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IMO, Chi Square is a good test to use for stuff like this. In fact,
Arthur Merrill did several ground breaking TA studies using Chi Square
many years ago.
Some would say the Yates correction (subtracting .5) is unnecessary
in this example because of the high frequencies but I'd always apply
it because it makes the final value more conservative.
--- In amibroker@xxxxxxxxxxxxxxx, "brian.z123" <brian.z123@xxx> wrote:
>
> Hypothesis for Bill.
> I promised Bill *The Wave Mechanic* that I would provide the forum
> with something more substantial than the *candy floss* of philosophy
> and psychology.
> Honouring my promise here is my attempt.
>
> It is an example of proceeding from a subjective view of the markets
> (theory, intuition, guess, hunch etc) to an objectively verified
> hypothesis that could form the basis of a trading plan.
> It is intended as an introductory topic to trading.
>
> I dedicate this post to all mathematicians past and present.
> God knows why he/she didn't include me in that group; it appears
> he/she had other plans for me.
>
>
> *******************************************************************
> General Theory (of market relativity) No1.
>
> The behaviour of markets in the major western cultures is similar
> (USA, Australia, UK & others?)
> The markets are moved by institutional investors who control the
> major portion of the money.
> Institutional behaviour has characteristics that can be utilised by
> freelance traders.
> Institutional investors are people and will exhibit some behaviours
> typical of people in general.
> Based on personal observation of institutions, people and people in
> institutions I expect markets to exhibit some of the following
> behaviours to some extent:
> ( I don't comment on other markets because I haven't lived in those
> countries and don't understand the psyche the way I understand the
> psyche of the above group. That doesn't place any relative value
> judgement on other cultures).
>
> Institutions have budget cycles (weekly, monthly, quarterly, yearly?)
> Institutions are bound by rules of governance and obligations.
> It is not in the interests of institutional players to stick their
> heads up out of the trench.
> Institutions set employees targets which are benchmarked against
> industry norms.
> People have short memories.
> People *work* from Mon-Fri, 9-5 .
> People get Mondayitis and Fridayitis.
>
> There are many more similar observations.
> I have only provided a few as examples.
>
> ********************************************************************
>
> Hypothesis derived from General Theory No1.
>
> The markets will behave differently on Mondays compared to average.
>
> ********************************************************************
>
> Verification of the Hypothesis.
>
> The following is summarised from R.W Colby's *Encyclopedia of
> Technical Market Indicators*, published by McGraw-Hill.
> The original is from the writings of Arthur A. Merrill author of
> *Behaviour of Prices on Wall St*.
> It is presented for educational purposes.
>
> The Chi-squared test ( a statistical method) is used to tell us how
> reliable an indicator is and if the patterns exhibited by data could
> have been produced by chance.
> The source of the data that the test is performed on is not given,
> which means that the results are not independently verifiable by the
> forum.
> On that basis it is only provided to demonstrate the principles.
>
> Trading from 1952 to 1983:
>
> the number of Mondays when the market rose was 669
> versus Monday falls 865
> (1534 in total).
> Average for all trading days = = 52.1% updays.
> Expected rises for Monday = = 52.1% x 1534 = = 799.
> Expected downs for Mondays = = 47.9% x 1534 = = 735.
>
> Using the absolute of the (actual ? expected) values for up/down
> days the Chi-squared test (with Yates correction) for statistical
> signifance returns the value 43.81;
>
> (((abs(a1-e1) ? 0.5)^2)/e1) + (((abs(a2-e2) ? 0.5)^2)/e2)
>
> (((abs(669-799) ? 0.5)^2)/799) + (((abs(865-735) ? 0.5)^2)/735) = =
> 43.81
>
> Based on the Chi-test score there is less than one chance in 1000
> that the observed outcome for Mondays was due to chance alone.
>
> ********************************************************************
>
> Please note!
>
> I can't comment on the veracity of the Chi-squared test.
> I will have to leave that to the mathematicians and rightly so.
> I provided the example only to stimulate debate or interest in
> statistics as a powerful trading tool.
>
> The general theory of the market is my own personal view.
> I have not verified the above results myself nor have I attempted to
> develop a trading system based on a Monday trading cycle, or any
> other calender cycle for that matter.
> I have, however, successfully developed and tested a trading system
> based on another hypothesis that was derived from the above
> GeneralTheory.
>
>
>
> BrianB2......<:-)......(the last of the coneheads?).
>
>
>
>
> --- In amibroker@xxxxxxxxxxxxxxx, "brian.z123" <brian.z123@>
> wrote:
> >
> > Statistics for traders.
> > Can anyone recommend a book on statistics written specifically for
> > traders or that applies statistical methods to trading examples?
> > I am looking for an author who has done a good job on the subject.
> > Even if it is only a section of a book that would do provided it
> > goes beyond a superficial treatment of the subject.
> >
> > For anyone interested here is a link to a very good introduction
> or
> > refresher for statistics.
> > The HTML *book* takes your from 0-50kph in approx 100 pages.
> > Please note; the site does contain a lot of advertisements but it
> is
> > also a mini portal for stats and it does have links to free
> > statistical stuff and free tools.
> >
> > Outside of writing indicators I find statistics to be one of the
> few
> > maths disciplines that has a high degree of relevance to trading.
> >
> > http://davidmlane.com/hyperstat/index.html
> >
> > BrianB2.
> >
>
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