4.7 Article

A differential geometric approach to time series forecasting

Journal

APPLIED MATHEMATICS AND COMPUTATION
Volume 402, Issue -, Pages -

Publisher

ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2021.126150

Keywords

Time series; Forecast; Manifolds; Geodesic

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This approach proposes a differential geometry-based method for time series forecasting by treating time series data as paths on a manifold, and computing the manifold connection to forecast the variables.
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.

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