Dynamic Ordering Learning in Multivariate Forecasting

TL;DR

This paper introduces a flexible, fast method for dynamic ordering learning in multivariate forecasting, improving covariance estimation and decision-making in finance and macroeconomics by adaptively capturing relationships among variables.

Contribution

It proposes a novel approach using Dynamic Order Probabilities to address ordering uncertainty in covariance matrix estimation dynamically.

Findings

Enhanced portfolio allocation decisions through learned relationships among currencies.

Improved macroeconomic modeling by adapting to changing variable relationships.

Demonstrated computational efficiency and flexibility of the proposed method.

Abstract

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 Order 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.