Forecasting the BET-C Stock Index with Artificial Neural Networks

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Forecasting the BET-C Stock Index with Artificial
Neural Networks
DOCTORAL SCHOOL OF FINANCE AND BANKING
DOFIN ACADEMY OF ECONOMIC STUDIES
MSc Student Stoica Ioan-Andrei Supervisor
Professor Moisa Altar
July 2006
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Stock Markets and Prediction

• Predicting stock prices - goal of every investor
  trying to achieve profit on the stock market
• predictability of the market - issue that has
  been discussed by a lot of researchers and
  academics
• Efficient Market Hypothesis - Eugene Fama
• three forms
• Weak future stock prices cant be predicted
  using past stock prices
• Semi-strong even published information cant be
  used to predict future prices
• Strong market cant be predicted no matter what
  information is available

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Stock Markets and Prediction

• Technical Analysis
• castles-in-the air
• investors behavior and reactions according to
  these anticipations
• Fundamental Analysis
• firm foundations
• stocks have an intrinsic value determined by
  present conditions and future prospects of the
  company
• Traditional Time Series Analysis
• uses historic data attempting to approximate
  future values of a time series as a linear
  combination
• Machine Learning - Artificial Neural Networks

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The Artificial Neural Network

• computational technique that benefits from
  techniques similar to those employed in the human
  brain
• 1943 - W.S. McCulloch and W. Pitts attempted to
  mimic the ability of the human brain to process
  data and information and comprehend patterns and
  dependencies
• The human brain - a complex, nonlinear and
  parallel computer
• The neurons
• elementary information processing units
• building blocks of a neural network

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The Artificial Neural Network

• semi-parametric approximation method
• Advantages
• ability to detect nonlinear dependencies
• parsimonious compared to polynomial expansions
• generalization ability and robustness
• no assumptions of the model have to be made
• flexibility
• Disadvantages
• has the black box property
• training requires an experienced user
• training takes a lot of time, fast computer
  needed
• overtraining ? overfitting
• undertraining ? underfitting

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The Artificial Neural Network
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The Artificial Neural Network
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The Artificial Neural Network

• Overtraining/Overfitting

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The Artificial Neural Network
Undertraining/Underfitting
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Architecture of the Neural Network

• Types of layers
• input layer number of neurons number of inputs
• output layer number of neurons number of
  outputs
• hidden layer(s) number of neurons trial and
  error

• Connections between neurons
• fully connected
• partially connected
• The activation function
• threshold function
• piecewise linear function
• sigmoid functions

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The feed forward network
m number of hidden layer neurons n number of
inputs
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The Feed forward Network with Jump Connections
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The Recurrent Neural Network - Elman
allows the neurons to depend on their own lagged
values ? building memory in their evolution
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Training the Neural Network
Objective minimizing the discrepancy between
real data and the output of the network
O - the set of parameters ? loss function
? nonlinear ? nonlinear optimization problem

• backpropagation
• genetic algorithm

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The Backpropagation Algorithm

• alternative to quasi-Newton gradient descent
• O0 randomly generated

• ? learning parameter, in .05,.5
• after n iterations µ0.9, momentum parameter

• problem local minimum points

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The Genetic Algorithm

• based on Darwinian laws
• Population Creation N random vectors of weights
• Selection ? (Oi Oj) parent vectors
• Crossover Mutation ? C1,C2 children vectors
• Election Tournament the fittest 2 vectors passed
  to the next generation
• Convergence G generations
• G - large enough so there are no significant
  changes in the fitness of the best individual for
  several generations

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Experiments and Results
Data

• BET-C stock index daily closing prices, 16
  April 1998 until 18 May 2006
• daily returns
• conditional volatility - rolling 20-day standard
  deviation
• BDS-Test for nonlinear dependencies
• H0 i.i.d. data
• BDSm,eN(0,1)

Series m2 m2 m3 m3 m4 m4
e1 e1.5 e1 e1.5 e1 e1.5
OD 16.6526 17.6970 18.5436 18.7202 19.7849 19.0588
ARF 16.2626 17.2148 18.3803 18.4839 19.7618 18.9595
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Experiments and Results

• 3 types of Ann's
• feed-forward network
• feed-forward network with jump connections
• recurrent network
• Input Rt-1 Rt-2 Rt-3 Rt-4 Rt-5 Vt
• Output next-day-return Rt
• Training genetic algorithm backpropagation
• Data divided in
• training set 90
• test set 10
• one-day-ahead forecasts - static forecasting
• Network
• trained 100 times
• best 10 SSE
• best 1 - RMSE

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Experiments and Results
Evaluation Criteria

• In-sample Criteria
• Out-of-sample Criteria
• Pesaran-Timmerman Test for Directional Accuracy
• H0 signs of the forecast and those of the real
  data are independent
• DAN(0,1)

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Experiments and Results

• ROI - trading strategy based on the sign
  forecasts
• buy sign
• - sell sign
• Finite differences

Benchmarks

• Naïve model Rt1Rt
• buy-and-hold strategy
• AR(1) model LS overfitting
• RMSE
• MAE

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Experiments and Results
Naïve AR(1) FFN no vol FFN FFN-jump RN
R2 - 0.079257 0.083252 0.083755 0.084827 0.091762
SSE - 0.332702 0.331258 0.331077 0.330689 0.328183
RMSE 0.015100 0.011344 0.011325 0.011304 0.011332 0.011319
MAE 0.011948 0.008932 0.008929 0.008873 0.008867 0.008892
HR 55.77 (111) 56.78 (113) 57.79 (115) 59.79 (119) 59.79 (119) 59.79 (119)
ROI 0.265271 0.255605 0.318374 0.351890 0.331464 0.412183
RP 15.02 14.47 18.02 19.92 18.77 23.34
PT-Test - - 14.79 15.01 15.01 14.49
BH 0.2753 0.2753 0.2753 0.2753 0.2753 0.2753
FFN FFN-jump RN
Volatility -0.1123 -0.1358 -0.1841
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Experiments and Results
Actual, fitted ( training sample)
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Experiments and Results
Actual, fitted ( test sample)
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Conclusions

• RMSE and MAE lt AR(1) ? no signs of overfitting
• R2 lt 0.1 ? forecasting magnitude is a failure
• sign forecasting 60 ? success
• Volatility
• improves sign forecast
• finite differences ? negative correlation
• perceived as measure of risk
• trading strategy outperforms naïve model and
  buy-and-hold
• quality of the sign forecast confirmed by
  Pesaran-Timmerman test

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Further development

• Volatility other estimates
• neural classificator specialized in sign
  forecasting
• using data outside the Bucharest Stock Exchange
• T-Bond yields
• exchange rates
• indexes from foreign capital markets