Expertise:
Intermediate
A first look at the seasonal variation
Figure 1 zooms in on the data and the fitted curve for the period 1964
through 1967. We see a tendency to three peaks per year, with the largest
being in the fall. The low point of the index in each year is in mid December.
We can also see the linear trend over this period.
Figure 1: The log nondurable goods index for 1964 through 1966. The circles are the observed
values, and the smooth curve is the smoothing spline fit to the data.
In order to look more closely at seasonal variation, it is desirable to first
estimate the longterm nonseasonal trend. The straight line in the plot of the
log index is too crude; we need to estimate the finer scale wiggles in the curve
without trying to track variation within each year. To do this, we return to spline
smoothing, but this time place a knot at each year, and smooth with order 4
splines. This fit does not have the resolving power to show much curvature
within any twelvemonth period. We then subtract this longterm trend from
the fit to the data computed above to get a better view of the strictly seasonal
variation. This is shown in Figure 2.
Figure 2: The seasonal variation in the log nondurable goods index estimated by estimating the
longterm trend and then subtracting it from the highresolution smooth of the data.
Now we can see that the major events of the century are also reflected in the
seasonal trend. Seasonal variation balloons to 6% during the depression, and
again around the Treasury Board closure of the money supply, but drops to its
lowest level during World War II. The sixties are a remarkably orderly period,
but the end of the Vietnam War first shows up as increased variability, and
then in the following years as decreased stability. The size of seasonal variation
seems to be on the decrease in recent years.
