July 2003: 

1)  We've revised our "Monte Carlo" indicator so it's a bit more intuitively clear what we're doing.  What you'll see is "Revised h/l prob", followed by two numbers.  These numbers represent the % chance that our best long and short indicators were arrived at purely by chance.  If you see, for example, "Revised h/l prob:  50.0, 8.0", that means our best long ("high") indicator performed no better than chance, while there was only an 8% chance that the best short ("low") indicator was the result of "luck".

We've also increased our Monte Carlo iterations from 50,000 to 250,000, for more accuracy.  

All data tables generated after July 24, 2003, will have this feature.  For more on the Monte Carlo feature, look below to our March 2003 revisions.

2)  As above, we get the probability that our results are based on luck, but this time we operate on the assumption that our results are distributed "normally".  We ask how much higher (or lower) our results are than what would be expected via a normal distribution.  The results are output as percentages, as above.  You'll see something like "Market Focus: 0.3+0.4 (42.77, 36.54)", where 0.3 and 0.4 are the standard deviation units above what would be expected by chance (on both the long and short side of the market), and 42.77 and 36.54 represent the probabilities that our best indicators were the result of luck.

In doing the calculations, we err on the side of conservatism, sometimes considerably so.  That is, the "actual" probabilities that our indicators were the result of chance could be a good deal lower than what we give you, but not higher.  If we output a 42.77% chance, we don't mean to imply we're accurate down to two decimals.  As always on our website, the focus is on identifying significant patterns in a rapid and comprehensive way, not on preparing for a doctoral dissertation.

We'd tend to put more faith in the Monte Carlo approach for several reasons.  For one, the normal distribution approach assumes that the results are distributed normally.  The Monte Carlo approach doesn't.  Also, in doing our normal distribution calculations, we're often operating on the extremes of the normal curve...4, 5, 6 or more standard deviation units from the mean.  This is "sketchy" territory.

In any case, the normal distribution approach gives another way of assessing the significance of the results you see.  We're happy to note that the results of the two approaches usually aren't radically different.

3)  A "Similar Markets" output.  In the case of our daily market summaries, we scan the results of more than 10 years of daily data to find the five market days that most resemble the current session.  The idea is simply that by matching today's market "fingerprint" to historical "fingerprints", we might be able to get some idea where the market might head in the next session.  

What we show you is the dates of the five most similar sessions, followed by a rating.  The highest possible rating would be 100, meaning a perfect match.  The matching program looks only at the top performing indicators (long and short) in our historical tables...there are no, say, time-of-year or market-performance considerations.  These dates are output only in "10 slice" daily data tables.

We're currently testing the idea.  Early results are available here.  The procedure is to find the historical session that best resembles the current session, look one historical market session forward (call it "hist+1"), see which indicators from hist+1's session best predicted gains and losses, and apply those indicators to the upcoming market session.  It might sound complex, but the basic assumption is pretty simple:  similar markets perform similarly into the future.

March 2003:

1)  The standard deviation of all groups of indicators.  This is not the standard deviation of all the individual stock gains and losses.  It's the standard deviation of all the groups of indicators...if there are 40 columns of data and we slice each column 10 times, there will be 400 groups. 

2)  A "Monte Carlo" indicator.  Here, we take a random sampling of gains and losses from our total pool of gains and losses.  The number of samplings is the same as the number of samplings in our test data...if we have 1000 rows of data and we slice each column of data into 10 sections, we randomly select 100 gains and losses.  We repeat the process 50,000 times and get the number of times where a random sampling actually beats our best indicator data, positively or negatively.

Problem is, the random samplings often don't exceed our best indicators even once in the 50,000 attempts.  Therefore, we'll only output the results of this sampling if they're non-zero.  What you'll see is the number of samplings that beat our best indicator divided by 50,000.   To convert to a probability, multiply 10-slice data by 4.5, 25-slice data by 11.25, and dual data by 160 (an approximation).  If, say, you get an answer of .5, that means that a random sampling beats our best indicator 33% of the time (.5/(1+.5).  If you get an answer of 2, the random sampling would beat our best indicator 67% of the time (2/(1+2)).

In the next generation of our site, we'll do this math for you...pardon the obfuscation.  We'll also increase the 50,000 figure substantially for greater accuracy.  

3)  Often, one industry group or sometimes another group dominates our data.  The user is left wondering if the other, lesser-performing indicators are significant or not.  So we've added "Market Focus5", which simply measures the significance of the fifth best indicators in the table in the same way that "Market Focus" does.

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