Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling

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Standard

Bootstrapping Noncausal Autoregressions : With Applications to Explosive Bubble Modeling. / Cavaliere, Giuseppe; Nielsen, Heino Bohn; Rahbek, Anders.

I: Journal of Business and Economic Statistics, 18.06.2018.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

Cavaliere, G, Nielsen, HB & Rahbek, A 2018, 'Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling', Journal of Business and Economic Statistics. https://doi.org/10.1080/07350015.2018.1448830

APA

Cavaliere, G., Nielsen, H. B., & Rahbek, A. (2018). Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling. Journal of Business and Economic Statistics. https://doi.org/10.1080/07350015.2018.1448830

Vancouver

Cavaliere G, Nielsen HB, Rahbek A. Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling. Journal of Business and Economic Statistics. 2018 jun 18. https://doi.org/10.1080/07350015.2018.1448830

Author

Cavaliere, Giuseppe ; Nielsen, Heino Bohn ; Rahbek, Anders. / Bootstrapping Noncausal Autoregressions : With Applications to Explosive Bubble Modeling. I: Journal of Business and Economic Statistics. 2018.

Bibtex

@article{4ca27da3581a4ba48858e4a0b94997aa,
title = "Bootstrapping Noncausal Autoregressions: With Applications to Explosive Bubble Modeling",
abstract = "In this article, we develop new bootstrap-based inference for noncausal autoregressions with heavy-tailed innovations. This class of models is widely used for modeling bubbles and explosive dynamics in economic and financial time series. In the noncausal, heavy-tail framework, a major drawback of asymptotic inference is that it is not feasible in practice as the relevant limiting distributions depend crucially on the (unknown) decay rate of the tails of the distribution of the innovations. In addition, even in the unrealistic case where the tail behavior is known, asymptotic inference may suffer from small-sample issues. To overcome these difficulties, we propose bootstrap inference procedures using parameter estimates obtained with the null hypothesis imposed (the so-called restricted bootstrap). We discuss three different choices of bootstrap innovations: wild bootstrap, based on Rademacher errors; permutation bootstrap; a combination of the two (“permutation wild bootstrap”). Crucially, implementation of these bootstraps do not require any a priori knowledge about the distribution of the innovations, such as the tail index or the convergence rates of the estimators. We establish sufficient conditions ensuring that, under the null hypothesis, the bootstrap statistics estimate consistently particular conditionaldistributions of the original statistics. In particular, we show that validity of the permutation bootstrap holds without any restrictions on the distribution of the innovations, while the permutation wild and the standard wild bootstraps require further assumptions such as symmetry of the innovation distribution. Extensive Monte Carlo simulations show that the finite sample performance of the proposed bootstrap tests is exceptionally good, both in terms of size and of empirical rejection probabilities under the alternative hypothesis. We conclude by applying the proposed bootstrap inference to Bitcoin/USD exchange rates and to crude oil price data. We find that indeed noncausal models with heavy-tailed innovations are able to fit the data, also in periods of bubble dynamics. Supplementary materials for this article are available online.",
keywords = "Faculty of Social Sciences, Bootstrap, Bubble dynamics, Heavy tails, Noncausal autoregressions",
author = "Giuseppe Cavaliere and Nielsen, {Heino Bohn} and Anders Rahbek",
year = "2018",
month = "6",
day = "18",
doi = "10.1080/07350015.2018.1448830",
language = "English",
journal = "Journal of Business and Economic Statistics",
issn = "0735-0015",
publisher = "Taylor & Francis",

}

RIS

TY - JOUR

T1 - Bootstrapping Noncausal Autoregressions

T2 - With Applications to Explosive Bubble Modeling

AU - Cavaliere, Giuseppe

AU - Nielsen, Heino Bohn

AU - Rahbek, Anders

PY - 2018/6/18

Y1 - 2018/6/18

N2 - In this article, we develop new bootstrap-based inference for noncausal autoregressions with heavy-tailed innovations. This class of models is widely used for modeling bubbles and explosive dynamics in economic and financial time series. In the noncausal, heavy-tail framework, a major drawback of asymptotic inference is that it is not feasible in practice as the relevant limiting distributions depend crucially on the (unknown) decay rate of the tails of the distribution of the innovations. In addition, even in the unrealistic case where the tail behavior is known, asymptotic inference may suffer from small-sample issues. To overcome these difficulties, we propose bootstrap inference procedures using parameter estimates obtained with the null hypothesis imposed (the so-called restricted bootstrap). We discuss three different choices of bootstrap innovations: wild bootstrap, based on Rademacher errors; permutation bootstrap; a combination of the two (“permutation wild bootstrap”). Crucially, implementation of these bootstraps do not require any a priori knowledge about the distribution of the innovations, such as the tail index or the convergence rates of the estimators. We establish sufficient conditions ensuring that, under the null hypothesis, the bootstrap statistics estimate consistently particular conditionaldistributions of the original statistics. In particular, we show that validity of the permutation bootstrap holds without any restrictions on the distribution of the innovations, while the permutation wild and the standard wild bootstraps require further assumptions such as symmetry of the innovation distribution. Extensive Monte Carlo simulations show that the finite sample performance of the proposed bootstrap tests is exceptionally good, both in terms of size and of empirical rejection probabilities under the alternative hypothesis. We conclude by applying the proposed bootstrap inference to Bitcoin/USD exchange rates and to crude oil price data. We find that indeed noncausal models with heavy-tailed innovations are able to fit the data, also in periods of bubble dynamics. Supplementary materials for this article are available online.

AB - In this article, we develop new bootstrap-based inference for noncausal autoregressions with heavy-tailed innovations. This class of models is widely used for modeling bubbles and explosive dynamics in economic and financial time series. In the noncausal, heavy-tail framework, a major drawback of asymptotic inference is that it is not feasible in practice as the relevant limiting distributions depend crucially on the (unknown) decay rate of the tails of the distribution of the innovations. In addition, even in the unrealistic case where the tail behavior is known, asymptotic inference may suffer from small-sample issues. To overcome these difficulties, we propose bootstrap inference procedures using parameter estimates obtained with the null hypothesis imposed (the so-called restricted bootstrap). We discuss three different choices of bootstrap innovations: wild bootstrap, based on Rademacher errors; permutation bootstrap; a combination of the two (“permutation wild bootstrap”). Crucially, implementation of these bootstraps do not require any a priori knowledge about the distribution of the innovations, such as the tail index or the convergence rates of the estimators. We establish sufficient conditions ensuring that, under the null hypothesis, the bootstrap statistics estimate consistently particular conditionaldistributions of the original statistics. In particular, we show that validity of the permutation bootstrap holds without any restrictions on the distribution of the innovations, while the permutation wild and the standard wild bootstraps require further assumptions such as symmetry of the innovation distribution. Extensive Monte Carlo simulations show that the finite sample performance of the proposed bootstrap tests is exceptionally good, both in terms of size and of empirical rejection probabilities under the alternative hypothesis. We conclude by applying the proposed bootstrap inference to Bitcoin/USD exchange rates and to crude oil price data. We find that indeed noncausal models with heavy-tailed innovations are able to fit the data, also in periods of bubble dynamics. Supplementary materials for this article are available online.

KW - Faculty of Social Sciences

KW - Bootstrap

KW - Bubble dynamics

KW - Heavy tails

KW - Noncausal autoregressions

U2 - 10.1080/07350015.2018.1448830

DO - 10.1080/07350015.2018.1448830

M3 - Journal article

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

SN - 0735-0015

ER -

ID: 199638902