Random Walk Again

NOTE: I must not forget that the primary purpose of this questioning is to create a realistic stock market model to test cellular automata (bots) on. Altho I realise I could just try them out on actual data and maybe that would be better. However it is intriguing to know the nature of the beast.

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Using stochastic matrix method with a matrix (M) size 21x21 following this pattern and with data from the BP (NYSE) graph i.e. p(up) = 0.47, p(same) = 0.04, p(down) = 0.49

0.04	0.47	0	0	0
0.49	0.04	0.47	0	0
0	0.49	0.04	0.47	0
0	0	0.49	0.04	0.47
0	0	0	0.49	0.04

Then after nine moves i.e. M^9 the mid row corresponding to the probability of the system arriving at any one of the 21 states starting at the middle state is (and rotated into a column):

10	0.00079792
9	0.00065137
8	0.00789282
7	0.0056751
6	0.03487872
5	0.02192446
4	0.09070506
3	0.04929454
2	0.15376394
1	0.07108634
0	0.17756573
-1	0.06818486
-2	0.14146795
-3	0.04350149
-4	0.07677832
-5	0.01780073
-6	0.02716259
-7	0.00423922
-8	0.00565518
-9	0.00044765
-10	0.00052599

Which is like the computer model I produced by brute force. But doing this again and with a different mental state myself I see that the periodicity (last post) is a natural product of the maths. As a stock market shifts state up and down the probability of it arriving at various prices is not continuous by peaked with low probability troughs between the peaks, and the dy/dx will oscillate. So like electrons around the nucleus in classical physics it will seem to accelerate between levels and then stay relatively stable inside a probability channel. Of course this is a painfully simple model of something that has an indefinable number of influences but it maybe shows the origin of the periodicity and chartist patterns that are clearly visible in the charts.

Being able to remove this random effect from stock data might reveal other things.

Thinking some more however this is probably just a sampling feature since in this model there are only 3 options. A move up, down or no move and to get anywhere in the price space is thus severely restricted making certain positions very unlikely. In reality there is a continuum of moves so these restrictions don't exist. But if higher-order patterns do exist then they may interact with each other to create oscillations. Brain-storming but worth gathering as many ideas as possible!

This also suggests a method for working out an algebraic formula for the probabilities 2do...