Time series plot
Positively autocorrelated series are sometimes called persistent because positive departures
from the mean tend to be followed by positive departures from the mean, and negative departures
from the mean tend to be followed by negative departures (Figure 3.1). In contrast, negative
autocorrelation is characterized by a tendency for positive departures to follow negative
departures, and vice versa. Positive autocorrelation might show up in a time series plot as
unusually long runs, or stretches, of several consecutive observations above or below the mean.
Negative autocorrelation might show up as an unusually low incidence of such runs. Because the
“departures”
for computing autocorrelation are relative the mean, a horizontal line plotted at the
sample mean is useful in evaluating autocorrelation with the time series plot.
Visual assessment of autocorrelation from the time series plot is subjective and depends
considerably on experience. Statistical tests based on the observed number of runs above and
below the mean are available (e.g., Draper and Smith 1981), though none are covered in this
course. It is a good idea, however, to look at the time series plot as a first step in analysis of
persistence. If nothing else, this inspection might show that the persistence is much more
prevalent in some parts of the series than in others.