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I don't know if you could put it into AB, but instead of testing
against the zero mean, test against a random # of the same amount of
trades in the same market. This way if you have a long strategy in a
bull market, your t-test would claim more significance than it really
should. After all, aren't we looking for a true edge and not a lucky
run due to market activity? Also take in account for the type of
distribution you are getting from your winners and losers. The
distribution won't be a perfect bell curve as assumed by such test,
but more of a log distribution. So what you would have to do is add
x (the biggest loss) to every profit/loss and then take the natural
log and then run your discriptive statistics. Then you will have
your transformed mean and std. deviation.
--- In amibroker@xxxxxxxxxxxxxxx, Thomas Ludwig <Thomas.Ludwig@xxx>
wrote:
>
> 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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