The following chart (link at bottom) is the composite SPX chart I created last year, updated with current SPX daily figure (June a little inaccurate as daily historical not available for June on Yahoo today so approximated from a chart). This chart is the one based on the 'average SPX cycle data' where 40 wk average is approx 38 weeks...etc.
This pretty much represents all the cycles TQ mentioned in his post, EXCEPT sigma l.....those over 4.5 years. The 4.5 year cycle top appears to be in synch with the 80 week top and 40 week low in April, recognizing there is no right or left shift/offset shown and its low would have been approx 28 months ago as TQ said.
The BLUE curve is the composite of the cycles shown, and the lavender (pink if you like) shows the SPX which was "adjusted so it shows on the graph near where the composite is for correllation only". Ignoring the effects of sigma l, it would appear that the combination of 4.5 year and 80 week cycles could be influencing a turn down in near future.
My question, finally, is this. I don't see too much mention of the TOPS of given cycles and/or the amounts of phase shift postitive or negative might be existing. How does one make those determinations so as to affect the chart and the composite derived therefrom? How as well does one derive the value of sigma l (for over 4.5 years) and its slope and values?
your posts for reference purposes.... Current Cyclic Model for 7/5/2005:
sum of components larger than 4-4.5 year cycle (sigma l):up
4-4.5 yr cycle: avgs 50+-4 months...28 months along...next low 3/2007-9/2007...down