Thursday, October 13, 2016

Are lots of markets like so many random number generators that are actually not random but simply complexly determined ? 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 
     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.