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[amibroker] Re: Statistical tests as custom metrics



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Ok, so the chi-squared tests for independence (real vs. expected) so, 
looking at your algorithm I'm not seeing expected.  What exactly are 
you test significance against?

--- 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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