On the Non-parametric Prediction of Conditionally Stationary Sequences |
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Authors: | Email author" target="_blank">S?CairesEmail author J?A?Ferreira |
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Institution: | (1) KNMI, Royal Netherlands Meteorological Institute, P.O. Box 201, NL-3730, AE, De Bilt, The Netherlands;(2) CWI, Centrum voor Wiskunde en Informatica, P.O. Box 94079, 1090, GB, Amsterdam, The Netherlands |
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Abstract: | 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.
An erratum to this article is available at . |
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Keywords: | non-parametric prediction conditional distribution function conditional expectation time series data analysis |
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