Series Plots—Constant and Trends

Our initial impressions of the data are gained from looking at plots of the two series. The data plots are obtained in the usual way after importing the dataset. The data on U. S. and Australian GDP are found in the gdp. gdt file and were collected from 1970:1 – 2004:4.[76] Open the data and set the data structure to quarterly time-series using the setobs 4 command, start the series at 1970:1, and use the —time-series option.

open "@gretldirdatapoegdp. gdt" setobs 4 1970:1 —time-series

One purpose of the plots is to help you determine whether the Dickey-Fuller regressions should contain constants, trends or squared trends. The simplest way to do this is from the console using the scatters command.

scatters usa diff(usa) aus diff(aus)

The scatters command produces multiple graphs, each containing one of the listed series. The diff() function is used to take the differences of usa and aus, which appear in the graphs featured in Figure 13.1 below.

Figure 13.1: The levels of Australian and U. S. GDP appear to be nonstationary and cointegrated. The difference plots have a nonzero mean, indicating a constant in their ADF regressions.

This takes two steps from the pull-down menu. First, use the mouse to highlight the two series and then create the differences using Add>First differences of selected variables. Then, select View>Multiple graphs>Time series. Add the variables to the selected list box to produce Figure 13.1.

From the time-series plots it appears that the levels are mildly parabolic in time. The differences have a small trend. This means that the augmented Dickey-Fuller (ADF) regressions may need to contain these elements.

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