Forecasting Stock Price Index Using Artificial Neural Networks in the Indonesian Stock Exchange
Soukkhy Tiphimmala
Prof. Dr.J. Sukmawati Sukamulja
UNIVERSITY OF ATMA JAYA YOGYAKARTA 2014
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ABSTRACT
Stock price index is the initial significant factor influencing on investors' financial decision making. That's why predicting the exact movements of stock price index is considerably regarded. This study aims at evaluating the effectiveness of using technical indicators, such as A/D Oscillator, Moving Average, RSI, CCI, MACD, etc. in predicting movements of Indonesian Stock Exchange Price Index (IDX). An artificial neural network is employed for stock price index forecasting. The existing data are achieved from Yahoo.Finance. To capture the relationship between the technical indicators and the levels of the index in the market for the period under investigation, a back propagation neural network is used. The statistical and financial performance of this technique is evaluated and empirical results revealed that artificial neural networks are fairly good tools for financial market predicting.
Keywords: Forecasting, prediction, stock price index, technical indicators,
artificial neural networks (ANN)
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Table of Contents
ABSTRACT ...............................................................................................................ii List of Tables ........................................................................................................... viii List of Figures ............................................................................................................ xi ABBREVATIONS .................................................................................................. xiv CHAPTER 1 INTRODUCTION ................................................................................ 1 1.1. Problem Identification......................................................................................... 5 1.2. Objective of the Research ................................................................................... 6 1.4. Scope of the Research ......................................................................................... 8 1.5. Organization of the Thesis .................................................................................. 9 CHAPTER 2 LITERATURE REVIEW ................................................................... 10 2.1 Artificial Neural Network ................................................................................. 10 2.2 Review of previous researches .......................................................................... 11 2.3 Learning Paradigms in ANNs ........................................................................... 14 CHAPTER 3 RESEARCH METHODOLOGY ...................................................... 20 3.1 Statistical Performance Evaluation of the Model.............................................. 22 3.2 Financial Performance Evaluation of the Model .............................................. 24 3.3 Research Data................................................................................................... 25 3.4 Data preparation ............................................................................................... 26
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3.5 Variable Calculation......................................................................................... 26 CHAPTER 4 DESCRIPTIVE STATISTICS .......................................................... 31 CHAPTER 5 RESEARCH RESULTS AND ANALYSIS ..................................... 36 5.1 Comparison of Financial Performance.............................................................. 36 5.2 Comparison of Statistical Performance ............................................................. 44 CHAPTER 6 CONCLUSION .................................................................................. 48 REFERENCES ......................................................................................................... 53 Apendix A: Matlab code........................................................................................... 57 A. Preprocess code ................................................... Error! Bookmark not defined. B. Training code ....................................................... Error! Bookmark not defined. C. Testing code......................................................... Error! Bookmark not defined.
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List of Tables
Table 1. The number of sample in the entire data set ............................................... 25 Table 2. Selected technical indicators and their formulas ........................................ 27 Table 3. Defined Variables ....................................................................................... 29 Table 4. ANN parameter levels tested in parameter setting ..................................... 32 Table 5. Summary statistics for the selected indicators ............................................ 33 Table 6. Three parameters for training and testing of ANN model .......................... 37 Table 7: Testing with parameter combination (10, 0.2 , 0.5, 1e6) ............................ 38 Table 8. Testing with parameter combination (30, 0.3, 0.5, 1e6) ............................. 38 Table: 9. Testing with parameter combination (50, 0.2, 0.5, 1e-6) .......................... 39 Table 10. Summary of the best forecasting, parameters (10, 0.2 , 0.5, 1e6) ............ 40 Table 11. Financial performance of ANN model ..................................................... 42 Table 12. The empirical result of other research ...................................................... 44 Table: 13 the best statistic & financial performance ............................................... 45 Table 14. Statistical performance of ANN model .................................................... 47
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List of Figures
Fig. 1 An artificial neural network is an interconnected group of nodes................. 11 Fig. 2 A Neural network with three-layer feed forward .......................................... 16 Fig. 3 Tan-Sigmoid Transfer Function and Linear Transfer Function ................. 31 Fig. 4 Data preparation (actual technical parameters & normalized technical parameters) ...................................................................................................... 34 Fig. 5 Training process of ANN model ................................................................... 34 Fig. 6 Testing of ANN model .................................................................................. 35 Fig.7 Predict next trading day, by entering new data to the network ...................... 35 Fig. 8 Training & Forecasting performance (%) of ANN model for a whole data set (n = 50, η = 0.2, μ = 0.5, ep = 1e6). ..........................................................41
Fig. 9 Forecasting performance (%) of ANN model for various η values .............. 43
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ABBREVATIONS
GDP : gross domestic product IA
: artificial intelligent
ANN : artificial neural network IDX
: Indonesian Stock Index
JKSE : Jakarta Stock Exchange (Pervious name of IDX) MAE : mean absolute error RMSE : root mean square error MAPE : mean absolute percentage error R2
: goodness of fit
APE
: absolute percentage error
PO
: predicted output
AO
: actual output
CCI
: commodity channel index
MACD: moving average convergence divergence ROC : price-rate-of change RSI
: relative strength index
PR
: predicted rate (forecasting rate)
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n
: neuron
η
: learning rate
μ
: momentum constant
ep
: epoch
IT
: information technology
LSM : The Libyan Exchange Stock Market TEPIX : The Tehran Exchange Price Index
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CHAPTER 1 INTRODUCTION
Trade decisions on a stock market are made on the basis of predicting the trend which it is driven by many direct and indirect factors. Effective decisions depend on accurate prediction. Even though there have been many empirical researches which deal with the issue of predicting stock price index; most empirical findings are associated with the developed financial markets. There are few researches exist in the literature to predict the direct of stock price index movement in emerging markets, especially in Indonesian Stock exchange. Accurate predictions of movement of stock price indexes are very important for developing effective market trading strategies (Leung et al. 2000) the stock market is essentially dynamic, nonlinear, complicated, nonparametric, and chaotic in nature (Abu-Mostafa & Atiya 1996). In addition, stock market is affected by many macro economical factors such as political events, firms’ policies, general economic conditions, investors’ expectations, institutional investors’ choices, movement of other stock market,
and psychology of investors etc. (Tan et al. 2007). So far, there are many techniques are applied to predict the market in order to maximize profit and minimize risks, it can be categorized into four groups; these techniques are included fundamental analysis, technical analysis, time series analysis, and machine learning. The results from these techniques is different, for example the fundamental analysis is used to define models which
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calculate the future price according to current indicators such as the gross domestic product (GDP), consumer price index, interest rate and exchange rate; the technical analysis is used for forecast the future price direction by studying past market data - primarily stock price and volume. The technical analysis basically use trading rules such as single moving trend, composite moving trend, and channel breakout. However, these techniques don’t have ability to learn nonlinear variables as artificial intelligent (IA) approach does. Artificial neural network (ANN) technique is one of data mining techniques that is gaining increasing acceptance in the business area due to its ability to learn and detect relationship among nonlinear variables. Also, it allows deeper analysis of larger set of data especially those that have the tendency to fluctuate within a short of period of time. If stock market return fluctuations are affected by their recent historic behaviour, neural networks which can model such temporal stock market changes can prove to be better predictors (Tang et al. 1991). The elasticity and adaptability advantages of the artificial neural network models have attracted the interest of many other researchers (Adebiyi Ayodele A. et al 2012). Since the last decade, the artificial neural network models have been used extensively in various branches such as computer science, engineering, medical and criminal diagnostics, biological investigation, analysing the business data, and econometric analysis research. Also they can be used for analysing relations among economic and financial phenomena, forecasting, data filtration,
