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A Graphical Aid for Analyzing Autocorrelated Dynamical Systems 469

FigurÄ™ 32. A representative sample extract from the third segment of the movie. The data in this extract covers the time period from September 1990 to August 1991.

The model for the first segment was also forced on the third segment of the data and the residuals were examined - clearly demonstrating a lack of fit. In addition, a forecast was madÄ™ and checked for the next two months of real data. The two actual observations were well within the confidence bounds. The December '92 forecast was 983,547 households on food stamps and the actual count was 988,297. The January '93 forecast was 997,472 and the actual was 998,371.

Conclusions

The univariate phase map movie appears to be a highly useful adjunct tool for examining and assisting the analyst working with time series data. MorÄ™ work surely needs to be done before the understanding of this tool is maturÄ™. Some of the demonstrated and other potential uses are: