As promised yesterday, I tried a small change to the original “time machine” strategy first introduced by CSS Analytics. Now if you still have not, please go read these background articles on statistical filters and their importance in a trade system:

– The Adaptive Time Machine: The Importance of Statistical Filters – CSS Analytics

– Transactional vs Confidence-based Trading Strategies – MarketSci

In yesterday’s post, I used the student t-test approach to filter the significance of every of the 50 strategies the algorithm can choose from. As you may know, the Student’s t-distribution used to estimate the mean of a *normally distributed population.* Such an assumption on the distribution contradicts the kind of fat tail returns the market throws at us. To relax the normality assumption, one can use a non-parametric statistical test. Non-parametric statistics make fewer assumptions regarding the distribution of the underlying and therefore can be more robust, thus making a prime choice for the “Time Machine” algorithm. More reading on Wilcoxon signed-rank test can be found here: http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test.

For this test, I used the Wilcoxon signed-rank test instead of the Student’s t-test to establish the significance of strategies. The results below are for the strategy using a 95% significance filter on the S&P 500.

The results obtained are not very different from the previous one. It is interesting to see that the maximum drawdown is smaller when using the Wilcoxon test. This is probably caused by the increased robustness of the statistical test. For the time being I will keep testing the algorithm on different equity indices and asset class stay tuned.

QF

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Hello GF – Michael from the MarketSci Blog. Wanted to pick your brain re: this post but couldn’t find an email addy. Can you ping me at michael @ marketsci.com when you get a moment? Tx!

Added the email address on the sidebar and sent you an e-mail. Looking forward to your questions.

Interesting post – I’m not clear on how you applied the Wilcoxon test on the different series – can you clarify a bit? Did you do it in Excel or use something like R?

Hi Damian, I used R and the function wilcox.test(.) from the stats package to perform the test.

QF

Great site and work!

Why do the return graphs for GSPC differ so much?

(for the t-test and for the wilcoxon)

Maybe i am missing something…