The first step in analyzing any data set is to plot it. For
time series, the first plot we generally look at is the ``time
series plot,'' which is a plot of the observed series
by time t. One
can find the time series plots for these two examples
in Figures 1 and 2.
The Splus code used to produce these plots may be found
in section 2.2 of the appendix.
Both of these series exhibit a marked ``periodicity,'' or seasonality. Basically, within a given year the maximum of the series occurs in the summer and the minimum in the winter. This is perhaps not so clear for the plots of the whole series as the ``cycles'' are rather ``squeezed.'' Figures 3 and 4 show a ``blow up'' of a small number of years within each series. Of course, we know the maximum temperature is in the summer, so the ``seasonality'' of a temperature series is not unexpected. The seasonality of economic series may be a little harder to understand, but in fact depends to a great extent on the weather as well.
The seasonal effect is demonstrated as well by computing averages across years within months. The results of this operation (see section 2.3 of the appendix for how to carry this out) are given in Figures 5 and 6. Considering the temperature series nottem, there are 20 years of data, so there are 20 January temperatures. We take these 20 January temperatures and average them to get an estimate of the over-all temperature in January. Similarly, this is repeated to get the average February, March, and so forth temperatures. The same process is carried out for the housing starts series hstart.
There is however a clear difference between these two series: the seasonal variations are the only obvious feature of nottem other than rough, irregular fluctuations. But for the hstart series, there is a trend which dominates even the seasonal component. Basically, we see that there was a clear increase in housing starts from ??? to ???, and a decline from ??? to ???.