Statistical Inference for Stochastic Processes

, Volume 8, Issue 2, pp 151–184 | Cite as

On the Non-parametric Prediction of Conditionally Stationary Sequences



We prove the strong consistency of estimators of the conditional distribution function and conditional expectation of a future observation of a discrete time stochastic process given a fixed number of past observations. The results apply to conditionally stationary processes (a class of processes including Markov and stationary processes) satisfying a strong mixing condition, and they extend and bring together the work of several authors in the area of non-parametric estimation. One of our goals is to provide further justification for the growing practical application of non-parametric estimators in non-stationary time series and in other `non-i.i.d.' settings. Some arguments as to why such estimators should work very generally in practice, often in a nearly `optimal' way, are given. Two numerical illustrations are included, one with simulated data and the other with oceanographic data.


non-parametric prediction conditional distribution function conditional expectation time series data analysis 


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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.KNMIRoyal Netherlands Meteorological InstituteDe BiltThe Netherlands
  2. 2.CWICentrum voor Wiskunde en InformaticaAmsterdamThe Netherlands

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