The first round of tests, consisting of tests of the Medium Term Solution for the S & P 500, is now complete and the summary results are given below.

Years 2007 to 2008 - 16th Aug 2007 to 6th Jan 2009 incl.

[1] 9.722222 - test statistic, the average error of identified turns, in days

[1] 103 - number of random permutations as good as or better than test stat

[1] 0.0206 - above expressed as % of permutations, the p-value

[1] 37.6425 - average of permutation error distribution, in days

[1] 16.32295 - standard deviation of permutation error distribution, in days

[1] 1.710493 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

Year 2009 - 20th Dec 2008 to 16th Jan 2010 incl.

[1] 10.42857 - test statistic, the average error of identified turns, in days

[1] 809 - number of random permutations as good as or better than test stat

[1] 0.1618 - above expressed as % of permutations, the p-value

[1] 33.43553 - average of permutation error distribution, in days

[1] 14.18181 - standard deviation of permutation error distribution, in days

[1] 1.622286 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

Year 2010 - 27th Nov 2009 to 28th Jan 2011 incl.

[1] 11.35714 - test statistic, the average error of identified turns, in days

[1] 1706 - number of random permutations as good as or better than test stat

[1] 0.3412 - above expressed as % of permutations, the p-value

[1] 34.92687 - average of permutation error distribution, in days

[1] 15.36711 - standard deviation of permutation error distribution, in days

[1] 1.533777 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

All out of sample data - 16th Aug 2007 to 28th Jan 2012

[1] 9.8 - test statistic, the average error of identified turns, in days

[1] 0 - number of random permutations as good as or better than test stat

[1] 0 - above expressed as % of permutations, the p-value

[1] 67.47298 - average of permutation error distribution, in days

[1] 29.38267 - standard deviation of permutation error distribution, in days

[1] 1.962823 - test statistic distance from average of permutation error distribution, expressed as a multiple of standard deviation of permutation error distribution

The histogram plot of the final, all out of sample data

I think the results are unambiguous - given the consistently low p-values the null hypothesis can be rejected and the alternative hypothesis accepted i.e. the S & P 500 Medium term solution is NOT random and therefore has some predictive value.

My next round of tests will be of the Intermediate term solution for the S & P 500. Before conducting these tests however, I would like to state my expectation that the results will not be as conclusive as those given above. This is due to the fact that the Intermediate term solution also has 12 points, but these 12 points occur within a time period that is approximately 120 days long, so the actual average error on this time frame will have to be 2 or 3 bars/days or better to match the above results.

## 1 comment:

Permutations definition

What is a permutation? , define Permutation, why we use permutation?

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