Estimating functional dependences based on time series with the use of classes of regression functions of infinite capacity
- 29 Downloads
The problem of estimating the functional dependence of time series on the time index is considered in the case of short data samples. It is proved that empirical risk functional uniformly converges to the theoretical one in the case where regression functions can be approximated by finite-degree polynomials. An example of estimating the functional dependence for a class of trigonometric functions is presented.
Keywordstime series estimation of functional dependences uniform convergence polynomial approximation
Unable to display preview. Download preview PDF.
- 2.M. Anthony and J. Shawe-Taylor, “A result of Vapnik with applications,” Discrete Applied Mathematics, No. 47(3), 207–217 (1993).Google Scholar
- 4.M. Anthony, Discrete Mathematics of Neural Networks: Selected Topics, SIAM (2001).Google Scholar
- 6.V. K. Dzyadyk, An Introduction to the Theory of Uniform Approximation of Functions by Polynomials [in Russian], Nauka, Moscow (1977).Google Scholar
- 7.S. A. Telyakovskii, “The rate of approximation of functions by the Bernstein polynomials,” Tr. IMM, 14, No. 3, 162–169 (2008).Google Scholar
- 8.O. G. Zrazhevskii, “Methods to develop models for the long-term prediction of financial time series,” Sist. Doslidzh. Inform. Tekhnol., No. 1, 123–142 (2010).Google Scholar