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I just tried this out with IMM currency futures, daily data from 1987 to
2002 for AD, BP, CD, EC, SF, ME, JY. Computed average move sizes for
1-bar, 16-bar and 64-bar intervals, then looked for factors as follows:
1-bar vs 16-bar move sizes
1-bar vs 64-bar move sizes
16-bar vs 64-bar move sizes
The expected factors for random walks would be 4, 8, and 2
respectively. Only JY and ME came in consistently stronger, ie factors
always above these thresholds. The other six were weaker.
What Alex mentioned below is conventional (and generally accepted) wisdom,
so I was surprised to find that at least for currency *futures* it doesn't
seem to be the case.
Any ideas what's going on ? (and yes, I did check my spreadsheet with
random data first ;-)
Regards,
Stefan Schulz
Suaviter Limited
prog1@xxxxxxxxxxxxxx
At 20:43 09/02/02 -0800, Alex Matulich wrote:
>[generating a random walk in Excel]
> > Trend lines, retracements, consolidations, breakouts, Support,
> >Resistance, Head and Shoulders, double tops, V-shaped
> >bottoms...........etc....etc.
> >
> >Any pattern you like in fact.
> >
> >They are all there if you have an eye for them.
> >
> >AND ALL ON CHARTS THAT ACTUALLY ARE RANDOM WALK!
>
>But markets are NOT random walks, as you can clearly demonstrate if you
>plot a distribution of periodic returns. A random walk will always have
>a normal distribution. Markets don't. Markets exhibit a distribution
>having fatter tails and a sharper peak than normal. The distribution
>can be modeled by the Stable Pareto family of distributions having a
>non-integer exponent (the Gaussian is a special case of the Stable
>Paretian family, and the only case having a finite variance). Market
>distributions have an infinite variance.
>
>This difference in gaussian versus actual distribution is clearly
>illustrated by the implied volatility smile which is an artifact
>of the Black-Scholes option pricing formula assuming a normal
>distribution of future returns when no normal distrubtion exists.
>
>A further demonstration you can do is measure how well a market
>trends against a random walk. If you pick some fixed number N
>periods, the distance you can expect a random walk to move is
>proportional to the average daily movement (in your case 1.0) times
>the square root of N. Such is not the case for markets. Currencies
>typically trend more strongly, for example, and grains like wheat
>trend more weakly than a random walk.
>
>A random walk may look the same as a market on the surface, but it's
>not the same at all.
>
>--
> ,|___ Alex Matulich -- alex@xxxxxxxxxxxxxx
> // +__> Director of Research and Development
> // \
> //___) Unicorn Research Corporation -- http://unicorn.us.com
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