In this paper we develop a canonical state space representation of autoregressive moving average (ARMA) processes with unit roots with integer integration orders at arbitrary unit root frequencies. The developed representation utilizes a state process with a particularly simple dynamic...

In this paper we extend fixed-<italic>b</italic> asymptotic theory to the nonparametric Phillips–Perron (PP) unit root tests. We show that the fixed-<italic>b</italic> limits depend on nuisance parameters in a complicated way. These nonpivotal limits provide an alternative theoretical explanation for the well-known...