Interpretation

The assumptions are addressed by the graphics shown above:
 The run sequence plot
(upper left) indicates significant shifts
in both location and variation. Specifically, the location
is increasing with time. The variability seems greater
in the first and last third of the data than it does in the
middle third.
 The lag plot
(upper right) shows a significant nonrandom
pattern in the data. Specifically, the strong linear
appearance of this plot is indicative of a model that
relates Y_{t} to
Y_{t1}.
 The distributional plots, the
histogram
(lower left) and the
normal probability plot
(lower right), are not interpreted
since the randomness assumption is so clearly violated.
The serious violation of the nonrandomness assumption means that
the univariate model
is not valid. Given the linear appearance of the lag plot, the
first step might be to consider a model of the type
\( Y_{i} = A_0 + A_1*Y_{i1} + E_{i} \)
However, discussions with the scientist revealed the following:
 the drift with respect to location was expected.
 the nonconstant variability was not expected.
The scientist examined the data collection device and determined
that the nonconstant variation was a seasonal effect. The
high variability data in the first and last thirds was collected
in winter while the more stable middle third was collected in the
summer. The seasonal effect was determined to be caused by
the amount of humidity affecting the measurement equipment. In this
case, the solution was to modify the test equipment to be less
sensitive to enviromental factors.
Simple graphical techniques can be quite effective in revealing
unexpected results in the data. When this occurs, it is important
to investigate whether the unexpected result is due to problems in
the experiment and data collection, or is it in fact indicative of an
unexpected underlying structure in the data. This determination
cannot be made on the basis of statistics alone. The role of the
graphical and statistical analysis is to detect problems or unexpected
results in the data. Resolving the issues requires the knowledge of
the scientist or engineer.
