Sparse Manifolds Graphical Modelling with Missing Values: An Application to the Commodity Futures Market

This paper is devoted to practical use of the Manifold Selection method presented in Desboulets (2020). In a first part, I present an application on financial data. The data I use are continuous futures contracts underlying commodities. These are multivariate time series, for the period 1985-2020. Representing correlations in financial data as graphs is a common task, useful in Finance for risk assessment. However, these graphs are often too complex, and involve many small connections. Therefore, the graphs can be simplified using variable selection, to remove these small correlations. Here, I use Manifold Selection to build sparse graphical models. Non-linear manifolds can represent interconnected markets where the major drivers of prices are unobserved. The results indicate the market is more strongly interconnected when using non-linear manifold selection than when using linear graphical models. I also propose a new method for filling missing values in time series data. I run a simulation and show that the method performs well in case of several consecutive missing values.