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generating financial time-series, and optimization (Shachmurove & Witkowska 2000). Why neural network is best for prediction? Because there are several
distinguished features that propound the use of neural network as a preferred tool over other traditional models of prediction. Artificial neural networks are nonlinear in nature and where most of the natural real world systems are non linear in nature, artificial neural networks are preferred over the traditional linear models. This is because the linear models generally fail to understand the data pattern and analyse when the underlying system is a nonlinear one. ANNs are data driven models. It has ability to discover nonlinear relationship in the input data set without a priori assumption of the knowledge of relation between the input and the output. The input variables are mapped to the output variables by squashing or transforming by a special function known as activation function. They independently learn the relationship inherent in the variables from a set of labelled training example and therefore involves in modification of the network parameters (Soni 2011). It is of interest to study the extent of stock price index movement predictability using data from emerging markets such as of the Indonesia stock market. This emerging market’s performance is incredible for a long period of time. For example, in December 2002, composite index stand at 424.495 points, it was rapidly upwards to 2,745.826 at the end of 2007 and then decreased to 1,135.408 at the end of 2008 (-50.64%) due to the impact of global financial crisis and upwards again at the beginning of 2009 until
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November 2012, it reached 4,317. 277 points and 4,985.58 points on May 28, 2014. On an average day, transactions worth of between IDR 5 to 6 trillion (US $520 million to US $620 million), and it has an average daily volume of about six billion shares. In 2012, foreign investors purchased assets in the Indonesian capital markets totaled IDR 19.55 trillion (about US $2 billion). In the period of January to March in 2013, net foreign purchases already stood at IDR 18.5 trillion nearly 100% increase comparing to the previous year, which shows the attractiveness of these markets (David 2013). Market capitalization has increased 412% from IDR 801 trillion in 2005 to IDR 4,099.34 trillion November 2012. In term of trade value, showed a significant increased after 2006 (US$ 49.4 billion) to US$114.9 billion in 2007 and quite stable since then i.e. eleven months of 2012 totaled of US$104.6 billion. There are very little previous researches exist (accessible) in related to stock price prediction by using ANN techniques at IDX, such as Putra and Kosala (2011) used ANN to predict intraday trading signals and Veri and Baba (2013) forecasting the next closing price. As we understand the characteristic that all stock markets, including IDX, have in common is the uncertainty, which is related with their short and longterm future state. This feature is undesirable for the investor but it is also unavoidable whenever the stock market is selected as the investment tool. The best that one can do is to try to reduce this uncertainty. In this research ANN model is proposed to forecast the movement of stock price in the daily IDX Index.
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1.1. Problem Identification How to forecast the stock price index? The stock market index direction
prediction is regarded as one of the crucial issues in recent financial analysis studies (Wang & Choi 2013). Many techniques are employed to predict stock prices in the stock markets but the past results are being questioned. Generally, there are three schools of thought in terms of the ability to profit from the equity market. The first school believes that no investor can achieve above average trading advantages based on the historical and present information. The major theories include the Random Walk Hypothesis and the Efficient Market Hypothesis (Peters 1991). The Random Walk Hypothesis states that prices on the stock market wander in a purely random and unpredictable way. Each price change occurs without any influence by past prices. The Efficient Market Hypothesis states that the markets fully reflect all of the freely available information and prices are adjusted fully and immediately once new information becomes available. If this is true then there should not be any benefit for prediction, because the market will react and compensate for any action made from these available information. The second school’s view is the so-called fundamental analysis. It looks in depth at the
financial conditions and operating results of a specific company and the underlying behavior of its common stock. The value of a stock is established by analysing the fundamental information associated with the company such as accounting, competition, and management. The fundamental factors are overshadowed by the speculators trading.
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Technical analysis assumes that the stock market moves in trends and these trends can be captured and used for forecasting. Technical analysis belongs to the third school of thought. It attempts to use past stock price and volume information to predict future price movements The technical analyst believes that there are recurring patterns in the market behavior that are predictable. In fact, there is not any research proved the existing of such patterns due to each stock market has different characteristics, depending on the economies they are related to, and varying from time to time. Most of the techniques used by technical analysts have not been shown to be statistically valid and many lack a rational explanation for their use. However, technical analysis has its value on forecasting. Artificial Neural Networks are regarded by many as one of the more suitable techniques for stock market forecasting (Yao & Tan 2001). It has been demonstrated to be an effective technique for capturing dynamic non-linear relationships in stock markets, while technical analysis techniques unable to do so. 1.2. Objective of the Research
The core objective of this research is to forecast the direction of movement in the daily JKSE or IDX using artificial neural network, also to compare a financial performance model and statistical model of ANN on its precision of stock price prediction. At the same times, its empirical result will be comparing with some recently researcher’s works in this market that used ANN models. Also, this research will seek to prove against a validity of the
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Efficient Market Hypothesis and the Random Walk Hypothesis for short-term trading advantages in this stock market, which is considered as one of the most important emerging markets in Asia.
1.3. Contribution of the Research
Recently, a number of researchers have explored artificial intelligence techniques such as ANNs to solve financial problems significantly increased, but most has targeted the United States market (Suchira Chaigusin, 2011). There have been limited attempts to research stock markets of developing economies such as Indonesia. At the beginning of this research, the author find that there are some previous research using intelligent approach in this market, but there are not many existing research using artificial neural network technique, specifically, to predict the index movements of the JKSE. The major contributions of this study are to demonstrate and verify the predictability of stock price index direction using the financial and statistical performances of ANN model. It also benefit to other researchers/students who are interested in studying stock market price movement with ANN model. This study is one step along the path towards applying ANN to the IDX in order to clarify and predict stock performances. Enhancing the use of ANN in financial areas and contributing incrementally to the growing knowledge base of this financial forecasting field.
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1.4. Scope of the Research
As there are many ANN research techniques were used to predict stock price movement index mentioned in 1.1; some of recently research are using international market indicators, technical & fundamental indicators as inputs which it’s called “hybrid”. But some try to combined a lot of indicators as
input variable. However, the research finding indicated that many indicators/ or higher number of input variables is not mean such forecasting technique (model) will give a result more accuracy. In this research, we will attempt to forecast daily stock price movement at JKSE, using financial performance and statistical performance evaluations of ANN models. The data collection with total period of 9 years and 5 months, starting from January 3, 2005 to May 28, 2014. The reason we start from 2005 because the index prices at the beginning 2005 reached RP1.000 and has dramatically increased until the end of 2007 and then in the direction of decrease. At the beginning of 2009 index prices had in the direction of increased again. So, we would like to see how ANN model perform in the different period and direction. The data be divided into two separate sets, a period of January 3, 2005 to December 30, 2010 is for network training purposes. From January 3, 2005 to May 28, 2014 is for testing the predictive ability of the network. A three-layered feed-forward ANN model will be constructed (see Figure. 2). This ANN model consists of an input layer, a hidden layer and an output layer, each of which is connected to the other. Inputs for the network are twelve technical indicators which are represented by twelve neurons in the input layer (see table 2).
