Efficient prediction for linear and nonlinear autoregressive models

Details Efficient prediction for linear and nonlinear autoregressive models Efficient prediction for linear and nonlinear autoregressive models

2007-02-23

arxiv.org/abs/math/0702701v1

Annals of Statistics 2006, Vol. 34, No. 5, 2496-2533

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000812 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000812

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a uniform stochastic expansion for smoothed and weighted von Mises processes of residuals. We consider, in particular, estimation of conditional distribution functions and of conditional quantile functions.

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