A differential geometric approach to time series forecasting

•The methodology section in the paper is now divided into two sections namely, Mathematical Framework (Section 2) and (Computation Steps (Section 3) to improve the narrative.•Section 2.1 has been added to introduce some of the key concepts and definitions that are central to this work. While most of these definitions are standard, presenting them will help with establishing the notation used in the paper.•Section 2.3 has been added to discuss the existence and uniqueness of a solution to the geodesic equations.•Section 3.5 has been added to discuss the existence and uniqueness of a solution to the adjoint equations.•A typo is fixed. 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.