Title: Bootstrapping non-stationary stochastic volatility
Authors: Peter Boswijk - University of Amsterdam (Netherlands) [presenting]
Giuseppe Cavaliere - University of Bologna (Italy)
Iliyan Georgiev - University of Bologna (Italy)
Anders Rahbek - University of Copenhagen (Denmark)
Abstract: Recent research has shown that the wild bootstrap delivers consistent inference in time-series models with persistent changes in the unconditional error variance. Consistency means that bootstrap p-values are asymptotically uniformly distributed under the null hypothesis. The question whether this consistency result can be extended to models with non-stationary stochastic volatility is addressed. This includes near-integrated exogenous volatility processes, as well as near-integrated GARCH processes, where the conditional variance has a diffusion limit. We show that the conventional approach, based on weak convergence in probability of the bootstrap test statistic, fails to deliver the required result. Instead, we use the concept of weak convergence in distribution. Using this concept, we develop conditions for consistency of the wild bootstrap for testing problems with non-pivotal test statistics. Examples are the sample average of a martingale difference sequence, and unit root test statistics with martingale difference errors, both in the presence of non-stationary stochastic volatility. An important condition for wild bootstrap validity is the absence of statistical leverage effects, i.e., correlation between the error process and its conditional variance. The results are illustrated using Monte Carlo simulations and an empirical application.