An overview of methods for testing short- and long-run equilibrium with time series data: Cointegration and error correction mechanism

Abstract

Time series data are usually with a natural temporal ordering. This makes time series analysis distinct from other common data analysis problems, in which there is no natural ordering of the observations. This paper is about the methods used in economics when analyzing time series data. It shows the steps of testing for stationarity where unit root tests in which the Dickey-Fuller and Augmented Dickey-Fuller tests are discussed. For cointegration, Durbin-Watson, Engle-Granger and Augmented Engle-Granger tests are presented step by step. This paper does not end with the analysis of cointegration tests only, but it proceeds to error correction methods which is usually used to make adjustments in a dependent variable which depends not on the level of some explanatory variable, but to the extent to which an explanatory variable deviates from an equilibrium relationship with the dependent variable and half-life formula is introduced to show how long it may take for re-adjustment to equilibrium. With all discussions, policy implications and suggestions for future research are made in the paper.