Two problems exist in testing for (co-)integration. One is that current definitions of fractional integration in the time-domain can be incomplete. The other is that disregarding fractional orders of integration can cause incorrectly-sized inference about cointegration. This paper completes the...

We study the optimal choice of quasi-likelihoods for nearly integrated, possibly non-normal, autoregressive models. It turns out that the two most natural candidate criteria, minimum Mean Squared Error (MSE) and maximum power against the unit root null, give rise to different optimal...