Bootstrapping non-stationary stochastic volatility

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

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 volatility
of the innovations is random and possibly non-stationary. In fact, the volatility of
many economic and financial time series displays persistent changes and possible
non-stationarity. However, the theory of the bootstrap for such models has focused
on deterministic changes of the unconditional variance and little is known about
the performance and the validity of the bootstrap when the volatility is driven
by a non-stationary stochastic process. This includes near-integrated exogenous
volatility processes as well as near-integrated GARCH processes, where the condi-
tional variance has a diffusion limit; a further important example is the case where
volatility exhibits infrequent jumps. This paper fills this gap in the literature by de-
veloping conditions for bootstrap validity in time series and regression models with
non-stationary, stochastic volatility. We show that in such cases the distribution of
bootstrap 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 deliver
the required validity results. Instead, we use the concept of ‘weak convergence in
distribution’ to develop and establish novel conditions for validity of the wild boot-
strap, conditional on the volatility process. We apply our results to several testing
problems in the presence of non-stationary stochastic volatility, including testing
sufficient conditions for bootstrap validity that include the absence of statistical
leverage effects, i.e., correlation between the error process and its future conditional
variance. The results of the paper are illustrated using Monte Carlo simulations,
which indicate that a wild bootstrap approach leads to size control even in small
samples.
OriginalsprogEngelsk
TidsskriftJournal of Econometrics
ISSN0304-4076
StatusAccepteret/In press - 2021

ID: 255045435