Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models

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Standard

Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models. / Cavaliere, Giuseppe; Nielsen, Heino Bohn; Pedersen, Rasmus Søndergaard; Rahbek, Anders.

In: Journal of Econometrics, 2021.

Research output: Contribution to journalJournal articleResearchpeer-review

Harvard

Cavaliere, G, Nielsen, HB, Pedersen, RS & Rahbek, A 2021, 'Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models', Journal of Econometrics. https://doi.org/10.1016/j.jeconom.2020.05.006

APA

Cavaliere, G., Nielsen, H. B., Pedersen, R. S., & Rahbek, A. (2021). Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models. Journal of Econometrics. https://doi.org/10.1016/j.jeconom.2020.05.006

Vancouver

Cavaliere G, Nielsen HB, Pedersen RS, Rahbek A. Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models. Journal of Econometrics. 2021. https://doi.org/10.1016/j.jeconom.2020.05.006

Author

Cavaliere, Giuseppe ; Nielsen, Heino Bohn ; Pedersen, Rasmus Søndergaard ; Rahbek, Anders. / Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models. In: Journal of Econometrics. 2021.

Bibtex

@article{166929d60e3f40b791b9991f1d36c0eb,
title = "Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models",
abstract = "It is a well-established fact that – with an unknown number of nuisance parameters at the boundary – testing a null hypothesis on the boundary of the parameter space is infeasible in practice as the limiting distributions of standard test statistics are non-pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of the (possibly multiple) model parameters not restricted by the null hypothesis. We propose to solve this inference problem by a novel bootstrap, which we show to be valid under general conditions, irrespective of the presence of (unknown) nuisance parameters on the boundary. That is, the new bootstrap replicates the unknown limiting distribution of the likelihood ratio statistic under the null hypothesis and is bounded (in probability) under the alternative. The new bootstrap approach, which is very simple to implement, is based on shrinkage of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at an appropriate rate. As an application of our general theory, we treat the problem of inference in finite-order ARCH models with coefficients subject to inequality constraints. Extensive Monte Carlo simulations illustrate that the proposed bootstrap has attractive finite sample properties both under the null and under the alternative hypothesis.",
keywords = "Faculty of Social Sciences, Inference on the boundary, Nuisance parameters, Bootstrap, ARCH models",
author = "Giuseppe Cavaliere and Nielsen, {Heino Bohn} and Pedersen, {Rasmus S{\o}ndergaard} and Anders Rahbek",
year = "2021",
doi = "10.1016/j.jeconom.2020.05.006",
language = "English",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Bootstrap Inference on the Boundary of the Parameter Space with Application to Conditional Volatility Models

AU - Cavaliere, Giuseppe

AU - Nielsen, Heino Bohn

AU - Pedersen, Rasmus Søndergaard

AU - Rahbek, Anders

PY - 2021

Y1 - 2021

N2 - It is a well-established fact that – with an unknown number of nuisance parameters at the boundary – testing a null hypothesis on the boundary of the parameter space is infeasible in practice as the limiting distributions of standard test statistics are non-pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of the (possibly multiple) model parameters not restricted by the null hypothesis. We propose to solve this inference problem by a novel bootstrap, which we show to be valid under general conditions, irrespective of the presence of (unknown) nuisance parameters on the boundary. That is, the new bootstrap replicates the unknown limiting distribution of the likelihood ratio statistic under the null hypothesis and is bounded (in probability) under the alternative. The new bootstrap approach, which is very simple to implement, is based on shrinkage of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at an appropriate rate. As an application of our general theory, we treat the problem of inference in finite-order ARCH models with coefficients subject to inequality constraints. Extensive Monte Carlo simulations illustrate that the proposed bootstrap has attractive finite sample properties both under the null and under the alternative hypothesis.

AB - It is a well-established fact that – with an unknown number of nuisance parameters at the boundary – testing a null hypothesis on the boundary of the parameter space is infeasible in practice as the limiting distributions of standard test statistics are non-pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of the (possibly multiple) model parameters not restricted by the null hypothesis. We propose to solve this inference problem by a novel bootstrap, which we show to be valid under general conditions, irrespective of the presence of (unknown) nuisance parameters on the boundary. That is, the new bootstrap replicates the unknown limiting distribution of the likelihood ratio statistic under the null hypothesis and is bounded (in probability) under the alternative. The new bootstrap approach, which is very simple to implement, is based on shrinkage of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at an appropriate rate. As an application of our general theory, we treat the problem of inference in finite-order ARCH models with coefficients subject to inequality constraints. Extensive Monte Carlo simulations illustrate that the proposed bootstrap has attractive finite sample properties both under the null and under the alternative hypothesis.

KW - Faculty of Social Sciences

KW - Inference on the boundary

KW - Nuisance parameters

KW - Bootstrap

KW - ARCH models

U2 - 10.1016/j.jeconom.2020.05.006

DO - 10.1016/j.jeconom.2020.05.006

M3 - Journal article

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

ER -

ID: 231251513