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A differential geometric approach to time series forecasting

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  • Emami, Babak

Abstract

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.

Suggested Citation

  • Emami, Babak, 2021. "A differential geometric approach to time series forecasting," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300321001983
    DOI: 10.1016/j.amc.2021.126150
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