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.