Geodesic
Bootstrapping periodically autoregressive models
Ciołek, Gabriela1 ; Potorski, Paweł2
1 AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland; LTCI, Télécom ParisTech, Université Paris-Saclay, 46 Rue Barrault, 75013 Paris, France.
2 AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland.
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 394-411

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The main objective of this paper is to establish the residual and the wild bootstrap procedures for periodically autoregressive models. We use the least squares estimators of model’s parameters and generate their bootstrap equivalents. We prove that the bootstrap procedures for causal periodic autoregressive time series with finite fourth moments are weakly consistent. Finally, we confirm our theoretical considerations by simulations.

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DOI : 10.1051/ps/2017017
Classification : 62M10, 62F12, 62F40
Keywords: Bootstrap, least squares estimation, periodically autoregressive models, time series

Ciołek, Gabriela 1 ; Potorski, Paweł 2

1 AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland; LTCI, Télécom ParisTech, Université Paris-Saclay, 46 Rue Barrault, 75013 Paris, France.
2 AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland. 
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     author = {Cio{\l}ek, Gabriela and Potorski, Pawe{\l}},
     title = {Bootstrapping periodically autoregressive models},
     journal = {ESAIM: Probability and Statistics},
     pages = {394--411},
     publisher = {EDP-Sciences},
     volume = {21},
     year = {2017},
     doi = {10.1051/ps/2017017},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2017017/}
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%J ESAIM: Probability and Statistics
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%V 21
%I EDP-Sciences
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Ciołek, Gabriela; Potorski, Paweł. Bootstrapping periodically autoregressive models. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 394-411. doi: 10.1051/ps/2017017

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