Bootstrapping non-stationary stochastic volatility

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Bootstrapping non-stationary stochastic volatility. / Cavaliere, Giuseppe; Boswijk, Hans Peter; Georgiev, Iliyan; Rahbek, Anders.

I: Journal of Econometrics, 2021.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

Cavaliere, G, Boswijk, HP, Georgiev, I & Rahbek, A 2021, 'Bootstrapping non-stationary stochastic volatility', Journal of Econometrics.

APA

Cavaliere, G., Boswijk, H. P., Georgiev, I., & Rahbek, A. (Accepteret/In press). Bootstrapping non-stationary stochastic volatility. Journal of Econometrics.

Vancouver

Cavaliere G, Boswijk HP, Georgiev I, Rahbek A. Bootstrapping non-stationary stochastic volatility. Journal of Econometrics. 2021.

Author

Cavaliere, Giuseppe ; Boswijk, Hans Peter ; Georgiev, Iliyan ; Rahbek, Anders. / Bootstrapping non-stationary stochastic volatility. I: Journal of Econometrics. 2021.

Bibtex

@article{58f4ae27e3f946fbbd2d9ea5171e1d2d,
title = "Bootstrapping non-stationary stochastic volatility",
abstract = "In this paper we investigate to what extent the bootstrap can be applied to con-ditional mean models, such as regression or time series models, when the volatilityof the innovations is random and possibly non-stationary. In fact, the volatility ofmany economic and financial time series displays persistent changes and possiblenon-stationarity. However, the theory of the bootstrap for such models has focusedon deterministic changes of the unconditional variance and little is known aboutthe performance and the validity of the bootstrap when the volatility is drivenby a non-stationary stochastic process. This includes near-integrated exogenousvolatility processes as well as near-integrated GARCH processes, where the condi-tional variance has a diffusion limit; a further important example is the case wherevolatility exhibits infrequent jumps. This paper fills this gap in the literature by de-veloping conditions for bootstrap validity in time series and regression models withnon-stationary, stochastic volatility. We show that in such cases the distribution ofbootstrap statistics (conditional on the data) is random in the limit. Consequently,the conventional approaches to proofs of bootstrap consistency, based on the no-tion of weak convergence in probability of the bootstrap statistic, fail to deliverthe required validity results. Instead, we use the concept of {\textquoteleft}weak convergence indistribution{\textquoteright} to develop and establish novel conditions for validity of the wild boot-strap, conditional on the volatility process. We apply our results to several testingproblems in the presence of non-stationary stochastic volatility, including testingsufficient conditions for bootstrap validity that include the absence of statisticalleverage effects, i.e., correlation between the error process and its future conditionalvariance. The results of the paper are illustrated using Monte Carlo simulations,which indicate that a wild bootstrap approach leads to size control even in smallsamples.",
author = "Giuseppe Cavaliere and Boswijk, {Hans Peter} and Iliyan Georgiev and Anders Rahbek",
year = "2021",
language = "English",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Bootstrapping non-stationary stochastic volatility

AU - Cavaliere, Giuseppe

AU - Boswijk, Hans Peter

AU - Georgiev, Iliyan

AU - Rahbek, Anders

PY - 2021

Y1 - 2021

N2 - In this paper we investigate to what extent the bootstrap can be applied to con-ditional mean models, such as regression or time series models, when the volatilityof the innovations is random and possibly non-stationary. In fact, the volatility ofmany economic and financial time series displays persistent changes and possiblenon-stationarity. However, the theory of the bootstrap for such models has focusedon deterministic changes of the unconditional variance and little is known aboutthe performance and the validity of the bootstrap when the volatility is drivenby a non-stationary stochastic process. This includes near-integrated exogenousvolatility processes as well as near-integrated GARCH processes, where the condi-tional variance has a diffusion limit; a further important example is the case wherevolatility exhibits infrequent jumps. This paper fills this gap in the literature by de-veloping conditions for bootstrap validity in time series and regression models withnon-stationary, stochastic volatility. We show that in such cases the distribution ofbootstrap statistics (conditional on the data) is random in the limit. Consequently,the conventional approaches to proofs of bootstrap consistency, based on the no-tion of weak convergence in probability of the bootstrap statistic, fail to deliverthe required validity results. Instead, we use the concept of ‘weak convergence indistribution’ to develop and establish novel conditions for validity of the wild boot-strap, conditional on the volatility process. We apply our results to several testingproblems in the presence of non-stationary stochastic volatility, including testingsufficient conditions for bootstrap validity that include the absence of statisticalleverage effects, i.e., correlation between the error process and its future conditionalvariance. The results of the paper are illustrated using Monte Carlo simulations,which indicate that a wild bootstrap approach leads to size control even in smallsamples.

AB - In this paper we investigate to what extent the bootstrap can be applied to con-ditional mean models, such as regression or time series models, when the volatilityof the innovations is random and possibly non-stationary. In fact, the volatility ofmany economic and financial time series displays persistent changes and possiblenon-stationarity. However, the theory of the bootstrap for such models has focusedon deterministic changes of the unconditional variance and little is known aboutthe performance and the validity of the bootstrap when the volatility is drivenby a non-stationary stochastic process. This includes near-integrated exogenousvolatility processes as well as near-integrated GARCH processes, where the condi-tional variance has a diffusion limit; a further important example is the case wherevolatility exhibits infrequent jumps. This paper fills this gap in the literature by de-veloping conditions for bootstrap validity in time series and regression models withnon-stationary, stochastic volatility. We show that in such cases the distribution ofbootstrap statistics (conditional on the data) is random in the limit. Consequently,the conventional approaches to proofs of bootstrap consistency, based on the no-tion of weak convergence in probability of the bootstrap statistic, fail to deliverthe required validity results. Instead, we use the concept of ‘weak convergence indistribution’ to develop and establish novel conditions for validity of the wild boot-strap, conditional on the volatility process. We apply our results to several testingproblems in the presence of non-stationary stochastic volatility, including testingsufficient conditions for bootstrap validity that include the absence of statisticalleverage effects, i.e., correlation between the error process and its future conditionalvariance. The results of the paper are illustrated using Monte Carlo simulations,which indicate that a wild bootstrap approach leads to size control even in smallsamples.

M3 - Journal article

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

ER -

ID: 255045435