Design-Adaptive Pointwise Nonparametric Regression Estimation for Recurrent Markov Time Series

Emmanuel Guerre
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Emmanuel Guerre: Crest

No 2004-22, Working Papers from Center for Research in Economics and Statistics

Abstract: A general framework is proposed for (auto)regression nonparametric estimationof recurrent time series in a class of Hilbert Markov processes with a Lipschitzconditional mean. This includes various nonstationarities by relaxing usual dependenceassumptions as mixing or ergodicity, which are replaced with recurrence. The cornerstoneof design-adaptation is a data-driven bandwidth choice based on an empirical biasvariance tradeoff, giving rise to a random consistency rate for a uniform kernel estimator.The estimator converges with this random rate, which is the optimal minimaxrandom rate over the considered class of recurrent time series. Extensions to general kernelestimators are investigated. For weak dependent time-series, the order of the randomrate coincides with the deterministic minimax rate previously derived. New deterministicestimation rates are obtained for modified Box-Cox transformations of Random Walks.

Date: 2004
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Working Paper: DESIGN-ADAPTIVE POINTWISE NONPARAMETRIC REGRESSION ESTIMATION FOR RECURRENT MARKOV TIME SERIES (2004)
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