Random forests for time-dependent processes
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 801-826.

Random forests were introduced by Breiman in 2001. We study theoretical aspects of both original Breiman’s random forests and a simplified version, the centred random forests. Under the independent and identically distributed hypothesis, Scornet, Biau and Vert proved the consistency of Breiman’s random forest, while Biau studied the simplified version and obtained a rate of convergence in the sparse case. However, the i.i.d hypothesis is generally not satisfied for example when dealing with time series. We extend the previous results to the case where observations are weakly dependent, more precisely when the sequences are stationary β−mixing.

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DOI : 10.1051/ps/2020015
Classification : 62M10
Mots-clés : Statistics, random forests, time-dependent processes 
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Goehry, Benjamin. Random forests for time-dependent processes. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 801-826. doi : 10.1051/ps/2020015. http://archive.numdam.org/articles/10.1051/ps/2020015/

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