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The forecasting ability of the ANN model is accessed by using backpropagation neural network of errors such as MAE, RMSE, MAPE, and R 2, to improve their prediction performances two comprehensive parameter setting experiments for both technical indicators and the levels of the index in the market are performed. The logistic sigmoid transfer function will be used in neural network; this function converts an input value to an output ranging from 0 to 1 (see 2.3). If the connection weight is negative or (value < 0) then tomorrow close price value < than today’s price ( loss). If the value is positive
(value > 0.5) then tomorrow close price value > than today’s price (profit). As we want to see the direction of movement decrease or increase so the output will be categorized as 0 and 1. Therefore, if the forecasting value smaller than 0.5 it will be categorized as decreased direction. Published stock data will be collected from Yahoo.Finance especially daily closing price, daily high price, and daily low price of total price index . 1.5. Organization of the Thesis
This thesis is composed of six Chapters. The remaining portion of the thesis is broken up into the following Chapters: Chapter 2 describes Artificial Neural Network and related literature. Chapter 3 describes the research methodology which includes ANN modeling, research data and technical input variables. In Chapter 4 descriptive statistics are used simply to describe the sample. Chapter 5 the empirical results are summarized and discussed. Chapter 6 brief conclusion with some suggestions for the future work on the field of stock market prediction
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CHAPTER 2 LITERATURE REVIEW
2.1 Artificial Neural Network
Artificial neural network (ANN), usually called Neural Network (NN), is an algorithm that was srcinally motivated by the goal of having machines that can mimic the brain. A neural network consists of an interconnected group of artificial neurons. They are physical cellular systems capable of obtaining, storing information, and using experiential knowledge. Like human brain, the ANN’s knowledge comes from examples that they encounter. In human
neural system, learning process includes the modifications to the synaptic connections between the neurons. In a similar way, ANNs adjust their structure based on output and input information that flows through the network during the learning phase. Data processing procedure in any typical neural network has two major steps: the learning and application step. At the first step, a training database or historical price data is needed to train the networks. This dataset includes an input vector and a known output vector. Each one of the inputs and outputs are representing a node or neuron. In addition, there are one or more hidden layers. The objective of the learning phase is to adjust the weights of the connections between different layers or nodes. After setting up the learning samples, in an iterative approach a sample will be fed into the network and
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the resulting outputs will be compared with the known outputs. If the result and the unknown output are not equal, changing the weights of the connections will be continued until the difference is minimized. After acquiring the desired convergence for the networks in the learning process, the validation dataset is applied to the network for the validating step (Shahkarami A. et al. 2014).
Figure 1. An artificial neural network is an interconnected group of nodes. Source : SPE International, Colorado, USA, 16 –18April 2014.
2.2 Review of previous researches
Several economists advocate the application of neural networks to different fields in financial markets and economic growth methods of analysis (Kuan, C.M. and White, H. 1994). We focus the review of prior studies on prediction of financial market. Chen et al (2003) attempted to predict the trend of return
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on the Taiwan Stock Exchange index. The probabilistic neural network (PNN) is used to forecast the trend of index return. Statistical performance of the PNN forecasts is compared with that of the generalized methods of moments (GMM) with Kalman filter and random walk. Empirical results showed that PNN demonstrate a stronger predictive power than the GMM – Kalman filter and the random walk prediction models. Kim (2003) used SVM to predict the direction of daily stock price change in the Korea composite stock price index (KOSPI). This study selected 12 technical indicators to create the initial attributes. The indicators are stochastic K%, stochastic D%, Slow %D, momentum, ROC, Williams’ %R, A/D oscillator, disparity 5, disparity 10, OSCP, CCI and RSI. In addition, this study examined the feasibility of applying SVM in financial prediction by comparing it with back-propagation neural network (BPN) and case-based reasoning (CBR). Experimental results proved that SVM outperform BPN and CBR and provide a promising alternative for stock market prediction. Altay & Satman (2005) compared the forecasting performance artificial neural network and linear regression strategies in Istanbul Stock Exchange and got some evidence of statistical and financial outperform of ANN models. Kumar & Thenmozhi (2006) investigated the usefulness of ARIMA, ANN, SVM, and random forest regression models in predicting and trading the S&P CNX NIFTY Index return. The performance of the three nonlinear models and the linear model are measured statistically and financially via a trading experiment. The
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empirical result suggested that the SVM model is able to outperform other models used in their study. Hyup Roh (2007) introduces hybrid models with neural networks and time series model for forecasting the volatility of stock price index in two vision points: deviation and direction and the results showed that ANN-time series models can increase the predictive power for the perspective of deviation and direction accuracy. His research experimental results showed that the proposed hybrid NN-EGARCH model could be improved in forecasting volatilities of stock price index time series. Adebiyi Ayodele A. et al. (2009) presented a hybridized approach which combines the use of the variables of technical and fundamental analysis of stock market indicators for daily stock price prediction. The study used threelayer (one hidden layer) multilayer perceptron models (a feedforward neural network model) trained with backpropagation algorithm. The best outputs of the two approaches (hybridized and technical analysis) are compared. Empirical results showed that the accuracy level of the hybridized approach is better than the technical analysis approach. Liao & Wang (2010) applied a Stochastic Time Effective Neural Networks in predicting China global index and their study results showed that the mentioned model outperform the regression model. Kara et al (2011) compared neural networks performance and SVM in predicting the movement of stock price index in Istanbul Stock Exchange. The input variables in suggested models include technical indicators such as CCI, MACD, LW R%, etc. The results revealed that neural
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networks work better in prediction than SVM technique. Zhou Wang et al (2011), propose a new model to predict the Shanghai stock price. They used Wavelet De- noising- based Back propagation (WDBP) neural network. For demonstrating superiority new model in predicting, the results of it is compared with Back Propagation neural network and the total results showed that the WDBP model for forecasting index is better than BP model. Putra and Kosala (2011) try to predict intraday trading Signals at IDX they used technical indicators - the Price Channel Indicator, the Adaptive Moving Averages, the Relative Strength Index, the Stochastic Oscillator, the Moving Average Convergence-Divergence, the Moving Averages Crossovers and the Commodity Channel Index. The result of their experiments showed that the model performs better than the naïve strategy. Also Veri and Baba (2013) forecasting the next closing price at IDX, they used opening price, highest price, lowest price, closing price and volume of shares sold as experimental variables. The result showed that the most appropriate network architecture is 5-2-1 with dividing the data into two parts, with 40 training data with 95% accuracy of data and 20 test data with 85% accuracy of data. 2.3 Learning Paradigms in ANNs
The ability to learn is a peculiar feature pertaining to intelligent systems, biological or otherwise. In artificial systems, learning (or training) is viewed as the process of updating the internal representation of the system in response to external stimuli so that it can perform a specific task. This
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includes modifying the network architecture, which involves adjusting the weights of the links, pruning or creating some connection links, and/ or changing the firing rules of the individual neurons.
