Summary And Conclusions

1. Regression analysis based on time series data implicitly assumes that the underlying time series are stationary. The classical t tests, F tests, etc. are based on this assumption.

2. In practice most economic time series are nonstationary.

3. A stochastic process is said to be weakly stationary if its mean, variance, and autocovariances are constant over time (i.e., they are timeinvariant).

4. At the informal level, weak stationarity can be tested by the correlo-gram of a time series, which is a graph of autocorrelation at various lags. For stationary time series, the correlogram tapers off quickly, whereas for nonstationary time series it dies off gradually. For a purely random series, the autocorrelations at all lags 1 and greater are zero.

5. At the formal level, stationarity can be checked by finding out if the time series contains a unit root. The Dickey-Fuller (DF) and augmented Dickey-Fuller (ADF) tests can be used for this purpose.

6. An economic time series can be trend stationary (TS) or difference stationary (DS). A TS time series has a deterministic trend, whereas a DS time series has a variable, or stochastic, trend. The common practice of including the time or trend variable in a regression model to detrend the data is justifiable only for TS time series. The DF and ADF tests can be applied to determine whether a time series is TS or DS.

7. Regression of one time series variable on one or more time series variables often can give nonsensical or spurious results. This phenomenon is known as spurious regression. One way to guard against it is to find out if the time series are cointegrated.

8. Cointegration means that despite being individually nonstationary, a linear combination of two or more time series can be stationary. The EG, AEG, and CRDW tests can be used to find out if two or more time series are cointegrated.

9. Cointegration of two (or more) time series suggests that there is a long-run, or equilibrium, relationship between them.

10. The error correction mechanism (ECM) developed by Engle and Granger is a means of reconciling the short-run behavior of an economic variable with its long-run behavior.

11. The field of time series econometrics is evolving. The established results and tests are in some cases tentative and a lot more work remains. An important question that needs an answer is why some economic time series are stationary and some are nonstationary.