We propose a discrete-time multivariate model where lagged levels of the process enter both the conditional mean and the conditional variance. This way we allow for the empirically observed persistence in time series such as interest rates, often implying unit-roots, while at the same time...

Based on Cox and Reid (1987) adjustments of likelihood ratio (LR) tests for unit roots in higher-order autoregressive models are proposed. While unit root inference does not fit directly into the framework of Cox and Reid, the ideas are applied in models with multi-dimensional parameters of...