Stock Trading Following Stock Price Index Movement Classification Using Machine Learning Techniques

Transcription

1 Stock Trading Following Stock Price Index Movement Classification Using Machine Learning Techniques 6.1 Introduction Trading in stock market is one of the most popular channels of financial investments. But it is always hard to decide the best time to buy or sell due to the highly fluctuating and dynamic behavior of stock market. Technical indicators are the primary interest for most of the researchers to monitor the stock prices and to assist investors in setting up trading rules for buy sell hold decisions. Technical indicators are produced based on historical stock data. So trading decision taken based on particular technical indicators may not always be more profitable. In literature various data mining and artificial intelligence tools has been applied to analyze technical indicators in an attempt to find the best trading signals [74-82]. Gaining profit or loss from stock trading ultimately depends on analysis of future movement of highly fluctuating and irregular stock price values. Successful classification of up and down movements in stock price index values may not only helpful for the investors to make effective trading strategies, but also for policy maker to monitor stock market. Keeping track of upswings and downswings over the history of individual stocks will reduce the uncertainty associated to investment decision making. Investors can choose the best times to buy and sell the stock through proper analysis of the stock trends. Hence developing more realistic models to predict the rise and fall situations in the stock price index movement is a big challenge for most of the investors and professional analysts. In literature a number of models combining technical analysis with computationally intelligent techniques are available for prediction of stock price index movements [71-73]. This chapter contributes to literature by developing a classification model for stock price index movement classification followed by stock trading decision prediction. In the first part of the work, a classification model using the computationally efficient functional link artificial neural network (CEFLANN) is proposed for classifying the stock price index movements as up and down movements. Instead of training the CEFLANN network using traditional back propagation algorithm, the ELM 136

2 learning is proposed for the network. Six technical indicators calculated from the historical stock index price values are selected as inputs of the proposed model. The proposed model is compared with two other familiar networks used for classification Like Chebyshev FLANN [11, 42, 126, and 127] and Radial Basis Function (RBF) Network [9, 10, 83, and 85]. Performance of all the three networks is compared with both back propagation and ELM learning techniques, over two benchmark financial time series data set. Classification accuracy and F-measure are used to validate the model performance. Further the work is extended for generating the stock trading decisions. For stock trading the same CEFLANN model trained with ELM is used. The output from the CEFLANN model is transformed in to a simple trading strategy with buy, hold and sells signals using suitable rules. The model performance is evaluated based on profit percentage obtained during test period. The CEFLANN model is also compared with some other known machine learning techniques like support vector machine (SVM) [71, 72, 128, 130], Naive Bayesian model, K nearest neighbor model (KNN) [78, 130] and decision tree (DT) [129] model. The details of CEFLANN model and ELM training are discussed in chapter 2. So this chapter highlights the detailed steps of stock price index movement classification and stock trading using an ELM based CEFLANN. 6.2 Detailed Steps of Classification of Stock Price Index Movement In this section the prediction of stock price index movement is cast as a classification problem with two class values: one for the upward movement in stock index value and another for the downward movement in stock index value. A classification model using the computationally efficient functional link artificial neural network (CEFLANN) is proposed for classifying the stock price index movements as up and down movements. Instead of training the CEFLANN network using traditional back propagation algorithm, the ELM learning is proposed for the network. Few popular technical indicators derived from historical stock index prices are taken as input for the network where as the up down class values indicating the direction of daily change in stock index closing price are taken as output during training of the network. The frame work figure of the proposed model is shown in Fig

3 Fig. 6.1 Proposed Model for classification of Stock Price Index Movement Step 1: Input Output Preparation In literature, researchers have used different types of technical indicators for analysis of future movement of stock index values. In this study, total 6 popular technical indicators are chosen as input to the proposed model. The technical indicators are calculated from historical prices as follows: Simple Moving Average (SMA): It is the simple statistical mean of previous n day closing price, that normally smoothies out the price values. In this study value of n is set to 25. MA n 1 n n i 1 cp( i) (6.1) Where cp(i) is the closing price. Moving Average Convergence and Divergence (MACD): The MACD shows the relationship between two exponential moving averages of prices. 138

