| Issue |
ESAIM: PS
Volume 21, 2017
|
|
|---|---|---|
| Page(s) | 394 - 411 | |
| DOI | https://doi.org/10.1051/ps/2017017 | |
| Published online | 08 January 2018 | |
Bootstrapping periodically autoregressive models∗
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.
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2 AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland.
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Received: 28 October 2016
Revised: 10 August 2017
Accepted: 21 August 2017
Abstract
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.
Mathematics Subject Classification: 62M10 / 62F12 / 62F40
Key words: Bootstrap / least squares estimation / periodically autoregressive models / time series
This work was supported by a public grant as part of the Investissement d’avenir, project reference ANR-11-LABX-0056-LMH.
© EDP Sciences, SMAI, 2017
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