The symmetry of the S&P today, with the open and close at the bottom, two ascents from the mid-bottom to a round number of 1470 from 10am to 11am, and 2pm to 3:30pm, a rally from a midpoint to a high of 1472, and then closing in the last half hour, as happens so often, right at the bottom within a gnat's eyelash of the open, was quite remarkable, all within a very tame 10 point high to low range, same as yesterday, in contrast to the 30 point ranges of last week. Also remarkable was the previous run of four consecutive down Mondays followed by big up Tuesdays, in the best Frank Crossian tradition, with this Monday, the fifth big down in a row, followed by a miserable Tuesday.

Remarkable also was how the traditional pilot fish Israel and the new Israel-substitute pilot fish, Japan, had the move today in their sights.But how would you quantify all this, especially the symmetry. Is geology, architecture, chemistry, or biology the correct template? I'd be interested in readers' thoughts.

Anatoly Veltman remarks:

Symmetry: if you put up one month's hourly gold bar chart, you'll likely fall off your chair! I have been profitably trading every single wave for a month including today's, relying a lot on its symmetry. The thin (or gapping) areas tend to be repeated on the way back: those are low-volume price areas. The congestion areas also tend to repeat: those are price-volume areas. Alas, this exercise remains part of my discretionary trading — to try and quantify this, you'd probably need Jim Simons's resources!

Pitt Maner III adds:

From a geologist's perspective perhaps the best way to analyze the symmetry on display is to rotate the graph 90 degrees and pretend that it is a well (electric) log. The negative gray or dark space above the S&P line thus becomes transformed into layers of rocks. One might then interpret (if viewed as a caliper log) the market open as a "harder sandstone unit" which was followed by softer shales until another hard sandstone unit was drilled through at around 1130 AM. A bit of cyclicity on display.

In nature cyclical packages of deposited rock types that create these well log responses are sometimes related to world-wide sea level changes (e.g. coal cyclothems). It is the job of the stratigrapher to try and correlate different units on a local and global scale–somewhat analagous perhaps to trying to correlate responses in different world markets, although on entirely different timescales.

Of course knowing where you are in a geologic sequence, a depositional environment, etc. is critical to finding oil. Pattern recognition, mental visualization, imagination and interpretive experience would be useful attributes to have for finding "black gold-Texas tea".

It seems then that there would be very advanced signal processing techniques and data crunching software packages in use in the petroleum industry that might have applications useful to the financial community. The two most recognized companies in this field are Schlumberger and Halliburton. Images/examples from the Schlumberger website illustrate some of the advanced technologies in use.

Jim Sogi extends:

From the oceanographic point of view, in Hawaii this winter we hadn't had big waves for weeks, which is unusual for this time of year, but the last few days the waves have been over 15-20 feet. They start coming in waves of storm weather systems 3 or 4 days apart generated off ocean in Northern Japan. This is similar to market waves of volatility, and lulls between which seem to have a 3 or 4 day pattern to them. On a smaller scale, the waves themselves come in sets, with lulls in between. This pattern is a result of random groupings of waves overlapping from differing storms but that form a pattern of wave sets alternating big waves with lulls. December 4 was a lull in the market. November 28 was a big set wave. Last month was a big storm. The alternation in between seems to be quite sudden. Last night's Japan markets seemed to presage this morning's rise much as the storms there create our waves in Hawaii.

This post was started on December 4, and the open of December 5 shows a remarkable gap up in a rapid return to volatility after a lull.

The idea is that a regular but simple system, such as wave generation, cellular automata, and markets generate random patterns in systems, much in the same way as storms of Japan generate waves. The wave propagates at varying speeds and sizes due to normal variation then overlap and combine so as to form clusters of volatility and calmness as a regular result of the process in a pattern.  This happens in markets just as in the ocean. Big Al mentioned that increased volatility creates higher correlation even in purely random sequences. The clustering phenomenon might be similar. There are a number of mathematical wave models and algorithms used by oceanographers.

Newton's studied astronomical phenomenon in Principia such as the length of time for various orbits and time to return in addition to distance. The cycle of times in waves clusters in markets is critical, as is the measure of distance.

Kim Zussman presents his findings:

Continuous SP futures 1/31/07-12/04/07 were partitioned into 15 min return segments for each "day" session (630-1315 PST). The first return was for 630-645, next 645-700…..1315. This produced 27 15 min return segments; 13 before 1000 and 13 after. Then the returns were sorted to align the equivalent first half-day segments with their mirror-images for the second half day (the first 15min aligned with the last 15 min, etc). The time segment alignments were:

645 1315
700 1300
715 1245
730 1230
745 1215
800 1200
815 1145
830 1130
845 1115
900 1100
915 1045
930 1030
945 1015

Then the two mirror-return series were checked for correlation. The idea is that symmetrical days would have high correlation between the first half day and the mirror image of the second half (picture a graph of the day creased vertically at mid-day, and folded back on itself). For 2007, the mirror-correlation ranged from -0.71 to +0.60 (mean -0.007).

It is possible that categorizing days as to mirror-correlation symmetry, and further specifying o-c up/dn, and concave up/dn could have predictive value. Here are the 10 most mirror-correlated days:

date Mirr corr
02/22/07 0.60
03/29/07 0.60
04/25/07 0.60
07/05/07 0.55
10/04/07 0.55
11/19/07 0.54
11/08/07 0.53
02/20/07 0.53
07/23/07 0.48
08/13/07 0.47


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