Bivariate Functional Archetypoid Analysis: An Application to Financial Time Series

Archetype Analysis (AA) is a statistical technique that describes individuals of a sample as a convex combination of certain number of elements called archetypes, which in turn, are convex combinations of the individuals in the sample. For it’s part, Archetypoid Analysis (ADA) tries to represent each individual as a convex combination of a certain number of extreme subjects called archetypoids. It is possible to extend these techniques to functional data. This work presents an application of Functional Archetypoids Analysis (FADA) to financial time series. At the best of our knowledge, this is the first time FADA is applied in this field. The starting time series consists of daily equity prices of the S&P 500 stocks. From it, measures of volatility and profitability are generated in order to characterize listed companies. These variables are converted into functional data through a Fourier basis expansion function and bivariate FADA is applied. By representing subjects through extreme cases, this analysis facilitates the understanding of both the composition and the relationships between listed companies. Finally, a cluster methodology based on a similarity parameter is presented. Therefore, the suitability of this technique for this kind of time series is shown, as well as the robustness of the conclusions drawn.