Abstract
The problem of estimating the functional dependence of time series on the time index is considered in the case of short data sample. The uniform convergence of an empirical risk functional to a theoretical one is proved for the case where the parametric class of regression functions can be partially covered by a finite ε-net for some of its parameters. The functional dependence for the polynomial class of functions is estimated as an example.
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Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 77–87, March–April 2011.
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Pankratova, N.D., Zrazhevsky, O.G. Estimation of the functional dependence of time series for the class of regression functions partially covered by a finite ε-net. Cybern Syst Anal 47, 241–249 (2011). https://doi.org/10.1007/s10559-011-9306-6
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DOI: https://doi.org/10.1007/s10559-011-9306-6