Many time series exhibit unconditional heteroskedasticity, often in addition to conditional one. But such time-varying volatility of the data generating process can have rather adverse effects when inferring about its persistence; e.g. unit root and stationarity tests possess null distributions...

We discuss estimation of so-called long vector autoregressions for multivariate series exhibiting possibly time-varying mean and (co)variances. In applied work, such changes often escape undetected, and we ask how standard tools (least squares estimation, point forecasts, and estimated impulse...