Development of Neural Network Algorithms for Predicting Trading Signals of Stock Market Indices

1
Development of Neural Network Algorithms for
Predicting Trading Signals of Stock Market
Indices

• Presented By Nuha AlOjayan

2
Overview

• Paper Name
• Development of Neural Network Algorithms for
  Predicting Trading Signals of Stock Market
  Indices.
• Authors
• Chandima D. Tilakaratne, Musa A. Mammadov, and
  Sidney A. Morris
• Objective
• The aim of this paper is to develop new neural
  network algorithms to predict whether it is best
  to buy, hold or sell shares (trading signals) of
  stock market indices.

3
Introduction

• The most commonly used techniques to predict the
  trading signals of stock market indices are
• Feed Forward Neural Networks (FNN)
• Probabilistic Neural Networks (PNN)
• Support Vector Machines (SVM)
• The FNN outputs the value of the stock market
  index and subsequently this value is classified
  into classes (direction).
• Unlike FNN, PNN and SVM directly output the
  corresponding class.
• Almost all of these studies considered only two
  classes the upward and the downward trend of the
  stock market movement, which were considered as
  buy and sell signals.

4
Introduction

• It was noticed that the time series data used for
  these studies are approximately symmetrically
  distributed among these two classes.
• In practice, the traders do not participate in
  trading (either buy or sell shares) if there is
  no substantial change in the price level. Instead
  of buying/selling, they will hold the
  money/shares in hand.
• Where Y (t1) is the relative return of the
  Close price of day (t1) of the stock market
  index of interest while lu and ll are two
  thresholds.

5
Introduction

• FNN can be identified as a suitable alternative
  technique for classification when the data to be
  studied has an imbalanced distribution.
• FNN Disadvantages
• Use of local optimization methods which do not
  guarantee a deep local optimal solution
• FNN needs to be trained many times with different
  initial weights
• Use of the ordinary least squares (OLS) as an
  error function to be minimized may not be
  suitable for classification problems.

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Introduction

• This study aims at developing new neural network
  algorithms to predict the trading signals buy,
  hold and sell, of a given stock market index.
• Using a global optimization algorithm for network
  training to find deep solutions to the error
  function.
• Modifying the ordinary least squares error
  function to be suitable for the classification
  problem. (It is more important to predict the
  direction of a time series rather than its value.
  Therefore, the minimization of the absolute
  errors between the target and the output may not
  produce the desired accuracy of predictions)

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Development of New Algorithms

• The most commonly used error function is the
  Ordinary Least Squares function (OLS)
• Where N is the total number of observations in
  the training set while ai and oi are the target
  and the output corresponding to the ith
  observation in the training set

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Alternative Error Functions

• Caldwell and Yao Tan Function
• It penalized the incorrectly predicted
  directions more heavily, than the correct
  predictions. In other words, higher penalty was
  applied if the predicted value (oi) is negative
  when the target (ai) is positive or vice-versa.
• Caldwell proposed the Weighted Directional
  Symmetry (WDS) function which is given below
• N is the total number of observations

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Alternative Error Functions

• Yao Tan
• wds(i) should be heavily adjusted if a wrong
  direction is predicted for a larger change while
  it should be slightly adjusted if a wrong
  direction is predicted for a smaller change and
  so on.
• Based on this argument, they proposed the
  Directional Profit adjustment factor
• Where ?aiai-ai-1, ?oioi-oi-1 and is the
  standard deviation of the training data.

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Alternative Error Functions

• Based on this, they propose Directional Profit
  (DP) model
• They proposed Discounted Least Squares (LDS)
  function by taking the recency of the
  observations into account.
• Where wb(i) is an adjustment relating to the
  contribution of the ith observation and is
  described by the following equation

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Alternative Error Functions

• Yao Tan proposed another error function, Time
  Dependent Directional Profit (TDP) model
• Where fTDP (i)fDP (i) wb(i).

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Modified Error Functions

• The authors in this paper are interested in
  classifying trading signals into three classes
  buy, hold and sell.
• The hold class includes both positive and
  negative values. Therefore, the least squares
  functions in which the cases with incorrectly
  predicted directions (positive or negative) are
  penalized will not give the desired prediction
  accuracy.
• They proposed scheme based on the correctness of
  the classification of trading signals.
• If the predicted trading signal is correct, we
  assign a very small (close to zero) weight
• otherwise, assign a weight equal to 1

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Proposed Error Function 1

• Modify EDP error function by replacing fDP (i)
  with the new weighing scheme, wd(i)

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Proposed Error Function 2

• Combine ECC with the EDLS

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New Neural Network Algorithms

• The authors proposed the following algorithms
• NNOLS - Neural network algorithm based on
  Ordinary Least Squares error function, EOLS
• NNDLS - Neural network algorithm based on
  Discounted Least Squares error function, EDLS
• NNCC - Neural network algorithm based on the ECC
• NNTCC Neural network algorithm based on the ETCC

• These networks consist of three layers and out
  of these three one is a hidden layer.
• A tan-sigmoid function was used as the transfer
  function between the input layer and the hidden
  layer while the linear transformation function
  was employed between the hidden and the output
  layers.

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Network Training and Evaluation

• The Australian All Ordinary Index (AORD) was
  selected as the stock market index whose trading
  signals are to be predicted.
• Input Sets
• (1) A combination includes the GSPC, FTSE, FCHI
  and the GDAXI
• (2) A combination which includes the AORD in
  addition to the markets included in (1).

