21 September 2005
Near the End of the Wilshire 5000 Secondary Daily Decay Fractal
In order to qualify as a science, a potential new field must
have the quality of prospective predictability. In the 8 August
posting in the Economic Fractalist(EF), a prediction that the
secondary top (relative to March 2000) for the most heavily weighted
world equity index, the Wilshire 5000, was probably in. It apparently
was. Other smaller US indices and many of the EuroAsian indices have
made higher highs since 3 August. The latter highs of the EuroAsian
markets most likely reflects the summation macroeconomic effect of a
much stronger cash reserve and savings position of their respective
country citizen consumers.
From the 11 August EF posting, the Wilshire's final daily fractal
growth sequence to its secondary 3 August peak was identified as
6/15/10 with a 6/15/15 fractal sequence completing the whole 3 phase
up and 1 phase down fractal cycle. Fractals, just like the underlying
macroeconomic system they precisely reflect, are exquisitely
efficient. The first daily decay fractal was predicted to be found in
last daily fractal growth sequence containing the Wilshire peak. The
numerical possibilities of this first base decay cycle ranged from
1015 days. An 11 day base with an ideal x/2.5x/2x/1.5x pattern was
initially identified as the high probability correct decay sequence.
This elegantly matched the 11 day base of the primary 1929 devolution.
However, recent trading valuations have proven this supposition base
number to be incorrect. The expected second fractal of such a 11 day
base sequence of 2728 days would have had an underlying slope from
the first to last day that would have included all valuations of the
second fractal. This clearly did not occur, although a short term low
was made on an intraday level on day 28. This disqualifies the 11 day
base supposition.
Fractals by their nature have recurrent similar near quantum growth
and decay patterns with different time unit bases. For instance, the
daily growth pattern beginning in August 2004 was x/2.5x/2.5x,
roughly 9/23/22 days. The last portion of this growth cycle was 2.5x
and suggests the complex macroeconomic system would produce a
beginning decay fractal of likewise a 2.5x length but with the
different daily fractal base which included the Wilshire's peak. The
daily first fractal base leading to the peak was actually slightly
less than 6 days with averaged sequence of 6minus/14plus/14plus
conforming to a x/2.5x/2.5x fractal. By this proportional fractal
reckoning, the initial decay daily base is, therefore, slightly
longer than 14 days.
With a first decay base of slightly more than 14 days(x) the expected
length of the second decay fractal is 2.5x or 3536 days. This means
that on Monday 26 September 2005 or on perhaps an intraday level on
Tuesday 27 September, the Wilshire will make a significant low with a
slope line below all valuations for the inclusive 3536 days composing
the second decay fractal. After this a substantial rebound of 1014
days should occur before the final total third decay fractal of
1.62.5x, using the 14 day base, is made. This final drop should
contain the large nonlinear devaluation that will possibly
characterize the fall of 2005 as 1929's equivalent. This is not meant
to be investment advise, but rather an attempt to prospectively
confirm a testable hypothesis and suggest fractal analysis may be a
new science that can reasonably quantify the complex macroeconomic
system.
The coincidental fractal timing for Monday's (or Tuesday's on an
intraday level) intermediate low(at the end of the second decay
fractal) comes after Rita's landfall over the weekend. Any post hoc
ergo propter hoc logic used to explain a devalution should be compared
with Katrina's nearly absent effect on the Wilshire, whose valuation
timing was at the bottom of its fractal cycle during the Mississippi
landfall and moved up .6 percent that day.
Gary Lammert
