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Abstract:
The problem of time series prediction is studied within the
uniform convergence framework of Vapnik and Chervonenkis. The
dependence inherent in the temporal structure is incorporated into
the analysis, thereby generalizing the available theory for
memory-less processes. Finite sample bounds are calculated in terms
of covering numbers of the approximating class, and the trade-off
between approximation and estimation is discussed. Vapnik's
structural risk minimization procedure is applied to achieve
consistency, and convergence rates are established within a
nonparametric setting.
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