Download Why cellular automata for artificial financial time series generation?

Cellular Automata Based
Artificial Financial Time Series
Indrė Žliobaitė
Department of Informatics
Faculty of Mathematics and Informatics
Vilnius University
e-mail: [email protected]
Aim of this research: to develop a tool, which could be used for complex and changing
causality time series modeling.
The result so far: prototype model - cellular automata based technique for generation of
artificial financial series. For that purpose cellular automata model from [2] was adapted.
In this paper the adaptation technique is introduced and the reasoning why such generator
can be used to model financial time series is created. We have no information that similar
cellular automata method was used by other researchers.
The model assumes weak form of Efficient Market Hypothesis and models information
transmission among market participants. What is the core property of the model –
information reaches agents not at the same time and there are agents, which do not gate
that information at all. This lets to model factual situation in financial markets.
The model can also be used to model environmental changes in the market by randomly or
manually changing model parameters.
Many concepts presented in this paper appeared in the Master thesis written and defended
by the author in Y2006-06.
Six-angle cellular automata model [2]
Excited cell
Each cell is a single layer perceptron (SLP) having p
inputs and 1 output. Neighboring cells are connected
and interact with each other, thus each cell has p
connections (corresponding to SLP).
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8
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Special activation function (1) is used, which is similar
to widely used sigmoid function. 0 part was introduced
in order the model better reflects living cell.
(   S  )
 /(1  e
 , jeiX   *
f (S )  
0, jeiX   *

4
2
0
0
2
4
6
8
10
12
(1)
Here S = Σi=1..p(wixi) – weighted input sum, α, β, γ, η -coefficients selected in a way that
weights represent fraction of 1 (wi[0,1] ), i.e. for more understandable interpretation of
signal transmission. Δ* >= 0 is sensitivity threshold, below which signal is not transmitted
any further.
Cellular automata is suitable for signal transmission modeling, or wave propagation among
living cells. Using this tool interactions among living organisms or systems can be modeled,
where particular pieces of information need to be transmitted among agents.
Generating Artificial Financial Time Series Using Cellular Automata Model
Why cellular automata for artificial financial time series generation?
1. It is expected to be able to capture complex interrelations among financial variables.
When real financial time series are influenced by changing environment and their
underlying distributions are unknown or difficult to model, cellular automata is believed to
be suitable representation.
2. The data generated using presented cellular automata model are more alike to random
walk time series model than to autoregressive model, as autocorrelation is close to 1.
Is it similar to real financial market?
Assumption 1: the model cells space is simplified trade market. Each separate cell here is
assumed to be single trader.
Assumption 2: the signal transmitted from one cell to another and passing by the other cells
corresponds to information which reach the market. That information becomes available not to
all agents and what is even more important – not to all agents at he same time.
Assumption 3: information is of one type only (e.g. positive) and has only one direction.
How it works: single agent, after it has
got that positive information, increases
the price of financial asset by one basis
point. This way information waves while
shifting within cellular automata field,
influence price of an asset.
In the picture time moment from
generation of artificial financial time
series is depicted (this is one time
moment)
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Applicability: this model might be used
as additional information to assumed
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constant price asset or it might be
added as a noise to artificial time
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series, modeled using any other means.
It can also be used to assume weak form of Efficient Market Hypothesis [5] – more particularly
uneven information transmission, as the market reacts to new coming information not
immediately and not fully. When information wave leaves a particular agent, market price gets
back to normal.
How it practically works:
1. rectangular q x r fields (in the picture they are bold) represent one physically close
financial market. They could be scattered throughout the cellular automata as well to
represent distant market participants.
2. excited cells in that field are summed at each iteration, where iteration represents one
day. Artificial financial time series l = {l1, l2, …lt} are got as follows:
I t  i r 0  j q 0 oij (t )
r1
q1
(2)
here q = (q0, q0+1, q0+2, …, q1), r = (r0, r0+1, r0+2, …, r1) – sides of summation rectangular, t –
time moment, oij(t) – is the value of excitation of cell ij (coordinates) at time t.
An excerpt from artificially generated financial time series using the above described model:
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Dirbtines laiko eilutes
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0
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Experimental design for changing environment
Real time series usually are affected by changing environment, because of huge number of
value influencing factors. I use model parameters in order to artificially introduce environment
changes., such as:
1. changing SLP weights (w1 ≠ w2 ≠... ≠ wp), what makes model anisotropic, similar to wind
in a sea, adding bias to the direction of waves.
2. changing the sensitivity threshold of the model. This might be aligned to transaction costs
in reality.
3. changing the strength of signal transmission, that in reality could be attributed to the
“strength of word”, influence or persuasive power of the coming information.
4. changing the length of refraction time. This way we limit the time period between two
transactions that can be executed by one agent – limited volumes.
This way environmental changes of different nature like in real market are introduced. The
changes are long term and they change the influencers, which form the value of financial time
series.
Conclusion
A prototype technique based on cellular automata for generation of artificial financial series is
introduced and reasoning why such generator can be used to model financial time series is
presented.
The model assumes weak form of Efficient Market Hypothesis and models information
transmission among market participants. Core property of the model – information reaches
agents not at the same time and there are agents, which do not gate that information at all.
This lets to model factual situation in financial markets.
The model can be used to model environmental changes in the market by randomly or
manually changing model parameters.
As this model is in the prototype stage, FEETBACK IS MORE THAN WELLCOME 
References
[1] Raudys, S., Zliobaitė, I. (2006) The Multi-Agent System for Prediction of Financial Time Series. Lecture Notes in Artificial
Intelligence. To appear 2006 06 25.
[2] Raudys, S. (2004). Information transmission concept based model of wave propagation in discrete excitable media.
Nonlinear Analysis: Modeling and Control, 9(3):271-289.
[3] Aas, K., Dimakos, X.K. (2004). Statistical modeling of financial time series: An introduction. Note. Norwegian Computer
Center.
[4] Zliobaite, I. (2006). Prediction of Financial Time Series in Changing Environment Using Artificial Neural Networks. Master
thesis in progress. Vilnius University.
[5] Fama, E.F. Efficient capital markets (1970). A review of theory and empirical work. Journal of Finance, 25: 383-417.