4 MACD EMA 12 EMA EMA( i) ( CP( i) EMA( i 1)) Multiplier EMA( i 1) where Multiplier 2/( no of 26 days to be considered 1) (6.2) Stochastic KD: Stochastic provides a mean of measuring price movement velocity. K% measures the relative position of current closing price in a certain time range, whereas D% specifies the three day moving average of K%. cp( i) L K%( i) H L n n n 100 (6.3) D%( i) ( K%( i 2) K%( i 1) K%( i))/3 Where cp(i) is the closing price, L n is the lowest price of last n days, H n is the highest price of last n days. Relative Strength Index (RSI): RSI is a momentum indicator calculated as follows: 100 RSI RS Average of n day' s up closes where RS Average of n day' s down closes (6.4) Larry William s R%: William s R% is a stochastic oscillator, calculated as follows: H n cp( i) R%( i) 100 H L n n (6.5) Where cp(i) is the closing price, L n is the lowest price of last n days, H n is the highest price of last n days. The direction of daily change in stock price index is categorized as 0 or 1. The direction value 1 represents that index value at time t is greater than time t- 1indicating an upward movement and direction value 0 represents that index value at time t is smaller than time t-1indicating a downward movement. These 0 and 1 values are used as class values in the classification model. The up down movements used in the training stage of the network are calculated from historical closing prices using the following rule: 139

5 If cp(i)>cp(i-1) then signal is up (1) Else signal is down (0) Step 2: Data Normalization Originally the six technical indicator values represent continuous values in different ranges. So the input data is scaled in the range 0 to 1 using the min max normalization as follows: y x x x max min x min (6.6) Where y = normalized value. x = value to be normalized x min = minimum value of the series to be normalized x max = maximum value of the series to be normalized Scaling the input data ensures that larger value input attributes does not overwhelm smaller value inputs. Step 3: Creating Network Structure CEFLANN is a single layer neural network with only an output layer. The output layer contains a single neuron to provide the corresponding class value of the given input sample. The normalized values of the six chosen technical indicator values are given as input to the network. The network performance varies based on the selected expansion order and learning technique used. So a suitable order is chosen for expansion. The associate parameters used in expansion are initialized randomly. Step 4: Training and Testing the Network For training the network using ELM, data from the training set are fed to the network, so that the network can adjust its weights. The output weights of the network are obtained analytically using a robust least squares solution including a regularization parameter. The regularization parameter value is set through a parameter selection process. Finally the class values of the training and testing samples are obtained by comparing the weighted sum of the expanded inputs with a specified threshold value. 140

6 Step 5: Performance Evaluation The performance of the model is evaluated based on classification accuracy and F- measure value. Computation of these evaluation measures are done by estimating Precision and Recall values. In a classification task, the precision for a class is obtained as a ratio of the number of true positives (i.e. the number of items correctly labeled as belonging to the positive class) to the total number of elements of the positive class. Recall is defined as a ratio of the number of true positives divided by the total number of elements belongs to the positive class. True Positive Pr ecision True Positive False Positive (6.7) True Positive Re call True Positive False Negative True Positive True Negative Accuracy True Positive False Positive True Negative False Negative (6.8) (6.9) 2 Precision Recal F measure Precision Recal (6.10) 6.3 Detailed Steps of Stock Trading In this section a novel trading model using the CEFLANN network is proposed to generate the short term trading decisions more effectively. The six popular technical indicators used in stock price index movement classification are also used as the input features for this model. The CEFLANN network is applied to capture the nonlinear relationship exists between the technical indicators and trading signals. Predicting trading decisions is also cast as a classification problem with three class values representing the buy, hold and sell signals. Instead of using three discrete class values during training of the network, a continuous trading signal within range 0 to 1 are fed to the network. The new trading signals in the range 0 to 1 can provide more detailed information regarding stock trading related to the original price variations. Further the output trading signals are used to track the trend and to produce the trading decision based on that trend using some trading rules. The frame work figure of the proposed model is shown in Fig

7 Fig. 6.2 Proposed Model for Stock Trading The detailed steps of stock trading using CEFLANN model trained with ELM are as follows: Step 1: Extract Technical indicators In this study, six popular technical indicators i.e. MA 15, MACD 26, K 14, D 3, RSI 14, WR 14 are used to monitor the future movement of stock prices and in setting up trading rules for buy sell hold decisions. The technical indicators are calculated from the historical stock prices as discussed in section 6.2. Step 2: Trend Analysis using Technical Indicators Gaining profit or loss from stock trading ultimately depends on analysis of future movement of stock price values. In literature different technical indicators are used for successful classification of up and down movements in stock price index values. In this 142

