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Paul,
I believe that your degrees of freedom math is not in agreement with
that of Pardo.
In "The Evaluation and Optimization of Trading Strategies", pages
292 - 295, Pardo states that data containing O/H/L/C will represent 4
available degrees of freedom per bar, whether you use them or not.
Further, Pardo writes that each data point used in the calculation of
a rule counts as 1 degree of freedom, but is not double counted. The
rule itself counts as an additional degree of freedom.
So, using your example below;
pds = optimize("pds", 30, 10, 100, 1);
c > ema(c, pds);
If I understand Pardo correctly, then:
- You will have used up 100 degrees of freedom as a result of using
100 Close values when the optimize statement caused pds to be set to
its maximum value of 100.
- You would not count the Close values used for the lesser pds (i.e.
for 10, 11, ... 99) since the max of 100 already accounted for all
those Close values.
- It is not clear to me whether Pardo considers each of the
variations of the C > EMA(C, pds) rule as being a degree of freedom
(i.e. 91 variations = 91 degrees of freedom) or just the variation
ultimately selected (i.e. 1 degree of freedom). I suspect that he
means all 91. David Aronson in "Evidence Based Technical Analysis" is
clear that he believes that each variation must be counted as a rule.
So, continuing with your example, and taking the conservative
approach of assuming all 91 rule variations each count for 1 degree
of freedom, Pardo would say that we have used 100 closes + 91 rules =
191 used degrees of freedom out of 2000 bars x 4 data points = 8000
available degrees of freedom.
In other words, you will have used up 191/8000 = 2.4% of the
available degrees of freedom, leaving 97.6% remaining. As a rule of
thumb, Pardo advises having not less than 90% degrees of freedom
remaining.
I believe that it is irrelevant how many symbols the strategy is run
on, the math is constant per symbol.
I have not yet got around to trying to automate this calculation,
since it is relatively easy to count by hand.
I do plan to eventually have a look at automating the calculation of
perfect profit though. So if and when I do it, I'll try to remember
to update this thread with my conclusions. Unless of course someone
beats me to it ;)
Mike
--- In amibroker@xxxxxxxxxxxxxxx, "Paul Ho" <paultsho@xxx> wrote:
>
> I didnt see the Degree of freedom question
> Suppose we have one rule set buy = c > ema(c, pds);
> we put this through our dataset of 200 symbols each with 2000 bars
> So there is 200 * 2000 = 400000 Dof in terms of the Closing price.
> Note that Dof in h, l, o and volume is irrelevant because we dont
use
> them.
> if pds is a single no. then we have used up only 1 dof, but if
> pds = optimize("pds", 30, 10, 100, 1);
> then we effectively have 91 rules, just that we only choose one of
> them after looking at the results of 91 rules.
> So I believe the Used dof is the no of possible permutations
> expressed in your optimization statement + other fixed rules,
implied
> or otherwise.
> Hope that helps
> /Paul.
> --- In amibroker@xxxxxxxxxxxxxxx, Thomas Ludwig <Thomas.Ludwig@>
> wrote:
> >
> > Hi all,
> >
> > Rober Pardo suggests in his book "The Evaluation and Optimization
> of
> > Trading Strategies" the calculation of "Perfect Profit" (PP)
> which "is
> > the sum total of all of the potential profit that could be
realized
> by
> > buying every bottom and selling every top". By comparing Net
Profit
> of
> > your trading system with PP you can calculate the "Model
> Efficiency"
> > (ME).
> >
> > I think PP can be easily calculated as a stand-alone code by
> applying a,
> > say, 1% Zigzag. But how can it be done if I want to add ME as an
> > additional metric in the Custom Backtester? The Equity() function
> is
> > used for your trading system and cannot be used for the Zigzag
> system
> > at the same time in order to compare both, IMHO. So the only
> solution I
> > can think of is to loop through all Zigzag signals and calculate
> the
> > profit programmatically. Or am I overlooking something?
> >
> > Pardo also suggests to calculate the Remaining Percentage of
> Degrees of
> > Freedom (through Used Dgrees of Freedom and Original Degrees of
> > Freedom). Any idea if and how they can be counted in AFL?
> >
> > Regards,
> >
> > Thomas
> >
>
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