ANN approach learning has demonstrated their capability in financial modelling and prediction as the network is presented with training examples, similar to the way we learn from experience. In this paper, a three-layered feed-forward ANN model was structured to predict stock price index movement is given in Fig. 2. This ANN model consists of an input layer, a hidden layer and an output layer, each of which is connected to the other. At least one neuron would be employed in each layer of the ANN model. Inputs for the network were twelve technical indicators which were represented by twelve neurons in the input layer. Each neuron (unit) in the network is able to receive input signals, to process them and to send an output signal. Each neuron is connected at least with one neuron, and each connection is evaluated by a real number, called the weight coefficient, that reflects the degree of importance of the given connection in the neural network (Daniel et al. 1997). The error between the predicted output value and the actual value is backpropagated through the network for the updating of the weights. This method is proven highly successful in training of multi-layered neural networks. The network is not just given reinforcement for how it is doing on a task. Information about errors is also filtered back through the system and
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is used to adjust the connections between the layers, thus improving performance. Hidden Layer
12 Technical indicators
Input Layer
A/D Oscillator
2
CCI Larry William’s (R%)
Output Layer
MACD Momentum ROC
Direction of Movement
RSI Simple MA Stochastic K% Stochastic D% Stochastic slow (D%) Weighted MA
n Fig. 2. A Neural network with three-layer feed forward Source: Y. Kara et al. / Expert Systems with Applications 38 (2011) 5311–5319 This a supervised learning procedure that attempts to minimise the error between the desired and the predicted outputs. If the error of the validation
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patterns increases, the network tends to be over adapted and the training should be stopped. The most typical activation function used in neural networks is the logistic sigmoid transfer function. This function converts an input value to an output ranging from 0 to 1. The effect of the threshold weights is to shift the curve right or left, thereby making the output value higher or lower, depending on the sign of the threshold weight. The output values of the units are modulated by the connection weights, either magnified if the connection weight is positive and greater than 1.0, or being diminished if the connection weight is between 0.0 and 1.0. If the connection weight is negative or (value < 0) then tomorrow close price value < than today’s price (loss). If (va lue > 0.5) then then tomorrow close price value > than today’s price (profit). As
shown in Fig. 2, the data flows from the input layer through zero, one, or more succeeding hidden layers and then to the output layer. The backpropagation (BP) algorithm is a generalisation of the delta rule that works for networks with hidden layers. It is by far the most popular and most widely used learning algorithm by ANN researchers. Its popularity is due to its simplicity in design and implementation. The idea is to train a network by propagating the output errors backward through the layers. The errors serve to evaluate the derivatives of the error function with respect to the weights, which can then be adjusted. It involves a two stage learning process using two passes: a forward pass and a backward pass. The basic back propagation algorithm consists of three steps (Fig. 2). Although, the most
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commercial back propagation tools provide the most impact on the neural network training time and performance. The output value for a unit is given by the following Equation:
( ) (∑ ) {
(i = 1,2,…n)
(1)
Where y the output value is computed from set of input patterns, X i of ith unit in a previous layer, Wij is the weight on the connection from the neuron ith to j,
j
is the threshold value of the threshold function f, and n is
the number of units in the previous layer. The function ƒ(x) is a sigmoid
hyperbolic tangent function (Barndorff-Nielsen et al. 1993)
Threshold:
{
2
where ƒ(x) is the threshold function remains the most commonly applied in
ANN models due to the activation function for time series prediction in back-propagation (Najeb Masoud, 2014):
(3)
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Once the output has been calculated, it can be passed to another neuron (or group of neurons) or sampled by the external environment. In terms of the weight change, Δwij, the formula equation is given as:
(4)
where η is the learning rate (0<η<1), δj is the error at neuron j, xi is an input vector and wi the weights vector. This rule of IDX can also be rewritten as:
(5)
Although a high learning rate, η, will speed up training (because of the large step) by changing the weight vector, w, significantly from one phase to another. According to Wythoff BJ. (1993) suggests that η[0.1,1.0].
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CHAPTER 3 RESEARCH METHODOLOGY
Chaigusin (2011) mentioned that stock markets have different characteristics, depending on the economies they are related to, and, varying from time to time, a number of non-trivial tasks have to be dealt with when developing Neural Networks for predicting exchanges. It is not easy task to design artificial neural network model for a particular forecasting problem or a stock market index movement. Therefore, Modelling issues must be considered carefully because it affects the performance of an ANN. One critical factor is to determine the appropriate architecture, the number of optimal hidden layers as well as the number of hidden nodes for each layer. Other network design decisions include the selection of activation functions of the hidden and output nodes, the training algorithm, and performance measures. The design stage involves in this study to determine the input (independent) and output (dependent) layers through the hidden layers in the case where the output layer is known to forecast future values. Output of the network was two patterns 0 or 1 of stock price direction. The output layer of the network consisted of only
one neuron that represents the direction of movement. The number of neurons in the hidden layer was determined empirically. The determination of the formulation between input and output layers is called learning and through the learning process, model recognises the patters in the data and produces estimations.
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From the literature, multi-layer feed-forward ANN with back-propagation is the most commonly used architecture in this area. So, we use the three-layered feed-forward architecture (see Fig. 2). The entire data set covers the period from 03/01/2005 to 30/12/2010 for network training, while data from 03/01/2005 to 28/05/2014 is to test the predictive ability of the network. There are some steps as follow: 12 indicators has to be calculated in excel and then the results will be loaded to the network for training and testing, The data will be loaded to the network and then Normalization will take place ranging between -1, 1 so that the network will able to learn faster, training period will be in yearly because of avoiding too much of time consuming. Training process will take place within time frame (20 minutes), if the process cannot reach the goal, and then changing its learning rate and momentum constant will be needed. Looking for the best parameter combination that enhance the best output and save as “net” for testing step(forecasting) The testing process can be conducted in the new set of data to see how best the performance of the model The basic methodologies applied in this research are based on previous researches such as (Kim 2003, Mahmood Moein Aldin et al. 2012, Najeb Masoud 2014,...) The performance evaluation of the model can be described below:
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3.1 Statistical Performance Evaluation of the Model
In order to estimate the forecasting statistical performance of some methods or to compare several methods we should define error functions. Many previous research works had applied some of the following forecast accuracy measures: Mean Error (ME), Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Standard Deviation of Errors (SDE), Mean Percent Error (MPE) and Mean Absolute Per cent Error (MAPE), etc. In our study we use four performance criteria namely mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE) and 2
goodness of fit R . The back-propagation learning algorithm was used to train the three-layered feed-forward ANN structure in this study were the most used error functions is as following: The mean absolute error is an average of the absolute errors E = (P-i where
Pi and
),
are the actual (or observed) value and predicted value,
respectively. Lesser values of these measures show more correctly predicted outputs. This follows a long-standing tradition of using the “ex-post facto” perspective in examining forecast error, where the error of a forecast is evaluated relative to what was subsequently observed, typically a census based benchmark (Poon 2005). The most commonly used scale-dependent summary measures of forecast accuracy are based on the distributions of absolute errors
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(|E|) or squared errors (E2) observations (n) is the sample volume. The mean absolute error is given by: Mean Absolute Error (MAE) = E / n n
(i = 1, 2,…n)
(6)
i 1
The MAE is often abbreviated as the MAD (“D” for “deviation”). Both MSE and RMSE are integral components in statistical models (e.g., regression). As such, they are natural measures to use in many forecast error evaluations that use regression-based and statistical. The square root of the mean squared error as follows: E 2 / n 1 n
Mean Square Error (MSE) =
(i = 1, 2,…n)
i
n Root Mean Square Error (RMSE) = Sqrt E
2
/ n (i = 1, 2,…n)
(7)
1 i
If the above RMSE is very less significant, the prediction accuracy of the ANN
model is very close to 100%. Since percentage errors are not scaleindependent, they are used to compare forecast performance across different data sets of the area using absolute percentage error given by APE = (Pi -
)
*100. Like the scale dependent measures, a positive value of APE is derived by taking its absolute value (| APE |) observations (n). This measure includes:
MAPE
=
n APE / n i 1 (i = 1, 2,…n)
(8)
The use of absolute values or squared values prevents negative and positive errors from offsetting each other. All these features and more make MATLAB an indispensable tool for use in this work.
