## Thursday, October 13, 2016

### Are lots of markets like so many random number generators that are actually not random but simply complexly determined ?...in fact are they in many case bad random generators

Notice this
You can not build a true random generator
Just better or worse simulators of random generation

Is a market system stocastic or chaotic ?
Subject to randomly generate shocks
Or simply a bunch of more or less bad random generators
Ie  chaotic systems

Brock again

The problem is that empirically it is hard to distinguish between
a stochastic system
and
chaos buffeted by noise. " " noise ??
Let's pretend he didn't add that ...

".....take a random number generator.
To test whether a random number generator is any good, e.g. whether it genera- tes numbers that are totally unpredictable, you can let it generate a series of drawings from a uniform(0,1) distribution. "

" If you plot xt against xt+1 with a series of 100,000 the unit square should fill up completely. "

"So the plot should look uniformly grey."

"  But in practice, this kind of plots with drawings from a number generator will look like snowflakes."

" They will fill out the square, but you will see some patterns. "

" This means that some random number generators are lousy."

To continue this, you can add xt-1 and end up with a cube. It is hard to draw a cube, but if you are good, you can do so and you can see where  the points lie in the cube.

If the generated num- bers kind of fill out the cube, without sub pat- terns, you have got a good random number ge- nerator.

But some will create patterns inside the cube which you can see with your naked eye.

This implies there is some kind of predictability. You can use xt and xt-1 to make a forecast about xt+1, so it is not random.
In four dimensions you do not have the possi- bility to draw a graph any longer. This is where the BDS-test comes in. It tests whether there are any patterns or clusters in higher and hi- gher dimensional cubes. Working out the math on that is quite challenging to say the least. So the BDS-tests shows whether a series is sto- chastic or deterministic by testing for any kind of predictability in the series.