Estimating the Number of Latent Factors in High-Dimensional Financial Time Series

Various methods for modelling financial risk rely on factor models which assume that a smaller number of latent factors are responsible for a significant portion of the observed price dynamics. A critical step for accurate estimation of these factors is obtaining the true number of factors, which is additionally problematic in high-dimensional settings and in presence of heavy tailed data - both of which are common circumstances in financial time series. In this paper we propose a method for estimating the number of latent factors that tackles these issues. To find the number of factors, the method relies on properties of optimal portfolios estimated from the covariance matrices, given by the estimated factor structures. We also introduce a simulation environment for evaluating the selection of the number of factors on high-dimensional data with heavy tailed distributions, and test the performance of the proposed method against some well known estimators such as the Marčenko-Pastur law and parallel analysis. The results suggest that our method works very well and delivers more accurate and remarkably stable results.