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 === Example 2: U.S. government deficit as a percentage of outlays, for 1960-1989. === Again we are dealing with a time series, so the flowchart of Figure 4 recommends that our first step is to plot deficit percentage versus time (Figure 9b). Such a plot exhibits a strong secular trend of increasing deficit percentage, on which is superposed more ‘random’ year-to-year variations. In other words, the major source of variance in deficits is the gradual trend of increasing deficit, and annual variations are a subsidiary effect. Because our data are equally spaced in time, the superposition of these two variances gives a blocky, boxcar-like appearance to the histogram (Figure 9a), with too little tail. If the secular trend were removed, residuals would exhibit a more bell-shaped distribution.

If we ignore the secular trend, nonparametric statistics are more appropriate for this dataset than are parametric statistics. However, ignoring the major source of variance in a dataset is almost always indefensible. Instead, a secular trend can be quantified and used to refine our understanding of a dataset. Later in this chapter, we will return to this example and determine that secular trend.