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Russell

set. Especially when the retrace "pattem" is as complex as is the case for this portion of the data set, see FigurÄ™ 19. Using the univariate phase map movie, the beginning of the retrace and the duration of the retrace was found. This was checked against the published data set in the text. The electronically distributed data set was shown to have been mis-transcribed. In fact, once the correct number of observations was known from the text, it was obvious that the electronically distributed data set was too long by exactly 20 observations.

Going into this setting, nothing unusual was expected from this data set - and yet a repeated section of data of unknown length was discovered. With respect to the univariate phase map movie, the corrected plant yield data shows no strong pattems as is to be expected for the time series. In the text the yield data was modeled as a moving average process rather than an autoregressive process. The univariate phase map movie does not tend to show coherent pattems for moving average processes.

As we have seen in this portion of the paper, the univariate phase map movie can be useful in examining time series data sets. The pattems that appear in the movie in data sets that are autocorrelated are related to the order of the model that would be fit by a classical Box-Jenkins approach. In addition, the pattems are not overly sensitive to growth. Seasonality, at least when it is strong, is readily apparent. In addition it is possible to detect a number of problems that might exist in the data sets that would be difficult if not impossible to detect by other means.

In addition, although it was not demonstrated here, it should be noted that there is some potential to distinguish between outliers and mis-recorded data provided the autocorrelation of the observations is strong enough.

Plant Yield Data - Retrace

FigurÄ™ 19. The segment of the plant yield data where the univariate phase map movie retraces itself.