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This example looks at stationary and nonstationary time series. It provides the background for the importance of unit root tests in econometrics.
The EViews program and workfile were created for EViews 2.0.
A time series that is white noise is stationary: innovations are transient. We define a sequence to be a white-noise process if it is characterized by
To see the stationarity of a white noise process, we generate one and examine it. Look at the graph. The unit root test (Augmented Dickey Fuller test with 4 lags, no constant term, no trend) formally rejects the null-hypothesis of nonstationarity i.e. a unit root.
Of course, if we generate a second white noise process, we expect it to be completely unrelated to the first. Is it? We examine a scatter plot and formal OLS regression estimate.
A random walk is non-stationary: innovations are permanent. A random walk has no constant mean and no constant variance (these change whenever the sample period is shortened or lengthened). A random walk has high serial correlation.
We can generate a random walk by summing up a series of white noise shocks.
Note: we are able to get a cumulative sum with these program lines because EView updates cell-by-cell (i.e., when it updates the second cell, the first has already been updated).
Look at the graph of the random walk series and the unit root test conducted on it. Compare with the white noise series and comment.
Of course, if we independently generate a second random walk process, we expect it to be completely unrelated to the first. Is it? Granger and Newbold (1974) showed that unrelated random walks appear related about 75% of the time. Phillips (1986) showed that the larger your sample, the more likely you are to reject unrelatedness! However, take a look at the two series of regression residuals, and see if you can discover any clues to spurious regression in these.
Granger, C.W.J. and P. Newbold, 'Spurious regressions in econometrics,' Journal of Econometrics, vol.2 (2) July 1974: 111-20.
Phillips, P.C.B., 'Understanding spurious regressions in econometrics,' Journal of Econometrics, vol.33 (3) December 1986: 311-40.