Hi Bing, and all -- It really is Not a personal choice to decide whether to limit the number of data points counted, if you want the statistic to be a t-test. Mr Gossett (the actual name of the person who developed and published the t-test under the name "student") went to great lengths in detailing the behavior of empirical data and its agreement to statistical distributions. The t-test Always uses square root of number of observations.
Of course, you are always permitted to develop your own test statistic. But unless you also do the research to determine critical values for various situations, you have no way of knowing the probability of the result that was observed. If you limit the number of observations that are considered, Do Not use the t-test tables to determine significance. At least, do not use them expecting that they accurately reflect your new test statistic -- I have no idea what modification would need to be made, and the statistical world would not publish my paper if I did the research and tried to get it accepted. I sincerely wish Van Tharp had not published that suggestion. It is just plain bad science. Do not use it. .................................... But back to the reality check as the t-test is being applied to metrics for trading systems. Does anyone have truly out-of-sample results where the t-test statistic is embarrassingly large? If so, I want your kind of problem. Contact me and we will deal with the t-test issue from the comfort of our yacht in the Bahamas. If not, what is the issue? Thanks, Howard On Sat, Oct 17, 2009 at 11:52 PM, bingk66 <[email protected]> wrote: > > > Hi Mike, > > I understand what you are saying. I agree that the more data points in the > calculations the more confidence you are entitle to have in the results of > the system, and hence the usage of the sqrt(N) portion of the equation to > reflect that. The concept of it all is fine. > > However, where I am not entirely comfortable with the equation is the > sqrt(N) part, as sqrt(N) can have way too much weighting in the overall > t-test score once N gets too large. Perhaps using the cube root of N might > be better as a means of allowing N to be fully factored into the equation ( > as opposed to Van Tharp's proposal of limiting N to 100) without overbearing > the other parts of the equation. It boils down to a personal choice, I > guess, not unlike the calculation of the objective function that Howard > describes in his books whereby you wish to calculate a single number, and > that single number could be derived from a number of sources, each with > their own weighting and you like some form of partitioning across these > different sources so that no one source overbears the others, inorder to get > a balanced calculation can be obtained. > > Finally, the last part of your post would seem to indicate that as N > increases, expectancy/StdDevofR would tend to decrease. I can't see or > understand why that would be the case. I would appreciate it if you could > provide a brief explanation as to why that might be the case or at least > provide a link whereby I can read up a little more on this. > > Bing > > > --- In [email protected] <amibroker%40yahoogroups.com>, "Mike" > <sfclimb...@...> wrote: > > > > Bing, > > > > In this example, the t-test is calculated to give us a level of > confidence that the average of the sample is different than zero. > > > > If a trade strategy had no predictive power, then its results would be > purely random, producing a net gain (over the long run) of zero with an > equal number of winners and losers. > > > > Actually, it would be a net gain of zero *over the prevailing trend*, > where the trend itself might be greater than zero, as per Aronson. But, that > is another conversation. > > > > The more trades taken, the more likely the true average would show. For > example; Flip a coin 4 times. You might get 3 heads, 1 tail for an average > of 0.75 heads. Flip a coin 1000 times and the average number of heads will > be much much closer to 0.5. > > > > Going back to your trade example, if we are getting a non zero average > after thousands of trades, then we are more and more confident that in fact > the average is not zero. Thus, the larger t-test score is justified, and is > in fact built into the equation. > > > > In other words, you don't have to worry about getting a SQN score of 7 > after 5000 trades, because you will likely never find a trade strategy that > is capable of producing an expectancy of 0.1 after that many trades! > > > > Mike > > > > --- In [email protected] <amibroker%40yahoogroups.com>, > "bingk66" <bing.kwok@> wrote: > > > > > > Hi Howard, > > > > > > If there are no means to limit the number of transactions in the calcs, > then one seriously runs the risk of challenging the mystical t-test score of > 7 that you spoke about previously. > > > > > > As an example, if the OOS test was run over a 5 year period with 5000 > transactions (a mere 1000 transaction/year, which is not excessive, > especially for very short term trades), sqrt(5000) alone would yield in > excess of 70 for the multiplier. This would leave expectancy/StdDev of R > with just a target of 0.1, to reach the 7 t-tests score. > > > > > > Now, if you had 1,000,000 tranasctions in your OOS test.... > > > > > > The concept of limiting the trade count does make sense to me. Maybe > 100 is too low, and should be set higher. There does come a point whereby > the sqrt(N) part of the equation will render the rest of the equation > irrelevant once N gets too large. > > > > > > $0.02 > > > > > > Bing > > > > > > > > > > > > --- In [email protected] <amibroker%40yahoogroups.com>, Howard > B <howardbandy@> wrote: > > > > > > > > Hi Zozu -- > > > > > > > > I must disagree with Van Tharp on this. > > > > > > > > If the runs are truly out-of-sample, then each and every one > contributes to > > > > the computation. It makes no sense to limit the count to 100. It is > poor > > > > procedure to limit the count. It is bad science to limit the count. > Do not > > > > limit the count. > > > > > > > > If the runs are in-sample, then the test has no meaning anyway. > Computing > > > > the t-test statistic using any N will be misleading. Do not even do > the > > > > computation. If a decision to trade a system is made after computing > the > > > > t-test statistic on trades that came solely from in-sample results, > there is > > > > an extremely high probability that a Type I error will be committed. > That > > > > is, the trader will believe that his system is better than random, > when it > > > > is in fact not better than random. Type I errors result in loss of > money. > > > > > > > > Thanks, > > > > Howard > > > > > > > > > > > > On Tue, Oct 13, 2009 at 10:54 AM, zozuzoza <zozuka@> wrote: > > > > > > > > > > > > > > > > > > > Hi Howard, > > > > > > > > > > Limiting the number of N doesn't mean that you are not using all > trades for > > > > > the calculation of SQN. Only the sqrt(N) part of the formula is > limited in > > > > > order not to distort the results if there are many trades. It makes > sense. > > > > > The other part of the formula does count on all the trades. > > > > > > > > > > Zozu > > > > > > > > > > > > > > > > > > > > > > > > > > >