8 study rules using MA are used for classifying the stock market movement as upward (Uptrend) or downward (downtrend) as follows: If closing price value leads its MA 15 and MA 15 is rising for last 5 days then trend is Uptrend i.e. trend signal is 1. If closing price value lags its MA 15 and MA 15 is falling for last 5 days then trend is Downtrend i.e. trend signal is 0. However, if none of these rules are satisfied then stock market is said to have no trend. Step 3: Trading Signal Generation from Trend Analysis Instead of using the discrete trend signal in training of network, trading signals in range 0 to 1 are generated using momentum of the stock prices. The new trading signals are not only able to reflect the price variation, but also provide more detailed information to make precise stock trading decision. The continuous trading signals Tr i are generated using following rules: For up trend: [ cpi min cp] Tri [maxcp min cp] min cp min( cp, cp i 1 maxcp max( cp, cp i i, cp i 1 i 2, cp ) i 2 ) (6.11) For down trend: Tr i [ cpi min cp] 0.5 [max cp min cp] (6.12) Where cp i, cp i+1, cp i+2, are the closing price of the ith, (i+1)th, (i+2)th trading days respectively. Step 4: Data Normalization Originally the six technical indicator values represent continuous values in different ranges. So the input data is scaled in the range 0 to 1 using the min max normalization as given in equation (6.6). 143

9 Step 5: Network Structure Creation and Training using ELM The same structure of CEFLANN network used for stock price index movement classification is used for stock trading. The network has six inputs representing the normalized six technical indicator values and one output neuron for producing the trading signals. Initially with a suitable expansion order and random values of associated parameters used in expansion the network is created. Further with the ELM learning, the output weights of the network is obtained analytically using a robust least squares solution including a regularization parameter. The regularization parameter value is set through a parameter selection process. Step 6: Trend Determination from Output Trading Signal After the training process, a new set of test data is applied to the trained network to produce a set of outputs. Output value of the network is the trading signal i.e. the continuous value in range 0 to 1. To make trading decision, it is first required to track the trend and decide when to trade. The uptrend and down trend is classified from the output trading signals (OTR i ) using the following rules: If OTr i > mean (Tr) predicted trend is up(1) else predicted trend is down(0) Step 7: Trading Point Decision from Predicted Trend After obtaining the stock movement direction, trading points are obtained using straightforward trading rules as follows: If the next day trend=uptrend then decision is BUY If Buy decision exists then HOLD If the next day trend=downtrend then decision is SELL If SELL decision exists then HOLD Step 8: Profit Calculation The main parameter adopted for performance evaluation is the profit percentage obtained during the test period. The profit percentage is generated from a combination of buy and sells transactions as follows: 144

10 Profit % ( cp Where k number of transactions cp cp si bi k i 1 si cp selling price of buying price of bi i i th th ) / cp bi 100 transaction transaction (6.13) 6.4 Empirical Study In this study the performance of the CELANN model is validated for both stock price index movement classification and stock trading problem by applying it on two stock index data sets. The proposed model is compared with two other familiar networks like Chebyshev FLANN (CHFLANN) and Radial Basis Function (RBF) Network for stock price index movement classification problem. The CEFLANN model is also compared with some other known classifiers like support vector machine (SVM), Naive Bayesian model, K nearest neighbor model (KNN) and decision tree (DT) model for stock trading problem Experimental Outputs and Result Analysis for Stock Price Index Movement Classification Five years of historical stock index price values of two stock indices (BSE SENSEX and S&P 500) are used in this study. The detail of the data set is given in Table 6.1. Number of increase and decrease cases in each year in the entire dataset of BSE SENSEX and S&P 500 data set is shown in Table 6.2. Both the data sets are divided into training and testing sets. For BSE data set the training set consists of 650 patterns and 569 patterns are used for testing and for S&P dataset the training set consists of 650patterns leaving the 583 patterns for testing. The training set comprises nearly 50% samples from each year of the data set. Table 6.1 Data set Description Data Set BSE SENSEX S&P 500 Period 4- Jan to 31-Dec Jan to 31-Dec

