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Hello Ton,
Thankyou for the compliment.
In the example given it makes no difference what timeframe you are
working, as Win/Loss is a number ratio.
For other statistics that are measured in magnitude e.g. StDev, the
weekly value will be greater than the daily value so the maths will
take care of that for us.
There is a lot more to it than the brief discussion and small
example I attempted here.
Different measures,like StDev, might be treated differently in stats
e.g. StdErrorofStDev = = 0.71StDev/SqRt(N)
Keep in mind that I am not a mathematician and not the best person
to comment on maths specifics.
I do have a very good radar system so I am mainly sharing with the
forum my perception that a lot of us are short on skills in this
area and that it is a very important part of trading.
I would recommend that anyone who sees some relevance in the stats
component of this project should read some of the books written for
traders by mathematicians and/or ask some further questions of the
mathematicians in the forum.
I ahve thoroughly enjoyed every post in the topic so far; but I
would say Fred hit the nail right on the head.
BrianB2.
--- In amibroker@xxxxxxxxxxxxxxx, "Ton Sieverding"
<ton.sieverding@xxx> wrote:
>
> Good work Brian. Thanks. I like what I see but just one little
question. So the SE is based upon the number of trades N. Let's say
N = 1.000. Any difference between N = 1.000 days or N = 1.000 weeks
etc. ?
>
> Ton.
>
> ----- Original Message -----
> From: brian.z123
> To: amibroker@xxxxxxxxxxxxxxx
> Sent: Tuesday, November 07, 2006 1:51 AM
> Subject: [amibroker] Margin of Error
>
>
> Part1 of Project Based Training No1.
>
> The objective of the project is to introduce new traders to the
main
> concepts of system design/testing and demonstrate their
application
> in AmiBroker.
> At the same time it is hoped that the ideas presented will
provoke
> discussion and provide trading stimulation.
>
> All of the stages in the design process will not be demonstrated
as
> most have already been covered elsewhere in the AmiBroker
support
> material.
>
> A basic understanding of the application of some statistical
methods
> to the trading environment is a pre-requisite.
> The opening topics address this need.
>
> To those who find the subject matter new *the project* will be a
> workbook .
> To those who have experience in the subject it will be an
> opportunity to workshop.
>
> I would like to acknowledge my indebtedness to the academic
> community .
> I often refer to the material so generously interpreted for the
> layperson and made available at websites by academic
specialists,
> particularly those associated with Universities.
>
>
*******************************************************************
> Margin of Error.
>
> Back-testing of historical data provides traders with a sample,
> typical of the trade they are testing. From that sample they
make
> inferences about the larger group, or population, of all past
trades
> and future trades, of the same type, that were not included in
their
> test window.
> Despite the fact that the people who teach them to back-test
also
> teach them that the past can not predict the future, some
continue
> to act as if it can.
>
> If the past can't predict the future. How can anyone trade with
> confidence?
>
> The answer is that while the future can't be predicted, the
> likelihood of some mathematically defined outcomes can be
predicted
> with a degree of confidence.
> Statistics is the mathematical discipline that manages that very
> well.
>
> The caveat is that to apply statistical methods to trading
samples,
> the assumption is made that they are the result of a random
process.
> Where the trading system chosen is biased to non-random
behaviour it
> will be prone to failure if the market acts contrary to that
bias.
>
> For that reason system traders are faced with a choice between
> attempting to define market behaviour e.g. a trend, and pick a
> system to suit that, or search for a universal signal that is
> consistent irrespective of any assumed market bias.
>
> If statistics can predict the likelihood of future trading
outcomes,
> how accurate will it be?
>
> *Standard error* or *margin of error* offers traders a solution
but
> they are not subjects that are often discussed.
>
> In his book ,*Design, Testing, and Optimisation of Trading
Systems*
> (John Wiley & Sons, 1992), Robert Pardo raises the issue of the
> accuracy of trading *predictions* based on the size of the
sample
> used:
>
> * The sample size must be large enough to allow the trading
system
> to generate a statistically significant sample of trades.
> A sample of one trade is certainly insignificant, whereas a
sample
> of 50 trades or more is generally adequate.*
>
> He uses Standard Error as a measure of significance:
>
> StdError = = 1/SquareRoot(sample size),
>
> 1/SqRt(50) = = 14.1%.
>
> There is little by way of further explanation provided.
>
> Applying the formula to a greater number of samples:
>
> Where N = = the number of trades in the sample
>
> StdError factor = = 1/SqRt(N)
> StdError% = 1/SqRt(N) * 100
>
> If N = = 2500 the StdError% = = 1/SqRt(2500) * 100 = = +/- 2%
> If N = = 10000 the StdError% = = 1/SqRt(10000) * 100 = = +/- 1%
>
> A trade sample of 10000 to provide statistical accuracy of 1% is
not
> easily achievable for traders, although a lot easier than
accurately
> surveying the eye colour of Polar Bears.
>
> Pardos equation is in fact, a rounding of the StdError equation
for
> a 95% level of confidence:
>
> Margin of error at 99% confidence = = 1.29/SqRt(N)
> Margin of error at 95% confidence = = 0.98/SqRt(N)
> Margin of error at 90% confidence = = 0.82/SqRt(N)
>
> Later in the project I will use a basic random number generator,
> within Xcel, to provide a visual aid that traders can use to
> understand the *sample* concept and decide for themselves what
> constitutes an adequate sample.
>
> Wikipedia provides some additional clarity on the subject:
>
> http://en.wikipedia.org/wiki/Margin_of_error
>
> *The margin of error expresses the amount of the random
variation
> underlying a survey's results. This can be thought of as a
measure
> of the variation one would see in reported percentages if the
same
> poll were taken multiple times. The larger the margin of error,
the
> less confidence one has that the poll's reported percentages are
> close to the "true" percentages, that is the percentages in the
> whole population.*
>
> *An interesting mathematical fact is that the margin of error
> depends only on the sample size and not on the population size,
> provided that the population is significantly larger than the
sample
> size, and provided a simple random sample is used. Thus for
> instance...the running example with 1,013 random samples..would
> yield essentially the same margin of error (4% with a 99% level
of
> confidence) regardless of whether the population....consisted of
> 100,000 or 100,000,000.*
>
> In short the tail of the trading system sample is swinging the
> trading system cat.
>
> BrianB2
>
> The material contained in this topic is for educational and
> discussion use only.
> It is not intended as financial advice and should not be
construed
> as such.
> The author is not an accredited academic or financial advisor.
>
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