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n Goodness of Fit (R2) = ( E 2 ) /(e 2 ) i 1
where ei = pi -
pi
(9)
(i = 1, 2,…n)
, is the forecast error values. pi, the actual values and p i ,
denote the predicted values. The more R2 correlation coefficient gets closer to one, the more the two data sets are correlated perfectly. As the aim of all of the prediction system models proposed in this study is to predict the direction of the stock price index forecasting, the correlation between the outputs do not directly reflect the overall performance of the network. 3.2 Financial Performance Evaluation of the Model
In order to evaluate the financial performance of the model, the correct predicted positions by the model have been compared. Prediction performance is evaluated used in the formula to calculate the prediction accuracy (Kim 2003) and is as follows:
∑
(i = 1,2,...n)
(10)
Where Ri the prediction result is for the ith trading day is defined by:
{ th
POi is the predicted output from the model for the i trading day, and AOi is the actual output for the i th trading day, n the total predicted outputs. The error level was determined 5% and it means that those outputs with the error level less than the defined value are considered as correctly predicted values.
25
3.3 Research Data
The research data used in this study is the direction of change in the daily Jakarta composite stock price index (JKSE). This is composed of closing price, the high price and the low price of total price index. The grand total number of sample is 2,298 trading days, from January 3, 2005 to May 28, 2014. It is divided into two sub-periods. First sub-periods of January 3, 2005 to December 30, 2010 is in network training periods, its values are obtained with different combinations of parameters for testing the models. The second sub-period of January 3, 2005 to May 28, 2014 is in sample period for testing prediction rate. The whole data in the statistical population were employed in the analysis and this leads to non-selection of a specified sampling method. The number of sample with increasing direction is 1,303 while the number of sample with decreasing direction is 995. That is, 57% of the all sample have an increasing direction and 43% of the all sample have a decreasing direction. The research data used in this study is the direction of daily closing price movement in the JKSE. The number of sample for each year is shown in Table 1. Table 1. The number of sample in the entire data set
Description
Year 05
Increase (%) Decrease (%) Total
06
07
08
09
10
Total 11
14 May 136 144 151 123 141 140 137 135 131 62 1,300 56% 59% 60% 51% 58% 57% 55% 55% 55% 63% 57% 107 101 109 120 102 105 110 109 109 36 998 44% 41% 40% 49% 42% 43% 45% 45% 45% 37% 43% 243 245 250 243 243 245 247 244 240 98 2,298 Source: author calculation, 2014
12
13
26
3.4 Data preparation
Some data own a high amount in comparison with others and this might lead to the excessive effect on prediction process which is a source of errors and reduction of prediction ability of neural networks. That’s why the srcinal data should be normalized in a range of [l, h]. with regards to Mahmood Moein Aldin et al. (2012) normalizing data is done as follows:
(())
(i = 1,2,...n) (11)
Where: u = the normalized data xi = the srcinal data xi,min = the minimum value of the srcinal xi,max = the maximum value of the srcinal data hi = upper bound of the normalising interval and li = lower bound of the normalising interval Max-min normalization plans a value u of xi in the range ( hi – li) i.e. (-1.0; 1.0), in this case. As a value greater than 0 represents a buy signal while a value less than 0 represents a sell signal. (i = 1,2,3,...,n) the number of observations. 3.5 Variable Calculation
27
Closing price, the high and low price index are converted into technical indicators. Technical indicators are used as input variables in the construction of prediction models to predict the position of stock price movements. In this research, 12 technical indicators has to be calculated in Excel and then the network (Program matlab) will read the results from excel spreadsheet. Training or learning data will be year on year, because if we combine data of many years to train at one time it means the learning process is very long and sometimes may not reach the goal. The research applied indicators are selected based on indicator selection of different groups and also along with the previous studies Kim (2003), Kumar & Thenmozhi (2006), Kara et al. (2011), Mahmood Moein Aldin et al. (2012), A. Victor Devadoss (2013)… Table 2 demonstrates the titles of twelve technical indicators and their calculation method separately. Table 2. Selected technical indicators and their formulas
No Name of Formulas indicators 1
A/D Oscillator
2
CCI Commodity Channel index
Description
where Ct is the closing price at time t, Lt the low price at time t, Ht the high price at time t (J. Chang et al. 1996) Where Mt = (Ht + Ct + Lt)/3,
∑ |∑ |
(S.B. Achelis, 1995 & J. Chang et al. 1996)
28
3
Larry William’s
(R%) 4
MACD MACD(n)t-1+2/n+1* (moving MACD(n)t-1) average convergence divergence)
(DIFFt
(S.B. Achelis, 1995) - DIFF: EMA(12)t EMA(26)t, EMA is exponential moving average, EMA(k)t: EMA(k)t-1 + α ×(Ct t-1), α smoothing EMA(k) factor: 2/(1 + k), k is time period of k day exponential moving average (Gerald, 2005) Description
No Name of Formulas indicators 5 Momentum
6
7
8
ROC Pricerate-of change RSI (Relative strength index) Simple MA
(∑ )(∑
where Ct is the closing price at time t, n the price day (J. Chang et al. 1996) (J.J. Murphy, 1986) where Upt means upwardprice change and Dwt means downward pricechange at time t. (S.B. Achelis, 1995) It shows the average value of a security’s price over a
period of time. If the value of a security’s price over a
period of time. If the price moves above its MA, a buy signal is generated. If the price moves below its MA a sell signal is generated. (Mahmood Moein Aldin et al. 2012 & Najeb Masoud, 2014) 9
Stochastic (K %)
where LLt and HHt , mean lowest low and highest high in the last t days, respectively. (S.B. Achelis, 1995)
29
10
∑
Stochastic (D%)
11
12
Stochastic slow (D%) WMA
∑
(S.B. Achelis, 1995) (E. GiEord, 1995) Mahmood Moein Aldin et al. (2012), Najeb Masoud (2014)
Notes: In this study the srcinal data were normalized in a range of [-1,1]. Table 3. Defined Variables
Code A/D Oscillator
Definitions Accumulation/distribution oscillator. It is a momentum indicator that associates changes in price
CCI Commodity Channel index
It measures the variation of a security’s price from its statistical mean
Larry William’s
It is a momentum indicator overbought/ oversold levelsthat measures
(R%)
MACD (moving Moving average convergence divergence average convergence divergence) Momentum
It measures the amount that a security’s price has changed over a given time span
ROC Price-rate-of It displays the difference between the current price change and the price n days ago RSI
Relative strength index. It is a price following an oscillator that ranges from 0 to 100. A method for analysing RSI is to look for divergence in which the security is making a new high.
Simple MA
Simple 10-day moving average
Stochastic (K %)
It compares where a security’s price closed relative
to its price range over a given time period
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Stochastic (D%)
Moving average of %K
Stochastic slow (D%) Moving average of %D. WMA Weighted 10-day moving average Source: Kim K. (2003), Kara et al. (2011), Mahmood Moein Aldin et al. (2012), Najeb Masoud (2014)
31
CHAPTER 4 DESCRIPTIVE STATISTICS
The function of hidden layer is tansigmoid and the transferred function of output layer is linear in a three layer network, where input layer is simply distributing the inputs in various hidden layer and no processing takes place there, in general requires least number of training epochs.