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Optimization Problem

• Let Y (t1) be the relative return of the Close
  price of a selected dependent market at time t
  1 and Xj(t) be the relative return of the Close
  price of the jth influential market at time t.
  Define X(t) as
• Where the coefficient j 1, 2, ...,m, measures
  the strength of influence from each influential
  market Xj while m is the total number of
  influential markets.

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Input Sets

• The following six sets of inputs were used to
  train the new network
• Four input features of the relative returns of
  the Close prices of day t of the market
  combination (1) (that is GSPC(t), FTSE(t),
  FCHI(t), GDAXI(t))
• Four input features of the quantified relative
  returns of the Close prices of day t of the
  market combination (1) (that is ?1GSPC(t),
  ?2FTSE(t), ?3FCHI(t), ?4GDAXI(t))
• Single input feature consists of the sum of the
  quantified relative returns of the Close prices
  of day t of the market combination (1) (that is
  ?1GSPC(t) ?2FTSE(t) ?3FCHI(t) ?4GDAXI(t))
• Five input features of the relative returns of
  the Close prices of day t of the market
  combination (2) (that is GSPC(t), FTSE(t),
  FCHI(t), GDAXI(t), AORD(t))
• Five input features of the quantified relative
  returns of the Close prices of day t of the
  market combination (2) (that is ?1GSPC(t), ?2
  FTSE(t), ?3 FCHI(t), ?4 GDAXI(t), ?5 AORD(t))
• Single input feature consists of the sum of the
  quantified relative returns of the Close prices
  of day t of the market combination (2) (that is
  ?1 GSPC(t)?2 FTSE(t)?3 FCHI(t) ?4 GDAXI(t)?5
  AORD(t)).

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Evaluation Measures

• The performance of the networks was
  evaluated by

• The overall classification rate (rCA)
• Where N0 and NT are the number of test cases
  with correct predictions and the total number of
  cases in the test sample, respectively
• The overall misclassification rates (rE1 and rE2)
• Where N1 is the number of test cases where a
  buy/sell signal is misclassified as a hold
  signals or vice versa. N2 is the test cases where
  a sell signal is classified as a buy signal and
  vice versa.

From a traders point of view, the
misclassification of a hold signal as a buy or
sell signal is a more serious mistake than
misclassifying a buy signal or a sell signal as a
hold signal.
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Trading Simulations

• Two types of trading simulations were used
• Response to the predicted trading signals which
  might be a buy, hold or a sell signal
• Do not participate in trading but hold the
  initial shares in hand, and keep the money in
  hand until the end of the period.

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First Trading Simulation

• Let the value of the initial money in hand be M0
  and the number of shares at the beginning of the
  period be S0.
• S0 M0/P0, where P0 is the Close price of the
  AORD on the day before the starting day of the
  trading period.
• Also let Mt, St, Pt, V St be the money in hand,
  number of shares, Close price of the AORD, value
  of shares holding on the day t (t1, 2, ..., T),
  respectively.
• This simulation assumes that always a fixed
  amount of money is used in trading regardless of
  whether the trading signal is buy or sell.
• Suppose the trading signal at the beginning of
  the day t is a buy signal. Then the trader spends
  F minF0,Mt-1 amount of money to buy a number
  of shares at a rate of the previous days Close
  price.

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First Trading Simulation
Suppose the trading signal is a hold signal, then
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First Trading Simulation

• Let the trading signal at the beginning of the
  day t is a sell signal. Then the trader sells
  S0min(F0/Pt-1), St-1 amount of shares.
• At the end of the period (day T) the total value
  of money and shares in hand

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Second Trading Simulation

• In this case the trader does not participate in
  trading. Therefore, Mt M0 and St S0 for all
  t1, 2, ..., T. However, the value of the shares
  changes with the time and therefore, the value of
  shares at day t, V St S0 Pt.
• At the end of the period (day T) the total value
  of money and shares in hand

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Results Obtained from Network Training
Results obtained from training neural network,
NNDLS
Results obtained from training neural network,
NNOLS
Results obtained from training neural network,
NNTCC
Results obtained from training neural network,
NNCC
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Comparison of the Performance of the New
Algorithms

• Average (over six windows) Classification/
  Misclassification rates of the best prediction
  results corresponding to NNOLS

Average (over six windows) Classification/
Misclassification rates of the best prediction
results corresponding to NNDLS
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Comparison of the Performance of the New
Algorithms

• Average (over six windows) Classification/Misclas
  sification rates of the best prediction results
  corresponding to NNCC
• Average (over six windows) Classification/Misclas
  sification rates of the best prediction results
  corresponding to NNTCC

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Trading Simulations

• Average rate of return (over six windows)
  obtained by performing the first trading
  simulation on the best prediction results
  produced by each neural network algorithm

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Conclusions

• The results obtained from the experiments show
  that the neural network algorithms, based on the
  modified OLS error functions introduced by this
  study produced better predictions of trading
  signals of the AORD.
• Of the two algorithms, the one based on ETCC
  showed the better performance.
• This network prevented serious misclassifications
  such as misclassification of buy signals to sell
  signals and vice versa and also predicted trading
  signals with a higher degree of accuracy.
• The algorithms proposed in this paper can be used
  to predict the trading signals, buy, hold and
  sell, of any given stock market index or a sector
  of a stock market index.