11 Table 6.2 Number of increase and decrease cases in each year in the entire dataset of S&P 500, BSE SENSEX Data set Year Increase Decrease Total BSE SENSEX Total S&P Total In literature, researchers have used different types of technical indicators for analysis of future movement of stock index values. In this study, total 6 popular technical indicators are chosen as input to the proposed model. Table 6.3 summarizes the statistical analysis of the selected technical indicators for both the stock indices. To measure the generalization ability of the network initially the dataset is divided in to a single train and test set. Then simulation is done by passing each set of training and testing data to the individual models for 20 times. The average performance out of these 20 runs has been reported for both the dataset. For CEFLANN with order p, input size s, the number of associated parameters used in functional expansion is p(s+1) and number of weights between expanded pattern and output neuron is (p+s). Hence total number of unknown parameters need to be tuned by a learning algorithm is (p+s) + p(s+1). Using ELM the p(s+1) number of associated parameters are chosen randomly, and the remaining (p+s) number of parameters are obtained using the least square solution with regularization parameter. The performance of the proposed model depends on different factors like the order of expansion, value of regularization parameter, input 146

12 space size and so on. So initially through a number of simulations the controlling parameters of the model are derived. Table 6.3 Summary statistics of selected technical indicators Data set Technical Indicators Min Max Mean Std SMA e e e e+003 MACD BSE SENSEX K% D% RSI LW R% SMA e e e MACD S&P 500 K% D% RSI LW R% The mean accuracy and F- measure obtained, out of the 20 independent runs are reported in Table 6.4 with 3 different expansion order and 4 different regularization parameter values for both the data set. With the higher expansion order no sign of improvement in the classification accuracy is observed. Again with higher expansion order, size of parameter space will be higher and accordingly the training time will be more. Fig. 6.3 and 6.4 shows the classification accuracy of CEFLANN with order 2 and different regularization parameter values for both the data sets respectively. Performance comparisons of the proposed model with two other familiar networks like Chebyshev FLANN and Radial Basis Function (RBF) Network are listed in Table

13 Performance of all the three networks is compared with both back propagation and ELM learning techniques as shown in Fig. 6.5 and 6.6. Table 6.4 Performance comparison of CEFLANN+ELM with different parameter settings Data set Expansion order Regularization Parameter Training Testing Accuracy F- measure Accuracy F- measure BSE SENSEX S&P

14 test accuracy test accuracy Table 6.5 Performance comparison of CEFLANN+ELM with other networks Dataset Network Learning Algorithm Training Testing Accuracy F- measure Accuracy F- measure BSE SENSEX S&P 500 CEFLANN CHFLANN RBF CEFLANN CHFLANN RBF ELM BP ELM BP ELM BP ELM BP ELM BP ELM BP classification accuracy of CEFLANN with order 2 for BSE SENSEX data set classification accuracy of CEFLANN with order 2 for S&P 500 data set regularization parameter values regularization parameter values Fig. 6.3 Classification accuracy of CEFLANN with different regularization parameter values and order 2 (BSE SENSEX) Fig. 6.4 Classification accuracy of CEFLANN with different regularization parameter values and order 2 (S&P 500) 149

15 test accuracy test accuracy Performace comparision of three classifiers over BSE SENSEX dataset ELM BP : CEFLANN 2:CHFLANN 3:RBF Fig. 6.5 Performance comparison of three networks over BSE SENSEX Data set Performace comparision of three classifiers over S&P500 dataset ELM BP : CEFLANN 2:CHFLANN 3:RBF Fig. 6.6 Performance comparison of three networks over S&P500 data set Summarizing the results, the following inference is drawn: A comparison of back propagation and ELM learning over CEFLANN model shows clearly the superior performance of CEFLANN trained using ELM approach in comparison to back propagation. 150

