ISSN:
1572-9052
Keywords:
Riemannian metric
;
affine connection
;
divergence
;
spectral density
;
forecasting error variance ratio
;
yoke
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00121643
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