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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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