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12 demonstration. You should have a better idea of the characteristics of magnitude-duration fluctuation than can be gained via envelope analysis. The same is true for the expectations of the principle of commonality. EXTRACTING CYCLIC MODEL ELEMENTS Envelope analysis is a simple and fast technique for determining present status of cyclic components, but leaves much to be desired in the way of detail. To progress further, the techniques of numerical analysis are required. You will never need to apply these time-consuming methods as you trade, but you should be aware of their existence and power. Chapter Eleven and the Appendix will make method and function clear. Using such techniques, the plot of Figure 11-9 was prepared. Here, the 18-month (nominal) cycle of the model has been cleanly extracted from the closing prices of the DJIA over the time-period January 4, 1935, to December 28, 1951. Thirteen samples are present with an average duration of 68.3 weeks. This compares with the two samples previously seen in the 1965-1968 time period of 71-week duration. This is an example of the principle of variation in operation over a long period of time. | | FIGURE 0-9 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | w 10 | .... | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1935 | i«3e | | 1936 | 1939 | | | | 1943 | «44 | 1945 | 1946 | 1947 | | »40 | 1950 | |
The Time-Persistence Of Cyclicality Even more important, you can now get a much improved idea of the nature of the magnitude-duration fluctuation phenomenon. Using the envelope technique on this extracted fluctuation we arrive at the results of Figure 11-10. It is seen that such fluctuation is slow and smooth. The rate of change is much slower than the individual oscillations that comprise the envelope. This is very important, for it means that near past nominal magnitudes, durations, and variations are unlikely to be much different in the near future. CYCLICAUTY IN INDIVIDUAL ISSUES Model element demonstration to this point has employed only the Dow-Jones Industrial Average. The principle of commonality assures us that the results hold essentially true for all stocks, but neither this nor the extent of expected variation from commonality has yet been illustrated.
The Princqile Of Varfeition At Work For this purpose, turn to Figure II-l 1. This is a weekly plot of Warner Company {listed on the New York Stock Exchange) for the 1961-1963 time period. The cyclicality that has been extracted using numerical analysis techniques is clearly visible in the stock price as you compare the two. The following elements of commonaHty are noted: 1. Magnitude-duration fluctuation. 2. Five samples are present, the last of which is foreshortened per the principle of variation- 3. The remaining four average 18.5 weeks. This is the expression of the combined effects of the 13-and 26-week components noted in the model. The principles of commonality and variation can also be demonstrated to some extent using envelope analysis. For example, Figure II-12 plots Standard Packaging (New York Stock Exchange) from 5 May 1967 through 10 January 1969. Noting a seeming regularity with two lows appearing in 1967 and three more in 1968, we apply the constant-width envelope technique. The result is shown in Figure 11-13, sans all extraneous information. Four samples are present, averaging 18.75 weeks in duration-which we recognize as consistent with the cyclic model. Noting again that progress of prices from low to peak of this component is not smootii, we form a new envelope by connecting weekly lows and highs. The result of passing a smooth curve through the center of this envelope is depicted in Figure 11-14. This time 14 samples are present, with an average duration of 5.71 weeks. The ratio of 18.75 to 5.71 is 3.28, indicating once more the presence of approximately three of the shorter duration cycles within the span of the longer one. The 5.71-week duration compares favorably with the 6.766 number obtained for the DJIA in the same time period-and demonstrates both the principles of commonality and variation for this particular issue. Contracting the data produces Figure -15. Here Standard Packaging is shown from 9 April 1965 through 24 May 1968. The envelope technique reveals two samples of 70.0-week average duration. The two samples taken for the DJIA in the same tune period averaged 71.0 weeks!
1961 32-30- 2 -24- + - 0- III III 1943 fieOREIHI WAflNER CO.NYSE Cyclicality And Numerical Analysis STANDARD PACKAGING WEEKLY HI-LO FIGURE B-tZ 1687 loee Before Envelope Analysis
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