Fig. 3 Tan-Sigmoid Transfer Function and Linear Transfer Function Source: Beale.M.H et al. Neural Network Toolbox, User’s Guide R2013b The aim of linear scaling is to independently normalise each feature component to the specified choice. It ensures the larger value input attributes do not overwhelm smaller value inputs, and then helps to reduce prediction errors (Kim 2003). The number of neurons (n) in the hidden layer, value of learning rate (η), momentum coefficient (μ) and number of training epochs (ep) are ANN model
parameters that must be efficiently determined. Ten levels of neurons (n), five levels of momentum (μ) and 1e-6 levels of epochs (ep) were tested in the
parameter setting process. As suggested in the previous Chapter 2, literature, a
32
small value of η was selected as 0.1-1.0. The levels of the ANN parameters that are tested for choosing the best combination is presented in Table 4. Each parameter combination was applied to the training data sets and prediction accuracy of the models were evaluated. Therefore, the training performance were calculated for each parameter combination. The parameter combination that resulted in the best average of training performances are selected as the best one for the corresponding model. It is noteworthy that MATLAB software is the device used to implement the model. Table 4. ANN parameter levels tested in parameter setting Parameters
Level(s)
neurons(n)
10, 20, 30, 40, 50
Epochs(ep)
1e-6 or (1,000,000)
Momentum constant (μ) Learning rate (η)
0.1, 0.2, 0.3, 0.4, 0.5, 0.1, 0.2, 0.3, 0.4, 0.5
Source: author selection 2014 As we have mentioned above the srcinal data is converted to technical indicators. Twelve technical indicators are as input variables. The Mean and Standard Deviation of input variables is shown in Table 5. Summary statistics for the selected indicators (next page).
33
Table 5. Summary statistics for the selected indicators
Name of indicators
Max
Min
Mean
Standard Deviation
A/D Oscillator
3.7177
-2.0910
0.5333
0.5954
CCI
299.2441
-378.3367
36.4674
107.0075
Larry
100.00
0.00
36.4677
30.0590
MACD
107.1505
-165.0661
11.8421
41.6158
Momentum
400.0300
-510.1500
5.1798
72.3753
ROC
120.6309
73.0980
100.7319
4.5414
RSI
87.7758
16.6560
55.7838
12.7347
Simple MA
5162.5620
1017.6010
2774.3818
1234.6479
Stochastic K%
100.00
0.00
63.5323
30.0590
Stochastic D%
100.00
1.5892
63.5394
27.2896
Stochastic slow (D%)
33.3071
1.2065
21.1834
8.7109
Weighted MA
100827.61
19848.154
54198.6853
24081.7470
William’s
(R%)
Source: author calculation, 2014
34
Fig. 4 Data preparation (actual technical parameters & normalized technical parameters) Source: computer displays, 2014
Fig. 5 training process of ANN model Source: computer displays, 2014
35
Fig. 6 Testing of ANN model
Source: computer displays, 2014
Fig.7 Predict next trading day, by entering new data to the network Source: computer displays, 2014
36
CHAPTER 5
RESEARCH RESULTS AND ANALYSIS
The first concept of the training methodology in this research is to train data for 6 years
(2005-2010) at one time and then testing for a whole data set.
However, the train process it seems to require a lot of time consuming. So, the data is divided yearly for training and also for testing. The training time was set within 20 minutes for each year, if the training performance is not complete within the time frame, the higher learning rate, momentum constant is required. After the training completed but its result is not desired, so changing its parameter is needed. 5.1 Comparison of Financial Performance
The data between 03/01/2005-30/12/2010 period is in network training process, if the result of the training with any parameter combination provide the highest accuracy rate, which mean that the learning or training process is perfectly done as the network can know the direction of increase/decrease of stock price index well and then such result of parameter combination will be saved as a net or model so that we can use the model to test (forecast) the future direction of stock price index. If the tested result shows a significant accuracy rate, it will be adopted as the best parameter combination of the research. The data between 03/01/2005- 28/05/2014 period as input variable is used for testing and forecasting rate is calculated. In table 6 shows three parameters composition which are assumed to be the best ones in representing all cases in the entire data set.
37
As already mentioned in Chapter 4 about ANN model parameters, Each parameter combination consists of number of neurons (n), value of learning rate(η), momentum constant(μ) and epochs(ep).
Table 6. Three parameters for training and testing of ANN model No
n
η
μ
ep
Results (4ys) Average
1
10
0.2
0.5
1e6
98% - 99%
99%
2
30
0.3
0.5
1e6
97% -99%
98%
3
50
0.2 0.5 1e6 96% -99% Source: author calculation, 2014
98%
Through these parameter combinations, we are now able to perform comparison experiments of the ANN model, based on the data sets presented in Table 1. The average of training performance of the ANN model for these parameter combination was varied between 98% and 99%. It can be assumed that the training performances of the ANN model are significant for parameter combination setting data set. Based on selected parameters mention above, now we try to test each period of time to see how each parameter combination can generate the result, in general the testing (forecasting) process is very fast. All yearly testing results has presented in Table 7, Table 8 and Table 9. Each Table head shows Test-1 to Test-6, it can be classified i.e. Test-1 refers to data in 2005 be trained (learned) when the best training result be reached and then save it as
38
net(model) then we use this model to test the same year data and also the following year data, for other Test also refer to the same procedure Table 7: Testing with parameter combination (10, 0.2 , 0.5, 1e6) Year
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Average
Test-1
59% 42% 41% 53% 37% 43% 44% 46% 44% 37% 45%
Test-2
51% 56% 54% 60% 56% 54% 53% 55% 62% 56%
Test-3
52% 52% 48% 49% 49% 59% 52% 56% 52%
Test-4
Test-5
58% 53% 58% 59% 57% 58% 65% 58%
55% 60% 57% 55% 59% 66% 59%
Test-6
54% 52% 51% 54% 62% 55%
Source: author calculation, 2014 In Table 7 showed that the result of forecasting rate of year 2005 is 59% accuracy which higher rate than following year model in terms of testing the same year data as it was be trained. However, the following year forecasting ability of Test-1 is very low compare to others. The best results of parameter combination (10, 0.2 , 0.5, 1e6) is Test-5, meaning we train data of 2009, and then use this model to forecast the following year, the highest forecasting rate (66%) and the worse one (55%), by average is 59%. Table 8. Testing with parameter combination (30, 0.3, 0.5, 1e6)
Year 2005 2006 2007 2008 2009 2010 2011 2012
Test-1 59%
Test-2
54% 46% 40% 51% 50% 47% 52%
52% 48% 51% 49% 44% 48% 45%
Test-3
52% 50% 56% 55% 61% 55%
Test-4
60% 61% 54% 58% 59%
Test-5
55% 56% 60% 51%
Test-6
54% 56% 59%
39
2013 2014 Average
52% 56% 51%
46% 37% 46%
61% 62% 56%
55% 59% 58%
46% 38% 51%
63% 63% 59%
Source: author calculation, 2014 In Table 8 the higher rate of forecasting for the same year data (training and testing) is 60% in Test-4 (year 2008) and Test-1 also as good as 59% (year 2005).
However, if we look at a whole tested results in this parameter
combination. By average Test-6 can provide the highest forecasting rate (59%), but it is not significant outperform Test-4 (58%), therefore, two model can be considered as the best in this parameter combination which can be used for further forecasting. The worse one is Test-2 (2006) as the following year forecasting rate is not reached 50%, by average only 46%. The best results of parameter combination (30, 0.3, 0.5, 1e6) in term of yearly higher forecasting rate is 63% (year 2013 & 2014) in Test-6. Table: 9. Testing with parameter combination (50, 0.2, 0.5, 1e-6) Year 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Average
Test-1
59% 47% 43% 58% 43% 43% 46% 46% 46% 37% 47%
Test-2
52% 49% 45% 56% 58% 56% 54% 56% 63% 54%
Test-3
55% 59% 43% 58% 61% 61% 54% 63% 57%
Test-4
Test-5
59% 55% 51% 53% 55% 57% 59% 56%
57% 49% 49% 45% 46% 45% 49%
Test-6
54% 53% 50% 48% 58% 52%
Source: author calculation, 2014 The best results of parameters (50, 0.2, 0.5, 1e-6) is Test-3 ( 2007), the highest forecasting rate (63%) and the worse one (43%), by average is 57%. It is adopted as the best model in this parameter combination. For a whole data set,
40
model that proved higher forecasting rate for the same year data training and testing is Test-1 (2005) as same as forecasting rate of parameter combination (10, 0.2 , 0.5, 1e6) Test-1 in Table 7. But its ability to forecast the following year is very less, by average only reach 47% of accuracy.
