Dynamic Ordering Learning in Multivariate Forecasting

In many fields where the main goal is to produce sequential forecasts for decision-making problems, the good understanding of the contemporaneous relations among different series is crucial for the estimation of the covariance matrix. In recent years, the modified Cholesky decomposition appeared as a popular approach to covariance matrix estimation. However, its main drawback relies on the imposition of the series ordering structure. In this work, we propose a highly flexible and fast method to deal with the problem of ordering uncertainty in a dynamic fashion with the use of Dynamic ordering Probabilities. We apply the proposed method in two different forecasting contexts. The first is a dynamic portfolio allocation problem, where the investor is able to learn the contemporaneous relationships among different currencies improving final decisions and economic performance. The second is a macroeconomic application, where the econometrician can adapt sequentially to new economic environments, switching the contemporaneous relations among macroeconomic variables over time.