Example 213


Figure 21.12 shows the U.S. CPI from January 1947 to January 2000 for a total of 649 observations. The CPI series, like the M1 series considered previously, shows a sustained upward trend. The unit root exercise gave the following results:

ACPI, = -0.0094 + 0.000511 - 0.00066CPIt-1 + 0.5473ACPIt-1 t = (-0.6538) (4.3431) (-1.5472) (16.4448)

The t ( = t) value of CPIt—1 is —1.5472. The 10 percent critical value is —3.1317. Since, in absolute terms, the computed t is less than the critical t, the conclusion is that CPI is not a stationary time series. We can characterize it as having a stochastic trend (why?). However, if you take the first differences of the CPI series, you will find them to be stationary. Hence CPI is a difference-stationary (DS) time series.

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