Abstract
Differential geometrical structures (Riemannian metrics, pairs of dual affine connections, divergences and yokes) related to multi-step forecasting error variance ratios are introduced to a manifold of stochastic linear systems. They are generalized to nonstationary cases. The problem of approximating a given time series by a specific model is discussed. As examples, we use the established scheme to discuss the AR (1) approximations and the exponential smoothing of ARMA series for multi-step forecasting purpose. In the process, some interesting results about spectral density functions are derived and applied.
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Xu, D. Differential geometrical structures related to forecasting error variance ratios. Ann Inst Stat Math 43, 621–646 (1991). https://doi.org/10.1007/BF00121643
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DOI: https://doi.org/10.1007/BF00121643