Daily Speculations
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James Sogi
Philosopher, Juris Doctor, surfer,
trader, investor, musician, black belt, sailor,
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(address is not clickable)10-Feb-2006
Binary Modeling, by
James Sogi
Given that we are at the same price as 52 days ago, the question arises what will the outcome of this range be? Following up on Dr. Zussman's recent excellent studies on up days and down days, some counting is in order. Within the range 21 days were down open to close and 29 up. Within that same range, 21 days closed above the mean and 31 below. Does this mean anything?
Modeling Binary Data by David Collett is perhaps the most clearly written explanation of statistics terms that I have read. Collett gives excellent explanations of the the formulas he uses with good examples of models and how to insert the numbers from the data into the formula. Very few other authors writing about statistics have succeeded in such understandable writing. There is the best discussion of models and hypotheses ever. The trick is to convert the models of disease, growing rose cuttings and the like into stock price data use. The truly amazing thing to me is that 2x2 contingency tables of win/loss, success/failure, or up/down data can reveal valuable information and that formulas and models exist to quantify such things as up and down days in a range. This was made popular by Bernoulli in 1713 and is known as the Bernoulli Distribution. It is based on the rules of probability.
The key is to organize the data into meaningful criteria, and formulate a mathematical model or hypothesis that will, when tested on the data, render meaningful results and add to understanding. Knowing the limitations is a necessary part of the process. No model will provide all the answers, and no model will explain the phenomena. No hypothesis or model proves anything, as that is not the purpose of statistical analysis. The goal is to determine if there is a systematic element amid the random noise, and to identify the systematic component and the extent to which it is different, if at all, from the random component. The purposes are for prediction, explanation, description or criteria for further study and refinement. The computations, as the following will show, are simple. More difficult is characterizing the data in ways a million others have not, and getting an edge on them. One must ask the right question.
We return now to Dr. Zussman's idea of up days and down days and combine that with my idea of sales in the top of the range and on the bottom. Conventional advice is that increasing down days and down volume is bearish, and that momentum will continue. This theme is what creates those big down days like the 7th, the idea that selling will continue. My hypothesis is the opposite. What if we hypothesize the more selling at the lower end, as evidenced by down days and by days closing at lower prices in the range, exhausts the supply of available sellers, the so called 'weak hands'. Also assume that there is a pool of cash and investors who are not as exhaustible as the weak hands. This model gives us the criteria to count up/down days, and closes in up part of range or lower range as evidence of exhaustion of sellers on the idea that sellers use up their energy by down closes and driving price in low part of range. Market data is particularly computable with binary analysis due to the fact that a day is either up or down, as is your P&L. Thus the count is set as a 2x2 contingency table of up days, or closes in high or low range in binary success or failure of the criteria. A test of the proportions using the Chi squared distribution and Monte Carlo simulation computes an exact p score. Here is another amazing thing: that computers can solve the equations and do massive number crunching in a blink.
+ -
oc+ 31 21
hi/lo 21 31
The R script to test this follows.
o<-c(31,21,21,31)
m<-matrix(o,,nrow=2,byrow=T)
chisq.test(m,simulate.p.value = TRUE, B = 10000)
Pearson's Chi-squared test with simulated p-value (based on
10000 replicates)
data: m
X-squared = 3.8462, df = NA, p-value = 0.078
The result is not significant at the 5% level.
What does it mean? According to the hypothesis, it cannot be rejected that the sellers are getting real exhausted. So there still may be some sellers left out there. The similar 12/29 study indicated significant low end selling going on on an intraday basis. The New Year's rally followed. In any case, a fun study with good lessons for further use.
Jim Sogi, May 2005
(address is not clickable)