16 Again from the experimental result analysis it is clearly apparent that the proposed model provides superior classification accuracy and F- measure value compared to CHFLANN and RBF model. Analyzing the performance of the proposed model with different expansion order and regularization parameter values, it is observed that, the model provides better result with order 2 and regularization parameter value 0.6 for BSE SENSEX dataset and with order 2 and regularization parameter value 0.4 for S&P500 dataset Experimental Outputs and Result Analysis for Stock Trading After successful prediction of stock price index movement the CEFLANN network trained with ELM is used for predicting stock trading decision points. Same five years of historical stock index price values of two stock indices (BSE SENSEX and S&P 500) are used in this study. Initially the six technical indicators are extracted from the historical prices and normalized using min max normalization to be fed as input to the network. As the aim of the study is to derive short term trading points from trend analysis, so MA 15 has used for finding initial up down movements of the stock prices. Instead of using discrete value as output during training of the network, continuous trading signals are generated from the trend and used during training process. Both the data sets are divided into training and testing sets. For BSE data set the training set consists of 1000 patterns and remaining 208 patterns are used for testing and for S&P dataset the training set consists of 1000 patterns leaving the 221 patterns for testing. The simulation is done by passing each set of training and testing data to the individual models for 20 times. The average performance out of these 20 runs has been reported for both the dataset. The trading signal generated from CEFLANN model for both the dataset are shown in Fig. 6.7 and 6.8. Fig. 6.9 and 6.10 represents the initial trading points generated using the technical indicator MA 15. Trading points predicted by using the proposed model for both the data set are shown in Fig and The overall performance of the model compared to other soft computing techniques like SVM, Naïve Bayesian, KNN and decision tree (DT) for the two dataset are shown in Table 6.6 and 6.7 respectively. Through a series of experimental tests, the proposed model consistently generates highest profit among others. 151

17 Closing price Closing price Trading signal generated from CEFLANN Trading signal generated from CEFLANN Output of CEFLANN for BSE dataset trading signal avg of trading signal Output of CEFLANN for S&P500 dataset trading signal avg of trading signal Days Fig. 6.7 Output trading signal obtained from CEFLANN model for BSE SENSEX data set Days Fig. 6.8 Output trading signal obtained from CEFLANN model for S&P500 data set 2.9 x 104 Actual Buy and Sell signals (BSE) closing price buy sel Days Fig. 6.9 Initial Trading points generated using MA 15 for BSE SENSEX data set 2100 Actual Buy and Sell signals(s&p500) closing price buy sel Days Fig Initial Trading points generated using MA 15 for S&P500 data set 152

18 Closing price Closing price 2.9 x 104 Buy and Sell signals generated from CEFLANN (BSE) closing price buy sel Days Fig Trading points from CEFLANN model for BSE SENSEX data set 2100 Buy and Sell signals generated from CEFLANN (S&P500) closing price buy sel Days Fig Trading points from CEFLANN model for S&P500 data set Table 6.6 Performance comparison of stock trading models on BSE SENSEX data set Performance Metrics No. of Buy signals No. of hold signals No. of sell signals Actual (Using MA 15 ) CEFLANN SVM Naïve Bayesian KNN Profit % DT 153

19 Table 6.7 Performance comparison of stock trading models on S&P500 data set Performance Metrics No. of Buy signals No. of hold signals No. of sell signals Actual (Using MA 15 ) CEFLANN SVM Naïve Bayesian KNN Profit % DT 6.5 Summary Development of effective stock market trading strategies depends on accurate classification of stock price index movements. Successful classification of up and down movements in stock price index values usually affects the buying and selling decision of financial traders. It may promise attractive benefits for investors. Hence in this chapter, a classification model using the computationally efficient functional link artificial neural network (CEFLANN) with ELM learning approach is proposed for classifying the stock price index movements as up and down movements. Two other familiar networks like Chebyshev FLANN and Radial Basis Function (RBF) Networks are also used for comparative study. It is clearly demonstrated that the CEFLANN model completely outperforms the other two networks. Further the work is extended for generating the stock trading decisions. For stock trading the same CEFLANN model trained with ELM is used. The output from the CEFLANN model is transformed in to a simple trading strategy with buy, hold and sells signals using suitable rules. From the experimental result analysis it is clearly apparent that the proposed model provides superior profit percentage compared to some other known computationally intelligent techniques like support vector machine (SVM), Naive Bayesian model, K nearest neighbor model (KNN) and decision tree (DT) model. Hence instead of taking trading decision based on particular technical indicators, it is more profitable to take trading decision using combination of technical indicators with computational intelligence tools. 154