A differential geometric approach to time series forecasting

A differential geometry based approach to time series forecasting is proposed. Given observations over time of a set of correlated variables, it is assumed that these variables are components of vectors tangent to a real differentiable manifold. Each vector belongs to the tangent space at a point on the manifold, and the collection of all vectors forms a path on the manifold, parametrized by time. We compute a manifold connection such that this path is a geodesic. The future of the path can then be computed by solving the geodesic equations subject to appropriate boundary conditions. This yields a forecast of the time series variables. (C) 2021 Elsevier Inc. All rights reserved.