Ever wonder about what technical methods might help relate price movements and time in the financial markets? It's a fun Sunday morning exercise for students of financial markets.
As an example for an inquiry, how about wondering about to what degree do Fibonacci time extensions help identify potential swing points in a typical two dimensional chart. Many fractal market analysts use patterns on two dimensional price charts to identify potential trading opportunities in different time frames. They rely on two dimensional pattern similarities and scale factors, sometimes with great success.
An earlier post (search for Mandlebrot sets in the forums) links to Mandelbrot's paper in Scientific American on the use of fractal generators to create market chart like patterns and implies the inverse, that if one can identify the underlying generator form, one can use it to project price movements.
As it turns out, Mandlebrot suggests that the fractal generator forms are two, one for a Brownian type motion for price and a second that converts clock time to multifractal trading time.
When the two processes are placed on the side of a cube and are projected inwardly into the cube, an "offspring" is formed at the points of intersection of the Brownian motion generator and multifractal trading time generator that looks like a price chart in the inside of the cube. See Mandelbrots' "The (Mis)Behavior of Markets" @ pg 212-216. Mandelbrot calls this the "fractal market cube".
Pretty neat! (note to self--code a fractal market cube charting package)
But here's the icing on top, outlined by a very good mathematician, J. Orlin Grabbe. I quote from his excellent work with the subtitle "An Ode to Robert Prechter": (he obviously has a sense of humor) and provide a link below.
+.....,
Interestingly, however, many financial variables are symmetric stable distributions with an a parameter that hovers around the value of h = 1.618033, where h is the reciprocal of the golden mean g derived and discussed in the previous section. This implies that these market variables follow a time scale law of T1/a = T1/h = Tg = T0.618033... That is, these variables following a T-to-the-golden-mean power law, by contrast to Brownian motion, which follows a T-to-the-one-half power law.
For example, I estimated a for daily changes in the dollar/deutschemark exchange rate for the first six years following the breakdown of the Bretton Woods Agreement of fixed exchange rates in 1973. [1] (The time period was July 1973 to June 1979.) The value of a was calculated using maximum likelihood techniques [2]. The value I found was
a = 1.62
with a margin of error of plus or minus .04. You can’t get much closer than that to a = h = 1.618033…
In this and other financial asset markets, it would seem that time scales not according to the commonly assumed square-root-of-T law, but rather to a Tg law."
Voila^!!! So much for a nerdy Sunday post. Enjoy!
If you are interested here is the link to his paper, which is part 6 of an 8 part series.
https://www.memresea...abbe/chaos6.htm
ATB
Geomean