Among these testing with different parameter combination as mentioned in three tables above, by comparison, the best average result is 59% Test-5 with parameter combination (10, 0.2 , 0.5, 1e6) in Table 7 and Test-6 of parameter combination (30, 0.3, 0.5, 1e6) in Table 8 with the same rate (59%). As we observe that the highest forecasting rate is 66% and the worse one is 55% in Test-5 that is relatively better than Test-6 in Table 8. Therefore, the forecasting performance of this parameter combination (10, 0.2 , 0.5, 1e6) can be adopted as the best of this ANN model. Table 10. Summary of the best forecasting, parameters (10, 0.2 , 0.5, 1e6) Year 05
06
PR
51% 52% 58%
59%
07
08
09
10
11
55% 60% 57%
12
13
55% 59%
14 66%
Source: author calculation, 2014
In Fig. 7 shows the training and forecasting performance of the best model in this research (Test-5), author noted that from year 2005 -2008
the
forecasting rate showed there come from the same year data for training and testing, but from year 2009 (as the model) and following forecasting rate be considered the best forecasting performance in this research.
41
Comparing training & forecasting rate 120% 99%
99%
100%
96%
98%
99%
97%
80%
66% 59%
60%
58% 51%
52%
2006
2007
55%
60%
57%
55%
2010
2011
2012
59%
40% 20% 0% 2005
2008
2009
Training
2013
May-14
Testing
Fig. 8 Training & Forecasting performance (%) of ANN model for a whole data set (n = 50, η = 0.2, μ = 0.5, ep = 1e6). Source: author calculation, 2014
In this research, we also find out how forecasting performance is, if we train data each year and test it for the same year data. The result of this method showed in Table 11. Table 11 shows the average training for a whole data set varies between 96% 99%,
which be considered as the best training result.
When testing is
conducted the results show that forecasting performance is lower than the results of our proposed methodology, the forecasting rate varies between 53% 55%. If comparing the forecasting rate values (as the measure of financial performance) presented in the table 11. We find that the best forecasting rate is 61% in 2014 with parameter combination (50, 0.2, 0.5, 1e-6), and the worst rate is 51% in all parameter combination.
42
As the results of this method for all of three parameter combination has not showed any significance different in term of better performance than others. Therefore, the prediction rate values performance of three parameter combination can be adopted as the worse of the ANN model for this methodology. Table 11. Financial performance of ANN model
Year
Parameter combination (n, η, μ , ep) (10, 0.2 , 0.5, 1e6) (30, 0.3, 0.5, 1e6) (50, 0.2, 0.5, 1e-6)
2005 2006 2007 2008 2009 2010 2011 2012 2013 May 2014
Training , Testing 0.99 0.59 0.99 0.51 0.99 0.52 0.98 0.57 0.99 0.55 0.99 0.53 0.99 0.53 0.97 0.53 0.99 0.50 0.91 0.53
Average %
98%
54%
Training , Testing 0.98 0.51 0.99 0.51 0.99 0.51 0.97 0.60 0.97 0.55 0.99 0.54 0.96 0.55 0.94 0.50 0.97 0.51 0.84 0.56 96%
53%
Training , Testing 0.99 0.59 0.99 0.52 0.96 0.54 0.98 0.59 0.99 0.57 0.97 0.54 0.99 0.52 0.97 0.51 0.96 0.52 0.83 0.61 96%
55%
Source: author calculation 2014
As 61% is the best forecasting rate in 2014(50, 0.2, 0.5, 1e-6). Therefore, we try to find out how forecasting performance generate the result, if we use various learning rate (η) as mentioned in Table 4. The results show in Fig. 8
which can be concluded that with different learning rate is not enhance the forecasting performance to better than (η =0.2).
43
Forecasting with differentη in 2014 70.00% 60.00%
61.62% 48.48%
50.51%
51.52%
51.52%
52.53%
51.52%
0.3
0.4
0.5
0.6
0.7
50.00% 40.00% 30.00% 20.00% 10.00% 0.00% 0.1
0.2
Forecasting rate
Fig. 9 Forecasting performance (%) of ANN model for various η values (n = 50, μ = 0.5, ep = 1e6).
Source: author calculation 2014
Author also try to find out why the forecasting performance as mention in Fig. 8 is less power in its prediction. Author has compared forecasting results in term of accuracy between direction number of increase and decrease of stock price index by percentage, the research finding show that direction of increase is more accuracy percentage. i.e. year 2014 (direction of increase 62 days & decrease 36 days) with parameter combination (50, 0.2, 0.5, 1e-6) forecasting results showed that 77% accuracy of increase and only 13% accuracy of decrease direction. The reason behind this issue still unable to be justified by author. In Table 12. We present the empirical result of other research work in the past which they used same technical indicators as input variables to forecast the index prices in different stock markets.
44
Table 12. The empirical result of other research Author name/year Kim (2003
Market KOSPI
Y.Kara et al.(2011) ISE (100) Mahmood Moein TEPIX Aldin et al. (2012) Najeb Masoud(2014) LSM
No. of inputs 12
Training rate 58.52%
Forecasting rate 54.73%
10 10
84% - 99%.
79.37% 94%
12
82 - 93%
91%
5.2 Comparison of Statistical Performance
Statistical performance of the three parameter combination is compared in Table 7 (Test-5), Table 8 (Test-6) and Table 9 (Test-3) due to it is considered as the best forecasting results. As we already mentioned in sub-section 3.1, MAE, RMSE, MAPE and R2, measures are used in order to compare the statistical performance of parameters combinations. Goodness of fit R2 is also referred to as the coefficient of multiple correlations. MAPE and RMSE measure the residual errors, which gives a global idea of the difference between the predicted and actual values. Although, the MAE is very similar to the RMSE but it is less sensitive to large forecast errors. The longer MAE means higher bias level and less accurate forecast to predict prices, but it does not mean that MAE is not suitable to predict stock market fluctuations.
