Strongly Consistent Nonparametric Forecasting and Regression for Stationary Ergodic Sequences

Sidney Yakowitz, László Györfi, John Kieffer and Gusztáv Morvai

Journal of Multivariate Analysis, 1999, vol. 71, issue 1, 24-41

Abstract: Let {(Xi, Yi)} be a stationary ergodic time series with (X, Y) values in the product space Rd[circle times operator]R. This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance) algorithm for inferring m(x)=E[Y0  X0=x] under the presumption that m(x) is uniformly Lipschitz continuous. Auto-regression, or forecasting, is an important special case, and as such our work extends the literature of nonparametric, nonlinear forecasting by circumventing customary mixing assumptions. The work is motivated by a time series model in stochastic finance and by perspectives of its contribution to the issues of universal time series estimation.

Keywords: time-series; regression; nonparametric; estimation; forecasting; universal; prediction (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (4)

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