scholarly journals Efficient bootstrap with weakly dependent processes

2012 ◽  
Vol 56 (11) ◽  
pp. 3444-3458
Author(s):  
Francesco Bravo ◽  
Federico Crudu
Keyword(s):  
Dependent Processes ◽  
Weakly Dependent

Frequency polygons for weakly dependent processes

1997 ◽  
Vol 33 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Michel Carbon ◽  
Bernard Garel ◽  
Lanh Tat Tran
Keyword(s):  
Dependent Processes ◽  
Frequency Polygons ◽  
Weakly Dependent

scholarly journals Random forests for time-dependent processes

2020 ◽  
Vol 24 ◽  
pp. 801-826
Author(s):  
Benjamin Goehry
Keyword(s):  
Time Series ◽  
Random Forest ◽  
Rate Of Convergence ◽  
Random Forests ◽  
Time Dependent ◽  
Dependent Processes ◽  
Weakly Dependent ◽  
Independent And Identically Distributed

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.

PREDICTION AND SIGNAL EXTRACTION OF STRONGLY DEPENDENT PROCESSES IN THE FREQUENCY DOMAIN

2002 ◽  
Vol 18 (3) ◽  
pp. 584-624 ◽  
Author(s):  
J. Hidalgo ◽  
Y. Yajima
Keyword(s):  
Spectral Density Function ◽  
Signal Extraction ◽  
Dependent Data ◽  
Canonical Factorization ◽  
Linear Least Squares ◽  
Preceding Work ◽  
Finite Set ◽  
Weakly Dependent Data ◽  
Dependent Processes ◽  
Weakly Dependent

We frequently observe that one of the aims of time series analysts is to predict future values of the data. For weakly dependent data, when the model is known up to a finite set of parameters, its statistical properties are well documented and exhaustively examined. However, if the model was misspecified, the predictors would no longer be correct. Motivated by this observation and because of the interest in obtaining adequate and reliable predictors, Bhansali (1974, Journal of the Royal Statistical Society, Series B 36, 61–73) examined the properties of a nonparametric predictor based on the canonical factorization of the spectral density function given in Whittle (1963, Prediction and Regulation by Linear Least Squares) and known as FLES.However, the preceding work does not cover the so-called strongly dependent data. Because of the interest in this type of processes, one of our objectives in this paper is to examine the properties of the FLES for these processes. In addition, we illustrate how the FLES can be adapted to recover the signal of a strongly dependent process, showing its consistency. The proposed method is semiparametric in the sense that, in contrast to other methods, we do not need to assume any particular model for the noise except that it is weakly dependent.

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