Isolating Stock Prices Variation with Neural Networks

In this study we aim to define a mapping function that relates the general index value among a set of shares to the prices of individual shares. In more general terms this is problem of defining the relationship between multivariate data distributions and a specific source of variation within these distributions where the source of variation in question represents a quantity of interest related to a particular problem domain. In this respect we aim to learn a complex mapping function that can be used for mapping different values of the quantity of interest to typical novel samples of the distribution. In our investigation we compare the performance of standard neural network based methods like Multilayer Perceptrons (MLPs) and Radial Basis Functions (RBFs) as well as Mixture Density Networks (MDNs) and a latent variable method, the General Topographic Mapping (GTM). As a reference benchmark of the prediction accuracy we consider a simple method based on the average values over certain intervals of the quantity of interest that we are trying to isolate (the so called Sample Average (SA) method). According to the results, MLPs and RBFs outperform MDNs and the GTM for this one-to-many