Forecasting Financial Time Series using AgentBased Games Nachi Gupta Computer Science Dept., Oxford

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Forecasting Financial Time Series using
Agent-Based GamesNachi Gupta
Computer Science Dept., Oxford UniversityRaphael
HauserDave Smith Math Dept., Oxford
University Neil Johnson Physics
Dept., Oxford University
2
sell -1
f
d
buy 1
b
e
strategy space
S
c
price-change
a
? a winning outcome ? reward traders
strategies
history of price-changes at time t . . . .
0 1
updated history at time t 1 . . . . 1
0
trader memory m 2
3
sell -1
f
d
buy 1
b
e
strategy space
S
c
price-change
a
? a winning outcome ? reward traders
strategies
actual history of price-changes at time t .
. . . 0 1
trader memory m 2
4
Estimate strategy distribution using constrained
optimization techniques
sell -1
f
d
buy 1
b
e
strategy space
S
c
price-change
a
? a winning outcome ? reward traders
strategies
actual history of price-changes at time t .
. . . 0 1
trader memory m 2
5
I. Predicting a simulated market
e.g. Minority Game
one standard deviation about zero
Pocket of Predictability

• standard deviation below threshold value

measurement residual process
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II. Predicting a real market
Pocket of Predictability timesteps 0 ? 90
one standard deviation about zero

• standard deviation below threshold value

measurement residual process
N.B. multiple memory m ? better prediction
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Pockets of Predictability

• Market decided traders undecided
  traders
• (deterministic)
  (stochastic)
• Estimate the probability distribution over a
  strategy space and account for this endogenous
  stochasticity
• Make predictions n timesteps ahead . . . .

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David Smith et al. cond-mat/0409036
The Future-Cast an example
Strat R
agents holding strategies i and j
Strat R
m 1
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Strat R
Strategy
Strat R
History
actions
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Strat R
? 2
-11
? 1
Strat R
? 4
-1-1
11
1-1
? 3
Time Horizon, T 1
Internal State Space
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Strat R
? 2
-11
? 1
Strat R
? 4
-1-1
11
1-1
? 3
Market-dependent actions
? 1
? 2
? 4
? 3
12
David Smith et al. cond-mat/0409036
The Future-Cast an example
Strat R
? 2
-11
? 1
Strat R
? 4
-1-1
11
1-1
? 3
Market-dependent actions
? 1
? 2
? 4
? 3
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Mapping to Output
?S S(t1) - S(t) n1 n-1
? 1
? 2
? 4
? 3
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Mapping to Output
?S S(t1) - S(t) n1 n-1
P?S ?
P?S ?
P?S ?
P?S ?
?S
?S
?S
?S
? 1
? 2
? 4
? 3
? 1
? 2
? 4
? 3
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Mapping to Output
Transition Probabilities
P?S ?
P?S ?
P?S ?
P?S ?
winning decision 1
-1
1
-1
-1
-1
1
1
?S
?S
?S
?S
? 1
? 2
? 4
? 3
? 2
-11
1
0. 5
? 1
? 4
0. 5
1
-1-1
11
1
1-1
? 3
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Mapping to Output
Transition Probabilities
P?S ?
P?S ?
P?S ?
P?S ?
winning decision 1
-1
1
-1
-1
-1
1
1
?S
?S
?S
?S
? 1
? 2
? 4
? 3
? 2
-11
1
0. 5
? 1
? 4
T
0. 5
1
-1-1
11
1
1-1
? 3
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David Smith et al. cond-mat/0409036
The Future-Cast an example
Mapping to Output
Transition Probabilities
P?S ?
P?S ?
P?S ?
P?S ?
e
a
b
c
d
?S
?S
?S
?S
? 1
? 2
? 4
? 3
?
T
Discrete convolution operator ?
18
David Smith et al. cond-mat/0409036
The Future-Cast an example
Mapping to Output
Known Initial State
19
David Smith et al. cond-mat/0409036
The Future-Cast an example
Mapping to Output
Unknown Initial State
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David Smith et al. cond-mat/0409036
The Future-Cast

• Generates future-distributions exactly
• Time-averaged properties through
  eigenvalue/vector solution
• Allows investigation into effects of
  perturbations
• Risk predictability vs. stochasticity
• Quick and easy calculation of means and
  variances without
• explicitly generating future distributions