To what extent can the bootstrap be applied to conditional mean models â€" such as regression or time series models â€" 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...

Asymptotic properties of the quasi-maximum likelihood estimator (QMLE) for non-linear ARCH(q) models -- including for example Asymmetric Power ARCH and log-ARCH -- are derived. Strong consistency is established under the assumptions that the ARCH process is geometrically ergodic, the conditional...

Many key macro-economic and financial variables are characterised by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as...