Abstract:
Dimensionality reduction techniques have been implemented to cope with problems related to the continuous stream of data due to the development of new technologies in all fields of science. In economics and finance, the increased availability of massive datasets opens new challenges in data modelling and forecasting. Among all the proposed DR techniques, the most widespread is Principal Component Analysis (PCA). Also, Random Projection (RP) techniques are widely used in many fields due to their simplicity and effectiveness. The basis of the RP technique relies on the remarkable result in the Johnson-Lindenstrauss Lemma. RP provides a really powerful tool to reduce the dimensionality of a dataset, not changing its information content and have been successfully applied in statistics and machine learning.
The main aim of this thesis is to introduce random projection method and show its effectiveness in financial time series analysis. Particularly, index tracking and forecasting problems are proposed. After a review of the most used dimensionality reduction techniques, RP method is presented and its mathematical foundations are explored. With the aim to apply RP to financial data, two new characterizations of the projection matrix are proposed. In the last part, some applications are presented. Results suggest that random projection preprocessing of the data does not jeopardize and sometimes even improves the tracking error and predictive performances.
