Bootstrapping non-stationary stochastic volatility

In this paper we investigate to what extent the bootstrap can be applied conditional mean models, such as regression or time series when volatility of innovations is random and possibly non-stationary. fact, many economic financial displays persistent changes possible non-stationarity. However, theory for models has focused on deterministic unconditional variance little known about performance validity driven by a non-stationary stochastic process. This includes near-integrated exogenous processes well GARCH processes, where diffusion limit; further important example case exhibits infrequent jumps. fills gap in literature developing conditions with non-stationary, volatility. We show that cases distribution statistics (conditional data) limit. Consequently, conventional approaches proofs consistency, based notion weak convergence probability statistic, fail deliver required results. Instead, use concept ‘weak distribution’ develop establish novel wild bootstrap, apply our results several testing problems presence volatility, including location model, structural change using CUSUM-type functionals, unit root autoregressive models. Importantly, work under sufficient include absence statistical leverage effects, i.e., correlation between error process its future variance. The are illustrated Monte Carlo simulations, which indicate approach leads size control even small samples.