This paper considers estimation and hypothesis testing in linear time series when some or all of the variables have (possibly multiple) unit roots. The motivating example is a vector autoregression with some unit roots in the companion matrix, which might include polynomials in time as...

For the first-order univariate autoregression without constant term, the joint density (corresponding to a flat prior) for the true coefficient and its least squares estimate is estimated by Monte Carlo and graphically displayed. The graphs show how a symmetric distribution for the coefficient...