Exploring economic time series: a Bayesian graphical approach

Abstract

Summary Many macroeconomic time series exhibit non-stationary behaviour. Whenmodelling such series an important problem is to assess the nature of this non-stationarybehaviour. Initial interest centred on two types of linear non-stationary models, namely thosefor which the removal of a trend induces stationarity and those for which taking the firstdifference produces a stationary series. The latter are referred to as unit root models. Morerecently, other models such as state space models have proved popular.The paper suggests a technique of exploratory data analysis that helps to shed light onthe two types of linear non-stationarity. It is a Bayesian estimative procedure, generally usingthe 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 Markovchain approach, is advocated. We propose a useful graphical template that can be gainfullyemployed at the initial stages of data investigation. It also indicates clearly when traditionaldifference/trend stationary models should not be considered further for data.Application of this graphical device to artificial series and real data provides insightinto inadequacies of more usual conditional forms of analysis where different types ofnon-stationarity are considered. Exemplars include cases where the bivariate plot leads toindications of non-stationary, and possibly non-linear, data generating mechanisms that maynot conventionally occur to the empirical modeller.Keywords: Bayesian, Graphical inference, Exploratory data analysis, Misspecification.