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The difference between a statistician and a trader is that a
statistician is paid for their mathematical theories while a trader
is made to pay for theirs.
BrianB2.
--- In amibroker@xxxxxxxxxxxxxxx, "brian.z123" <brian.z123@xxx>
wrote:
>
> 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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