R-EWRLS algorithm using various performance measures. A number of applications with real data from equities and foreign exchange are used. Various measures are computed to compare our algorithms to established portfolio allocation techniques. The results are promising and in many cases outperform benchmark allocation techniques.