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Hello,
in "Quantitative Trading Systems" on p. 256, Howard describes a z-score
test in order to evaluate the statistical significance of a trading
system. While the formula is easy to write in AFL, I don't think that
it can be done as a custom metric since the system to be evaluated is
compared with a Random System. Any idea how to sensibly implement it in
Amibroker?
I'm using another statistical test proposed by the late Arthur Merrill
some years ago in S&C. It's the "chi squared with one degree of
freedom, with the Yates correction". Here's how I implemented it in AB:
//chi squared with one degree of freedom, with the Yates correction
wi=st.GetValue("WinnersQty");
Lo=st.GetValue("LosersQty");
Chi = (abs(wi-Lo)-1)^2/(wi+Lo);
bo.AddCustomMetric( "Chi-Squared modif.: >10.83: very
significant(1000:1), >6.64: significant (100:1) , >3.84: probably
significant (20:1), <3.84: significance doubtful", Chi );
While this metric doesn't tell you anything if your system is
profitable, it tells you if its signals are only pure coincidence
(simply put). It's remarkable that many systems that seem to be
promising according to the usual metrics, are below 3.84, i.e.
significance doubtful. You need either a rather high number of trades
or a very high percentage of winning trades to shift this metric
significantly higher. At least for (medium-term) EOD systems (that's
what I trade) this is not easy to achieve.
What do you think about this metric? Are there other "better"
statistical metrics? If yes - would you mind sharing the AFL code?
Best regards,
Thomas
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