state transitions

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Detecting buy and sell signals for assets in a stock market. Calculates the transition from schooling to swarming with asset prices. It is NOT a technical analysis method.

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  • 1. Detecting State Transitions in a Stock Market with Many Agents Eric Van Horenbeeck PhD CNTS, University of Antwerp

2. Detecting State Transitions in a Stock Market with Many Agents

  • Main thesis:
  • Decisions based on state transitions perform better than decisions based on models of complex behavior
  • A transition occurs when an interactive system is triggered into an alternate state of organization

3. Detecting State Transitions in a Stock Market with Many Agents

  • Outline
  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling
  • 5. Detecting State Transitions
  • 6. Results
  • 7. Summary
  • 8. Future Work

4.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work 5.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • Red line: US funds with a range of annual return for ten years ending December 2000. Blue line: returns from random chance
  • The red and blue lines are on top of each other indicating that the number of above average funds is no different than if fund returns were based entirely on luck.
  • The number of fund managerswith above-average returns over the last ten years is no different than would be by chance

6.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work 7.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • Technical traders assume that prices follow a pattern
  • Fundamental analysts assume prices respond to underlying economic realities
  • Random Walk Theory and Efficient Market Hypothesis hold that the best bet for tomorrows stock price is its value today
  • But

8.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • Long term feedback effects
  • Erratic behavior under certain conditions
  • Fractal structure
  • Sensitive on initial conditions
  • Trading behavior is neither purely rational nor random

9.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • Distances between intraday prices are small relative to the length of the path covered, i.e. trade prices are clustered
  • Stock market as a system shows regularity in spite of unpredictable interaction between its agents
  • We have biological and physical models that exhibit similar behavior: ants, fish, plasma oscillations ...

10.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • From biological models *we learn:
  • Strong relation exists between the constantJ,coupling individual members and the strength of noise
  • In the swarming phase whereJ< 5 , the center of the school hardly moves, whereas ifJ> 5 the fish form a tighter group with a rectilinear movement
  • characterizes the non-linearity of the system, -1/2is the steady swimming speed of fish
  • AtJ -1/2 = 5/ -1/2the schooling structure is self-organizing

* Hiro-Sato Niwa (1994)Self-organizing Dynamic Model of Fish Schooling. InJournal of Theoretical Biology , 171,p. 23 136 11.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • / -1/2stands for the magnitude of random movementJwhere -1/2indicates the mean strength of influence on one individual by the other individuals as a group
  • A transition occurs when the system is no longer driven by the average behavior of individuals. At the sudden transition between incoherent and coherent interaction, the school takes over and the individual becomes a follower.

12. Always clustering (no ego trips) Always self-organizing (no leaders) Sometimes polarized behavior (schooling) Sometimes random (swarming) 1. Example 2. A Stock Market is a Complex Environment 3. Self-organization 4. Swarming and Schooling 5. Detecting State Transitions 6. Results 7. Summary 8. Future Work 13. Monday Tuesday Wednesday Thursday Friday 5 days of swarming and schooling by Philips (Nov. 29 - Dec. 3 99) 14.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • Even without formal communication, traders cluster
  • These clusters show self-organizing features (schooling)
  • The trace of alternating swarming and schooling phases exhibits fractal characteristics
  • Technical and fundamental analysts presume the existence of a limit circle attractor. It might exist but...
  • The path is unstable and the time scale unknown

15.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • Modeling a price path is hard and unsure
  • Knowledge of the (long term) past is not necessary when one knows to recognize a turning point
  • Perception of the current state is sufficient
  • Problem: how to detect a state transition?

16.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work -2 -1 1 2 13.6% 13.6% 34.1% 34.1% Normal distribution of the variance of the observations ( Gaussian noise ) Variance outsidethe normal distribution Variance outside the normal distribution 17.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • Gaussian noisestands for fluctuations with a probability density function of the normal distribution
  • The observed values should have a variance that is Gaussian distributed
  • Probability of errorerf ( x ) gives the probability that a single sample from a random process with zero-mean and unit-variance Gaussian probability density function will be greater or equal tox
  • We assume that the variables are correlated ( schooling )
  • However, if they behave independently & random the covariance would be zero ( swarming ).

18.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work

  • The autocorrelation coefficient (ACF) measures the covariance of a set with sizenattwith a setn +1att +1
  • The error functionerf ( x ) indicates the probability that the ACF belongs to a normally distributed population
  • ACF >erf ( x )phase wave = 1
  • ACF < 1- erf ( x )phase wave = -1
  • Transition point when phase wave changes sign, indicating a loss of coherence in the current state
  • Loss of coherence = loss of memory

19.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and Schooling

5. Detecting State Transitions 6. Results 7. Summary 8. Future Work Simplified meta model 20.

  • 1. Example
  • 2. A Stock Market is a Complex Environment
  • 3. Self-organization
  • 4. Swarming and School

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