ChapterRegression with Time-Series Data: Nonstationary Variables
The main purpose this chapter is to use gretl to explore the time-series properties of your data. One of the basic points we make in econometrics is that the properties of the estimators and their usefulness for point estimation and hypothesis testing depend on how the data behave. For instance, in a linear regression model where errors are correlated with regressors, least squares won’t be consistent and consequently it should not be used for either estimation or subsequent testing.
In time-series regressions the data need to be stationary. Basically this requires that the means, variances and covariances of the data series do not depend on the time period in which they are observed. For instance, the mean and variance of the probability distribution that generated GDP in the third quarter of 1973 cannot be different from the one that generated the 4th quarter GDP of 2006. Observations on stationary time-series can be correlated with one another, but the nature of that correlation can’t change over time. U. S. GDP is growing over time (not mean stationary) and may have become less volatile (not variance stationary). Changes in information technology and institutions may have shortened the persistence of shocks in the economy (not covariance stationary). Nonstationary time-series have to be used with care in regression analysis. Methods to effectively deal with this problem have provided a rich field of research for econometricians in recent years.