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Modeling the Behavior of the S&P 500 Index

Modeling the Behavior of the S&P 500 Index. Mary Malliaris Loyola University Chicago 10 th IEEE Conference on Artificial Intelligence for Applications. Structure of the S&P. Random or Chaotic?

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Modeling the Behavior of the S&P 500 Index

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  1. Modeling the Behavior of the S&P 500 Index Mary Malliaris Loyola University Chicago 10th IEEE Conference on Artificial Intelligence for Applications

  2. Structure of the S&P • Random or Chaotic? • If a neural network can determine market prices better than the random walk model, it would challenge the efficient market hypotheses and support a chaotic dynamics structure for the market

  3. Random Walk Model P(t+1) = P(t) + e(t+1) Where e(t+1) is from a distribution with mean mu and variance sigma-squared

  4. Chaotic Dynamics • A chaotic function must satisfy three requirements: • It must sample infinitely many values • It is sensitive to initial conditions • The periodic points of the function are dense in R

  5. Backpropagation Neural Network • Input layer • Hidden layer • Output layer • Each node applies a function to the sum of weighted inputs and computes one output

  6. Data • Weekly data from each Friday for two years • 1989 and 1990 • 10 variables: • S&P 500 closing Index • 3 month treasury bill interest rate • 30 year T. Bond interest rate • Weekly New York Stock Exchange volumn • M1, M2 • Price/earnings ratio • Gold price, Crude Oil price • CBOE put/call ratio

  7. Network Structure • One input layer • Two hidden layers • 24 nodes in the first hidden layer • 8 nodes in the second hidden layer • One output

  8. Comparison • 10 periods • MAD • MSE • Correlation between expected and actual

  9. Results • Neural network outperformed the random walk model in each period • This is supportive of the deterministic structure of the stock market returns • This is encouraging to researchers who wish to develop deterministic theories that may eventually replace the existing probabilistic paradigm.

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