45
As shown in Table 14, the parameter combination (30, 0.3, 0.5, 1e6) is relatively better than other parameter combination, by average its errors are smaller. While financial performance showed that parameter combination(30, 0.3, 0.5, 1e6) and (10, 0.2 , 0.5, 1e6) is given the same forecasting results by average (59%). If we look at the yearly forecasting rate in these parameter combination Table 7 (Test-5), Table 8 (Test-6); the research finding shows that (10, 0.2 , 0.5, 1e6) provided the highest forecasting rate as 66% (year 2014) and statistical error also less than the best forecasting rate (63%) of parameter combination(30, 0.3, 0.5, 1e6). While parameter combination (50, 0.2, 0.5, 1e6) Table 9 (Test-3) showed higher error rate than others. Therefore, parameter combination (30, 0.3, 0.5, 1e6) can be adopted as the best statistic performance by average for a whole data analysis, and parameter combination(10, 0.2 , 0.5, 1e6) – 66% forecasting rate can be adopted as the best performance in term of financial and statistical performance in this research. Table: 13 the best statistic & financial performance
Model ANN
No. of Obs. 10
R
MAE
RMSE
MAPE
0.00464 6 Source: author calculation, 2014
0.6283
0.001619
0.227642
Forecasting rate 0.66
In all cases the relationship strength between parameter combination and forecast accuracy measures such as MAE, MAPE, and RMSE is relatively weak and quite fluctuated, the best results (R2 = 0.98) and the worst one (R2≥0.46). According to Table 13, as good as ANN model can be, it is considered that this model may not really be a powerful tool in forecasting direction of Indonesian stock price index movement and this research study
46
results is not in consistent with the previous studies as mention in Table 12. Particularly, Mahmood Moein Aldin et al. (2012) and Najeb Masoud(2014). If we analyze from the training process, we found that the training results is very desired and similar to other research work using technical indicators as input variables, which its results varied between 0.96 to 0.99 and statistic performance also desired. When we test the model its power of forecasting is relatively low comparing with its high training results. Author observes that the forecasting power lessen may cause by a short period of data be trained (learned). So, the model unable to have enough experience to forecast. The other factor might be dataset-12 technical indicators(input variables) were calculated outside the network, as the best knowledge of author technical indicator be calculated inside the network (Program matlab). Therefore, the technique of coding may not prediction decrease.
perfectly done and caused the power of
47
Table 14. Statistical performance of ANN model
(10, 0.2, 0.5, 1e6) R MAE RMSE 0.6467 0.001945 0.004784 0.8224 0.001982 0.008130 0.9865 0.001920 0.003984 0.6885 0.001730 0.004098
Year MAPE 2005 0.004066 2006 0.004878 0.004820 2007 2008 0.004221 2009 0.6283 0.001619 0.227642 0.004467 2010 0.7317 0.001723 0.225806 0.004634 2011 2012 2013 2014
0.8205 0.6559 0.4673 0.6283
0.003096 0.001202 0.003469 0.001619
Parameter combination (n, η, μ, ep) (30, 0.3, 0.5, 1e6) R MAE RMSE MAPE 0.6467 0.001945 0.004784 0.004066 0.9875 0.001966 0.004065 0.004837 0.9865 0.001920 0.003984 0.004820 0.5901 0.001629 0.004098 0.003975 0.8266 0.001830 0.012295 0.004467 0.8776 0.001867 0.004065 0.004593
R 0.6467 0.9875 0.8716 0.6393 0.7596 0.7114
(50, 0.2, 0.5, 1e-6) MAE RMSE MAPE 0.001945 0.004784 0.004066 0.001966 0.004065 0.00483 0.001809 0.015936 0.004541 0.001679 0.114754 0.004098 0.001763 0.004098 0.004303 0.001702 0.109756 0.004186
0.3424660.004637 0.7971 0.001788 0.032258 0.004435 0.5683 0.001560 0.25 0.003870 0.291176 0.004647 0.6550 0.002814 0.164384 0.004109 0.5722 0.002674 0.253425 0.003904 0.30303 0.004911 0.5130 0.001098 0.267647 0.003735 0.8585 0.001349 0.147059 0.004588 0.227642 0.004646 0.5967 0.003775 0.232323 0.003737 0.5967 0.003775 0.171717 0.003737
Source: author calculation, 2014
48
CHAPTER 6 CONCLUSION
This paper aims to find the answer of the following question: how to forecast the stock price index in in Indonesian stock exchange? Whether the forecasted IDX through the learning procedure techniques of ANN model or not. Is it RWH and EMH theory true?. And comparing the results with some recent research using ANN model in this market. Due to the issue of accurately forecasting the direction of movements of the stock market price levels is highly significant for formulating the best market trading solutions. It is fundamentally affecting financial trader’s
decisions to buy or sell. The research finding can be concluded as follows: a. ANN technique can be applicable to forest stock price index in Indonesian stock market, The results of learning rate can be reached 99%, while the best result of forecasting rate is 66%, and the worst rate is 51%. This forecasting technique is considered as a new method which need to be improved in term of designing the model and find out its input variable that the market related to. So that it will enhance the better forecasting results. b. The power of prediction may not really high in this research methodology as the author’s expectation. However, the prediction result
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showed above is fairly good. So, it means that stock market price can be predictable. c. In terms of comparing ANN performance with recently research. Putra and Kosala (2011)-using technical variables as input data, the highest accuracy rate is 80.48% and the worst one is 49.90%, but their forecasting was focused on individual company, not index prices. For Veri and Baba (2013) forecasting index price of the next trading day they’ve used daily prices as input variables, the empirical results showed
that 95% of training accurate and for prediction value percentage varied from 95% to 5% of accuracy. Due to both research provided higher forecasting rate so this research model is not outperform their research methodology. d. However, author believes this methodology can be applied along with other techniques to help a trading decision. e. This research methodology has been proved very successful in other stock market research like LMY, TEPX, etc. there are some factors may affect the results of this research as to be mentioned in the limitation of this study. f. A few of input indicators in the research may not enhance the accuracy rate (unnecessary), because, this stock market can be affected by many macro-economic factors such as political events, investors’ expectations, institutional investors’ choices, firms’ policies, general economic
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conditions, interest rates, foreign exchange rates, movement of other stock market, psychology of investors etc. The limitations of current study:
Forecasting stock price index using
artificial neural network is a new methodology applied in emerging market (Suchira Chaigusin, 2011) comparing to other methodology i.e. fundamental analysis, technical analysis etc. accessibility to this methodology have some limited. The most important part of research work is to concentration on coding or programing to create the right forecasting model and find out the best training parameter combination in the goal of reaching the best forecasting results. Meanwhile the researcher himself has very less experience in the field of computer science and information technologies, as this knowledge/skill is required by the research itself. So, the forecasting model in this research may not perfectly done as same as IT expert does. However, author hope that this research will be the first step for other students who wish to continue improving this research methodology or other ANN model. For further research, author would like to provide some such suggestion as following: a. Improving this methodology through using matlab tool box, which will
enhance more accurate prediction rate. b. Each method has its own strengths and weaknesses. So, author suggest
to use technical indicators of this study and other combining techniques
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models by integrating ANN with other classification models such as Support Vector Machines (SVM), Genetics Algorithm (GA) etc. The weakness of one method can be balanced by the strengths of another by achieving a systematic effect. c. To the best knowledge of the author, the prediction performance of this
model can be improved by many ways
i.e. adjusting the model
parameters by conducting a more sensitive and comprehensive parameter setting.
Otherwise, reduction of current variables and adding more
different input variables i.e. macro-economic variables such as foreign exchange rates, interest rates and international stock indexes that related to IDX, etc.
Benefit of this research: author believes that this research method would
benefits to other students in many ways for their further study about using artificial neural network as a tool to forecast stock prices: a. For student who don’t know about ANN, this research can provide some information and idea on ANN, how its work and why it’s used
in financial field. b. It will be the basic idea for students who wants to try a new methodology of forecasting stock prices, especially, who are majoring finance or related fields. c. Student can learn some part of its function used in this research and its code in the matlab program. So that they can create their own
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methodology and may have more powerful prediction model than current research. d. Author believes that this research methodology cannot be done without any mistake. However, this research provides student some basic understanding on how to do it and also benefits to other researcher more or less in someway. e. As we are a student at present who want to be a successful investor in the future, we cannot reliance on the old ways of forecasting stock prices or using single analyzing technique for making investment decision. This technique (ANN) is highly supported for further study and author believes this research can be a reference or being the first step for other researcher who never used this forecasting technique before.
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Apendix A: Matlab code
(Blank)
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