Regression with Time-Series Data: Stationary Variables
As in chapter 9 of Principles of Econometrics, 4th edition, three ways in which dynamics can enter a regression relationship are considered-through lagged values of the explanatory variable, lagged values of the dependent variable, and lagged values of the error term.
In time-series regressions the data need to be stationary in order for the usual econometric procedures to have the proper statistical properties. Basically this requires that the means, variances and covariances of the time-series data cannot depend on the time period in which they are observed. For instance, the mean and variance of GDP in the third quarter of 1973 cannot be different from those of the 4th quarter of 2006. Methods to deal with this problem have provided a rich field of research for econometricians in recent years and several of these techniques are explored later in chapter 12.
One of the first diagnostic tools used is a simple time-series plot of the data. A time-series plot will reveal potential problems with the data and suggest ways to proceed statistically. As seen in earlier chapters, time-series plots are simple to generate in gretl and a few new tricks will be explored below.
Finally, since this chapter deals with time-series observations the usual number of observations, N, is replaced by the more commonly used T. In later chapters, where both time-series and cross sectional data are used, both N and T are used.