Summary: Many macroeconomic time series exhibit non-stationary behaviour. When modelling such series an important problem is to assess the nature of this non-stationary behaviour. Initial interest centred on two types of linear non-stationary models, namely those for which the removal of a trend induces stationarity and those for which taking the first difference produces a stationary series. The latter are referred to as unit root models. More recently, other models such as state space models have proved popular.
The paper suggests a technique of exploratory data analysis that helps to shed light on the two types of linear non-stationarity. It is a Bayesian estimative procedure, generally using the exact likelihood. A contour plot of the joint posterior density of interest, rather than a (possibly large) sample from this density that could be obtained from a Monte Carlo Markov chain approach, is advocated. We propose a useful graphical template that can be gainfully employed at the initial stages of data investigation. It also indicates clearly when traditional difference/trend stationary models should not be considered further for data.
Application of this graphical device to artificial series and real data provides insight into inadequacies of more usual conditional forms of analysis where different types of non-stationarity are considered. Exemplars include cases where the bivariate plot leads to indications of non-stationary, and possibly non-linear, data generating mechanisms that may not conventionally occur to the empirical modeller.