Random Projection Methods in Economics and Finance

Dimension reduction techniques have been proposed to cope with some modelling and forecasting issues with large and complex datasets such as overfitting, over-parametrization and inefficiency. Among all dimension reduction techniques, the most widespread are principal component analysis and factor analysis. Recently, Random Projection (RP) techniques became popular in many fields due to their simplicity and effectiveness and found applications to machine learning, statistics and econometrics. The basis of the RP technique relies on the remarkable result in the Johnson-Lindenstrauss lemma, which provides some conditions to achieve an effective reduction of the size of the data, without altering their information content. This chapter reviews the most used dimensionality reduction techniques, introduces random projection methods and shows their effectiveness in time series analysis through a simulation study and some original applications to tracking and forecasting financial indexes and to predicting electricity trading volumes. Our empirical results suggest that random projection preprocessing of the data does not jeopardize the validity of inference and prediction procedures and possibly improves their efficiency.