PREDICTION OF THE INDIAN STOCK INDEX USING NEURAL NETWORKS
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Jharkhand Journal of Development and Management Studies XISS, Ranchi, Vol. 16, No.1, March 2018, pp. 7609-7621 PREDICTION OF THE INDIAN STOCK INDEX USING NEURAL NETWORKS Sitaram Pandey1 & Amitava Samanta2 Stock prices prediction is an issue of interest in stock markets. Many prediction techniques have been reported in stock forecasting. Now a days, neural networks are viewed as one of the most suitable techniques. In this study also, an experiment on the forecasting of the nifty index of national stock exchange was conducted by using feed forward back propagation neural networks. The local and global fac to rs influencing the natio nal sto ck mark et we re used in developing the models that includes gold prices, dollar-rupee exchange rates & nifty volume. Three years’ historical data were used to train and test the models. Four suitable neural network models identified by this research are a four layer neural network. But it was found through performance measure MSE (Mean Square Error) that movement of nifty index is insensitive to gold prices’ fluctuations & dollar exchange rate fluctuations. Keywords : Artificial Neural Network, Nifty Index, Stock Prediction, Performance measures Introduction Prediction of future trends of any financial market is still a most lucrative field of research. Here, we are focusing our research on Indian stock market. There are innumerable numbers of researches based on different models from fundamental analysis to machine learning techniques are available globally on this topic but fewer in Indian context. Prediction in the stock market is the need of all the stock traders to take informed decisions in trading of stocks. Many researchers have concluded that Indian stock market does not follow efficient market hypothesis (EMH) which specifies that there is a room for stock market forecasting. While the debate on the various issues related to efficiency of market, predictive models, tools etc. is ongoing, this encourages various researchers to seek better model for stock prediction. Techniques of prediction vary greatly based on the availability of data, quality of data, requirement specification, and the underlying assumptions used. There are various linear and non-linear models to describe the behavior of time series but their success rate is diminishing in predicting the financial markets, though these techniques are statistically powerful. 1 Assistant Professor, Department of MBA, Cambridge Institute of Technology, Ranchi Jharkhand. Phone No. 7858882626, Mail Id : firstname.lastname@example.org 2 Associate Professor, Department of Commerce & Management, Vinoba Bhave University, Hazaribag, Jharkhand. Phone Number: 09431795999, Email ID: email@example.com 7609
7610 Pandey & Samanta As we know, stock markets are very unpredictable so their high frequency data are highly time-variant and in non-linear pattern. It is a challenging task to predict future prices of a stock based on past experiences. Bollerslev (1986) has given a solution in the form of general autoregressive conditional heteroscedasticity (GARCH) model which has solved the problem of time-series data to a greater extent. This model was proven as one of the strongest weapon since it was invented for the analysis of time-series data and successfully has been used for last 20 years. This model has a capacity to capture all the irregularities of economic time series data but these days the model has started losing its shine now. Now, neural networks has started replacing these models. Now a days, neural networks are regarded as more suitable for stock prediction than other techniques. Unlike other techniques that construct functional forms to represent relationships of data, neural networks are able to learn patterns of relationship from data itself. In modern quantitative and empirical finance, Artificial neural networks (ANN) are proven as one of the most powerful tool and have emerged as a significant statistical modeling technique. The ANN models are emerging technology that has capacity to detect the underlying functional relations within a set of data and perform data analysis in applications such as pattern recognition, prediction, classification, modeling, evaluation and control. Therefore, a variety of neural network models have been created. Several features of ANN model making it successful now a day. Firstly, it can handle non-linear data and able to model nonlinear systems without prior knowledge of relationship between the input and output variables. The back propagation neural network is a popular neural network model; there are many successful applications for back propagation neural networks in science, engineering and finance. Secondly, ANN models are capable of handling the limitations of time series data. Stock market is considered as the mirror of the economy whether developed or developing. It is now considered as a barometer to measure the economic condition of a country because every major change in economy is reflected in the prices of share. The rise and fall in the share prices indicates the boom or recession cycle of the economy. Now, it has been proved by various researchers that a well regulated stock market renders various economic services to their people. Emerging stock markets have recently been of great importance to the worldwide investment community. So, India is considered as one of the fastest emerging markets in the world due to its established stock exchanges with a long history of organized trading in securities. Over the last few years, there has been a rapid change in the Indian capital market in terms of technology, trading styles & settlement processes. According to the recent survey, there are around 28 emerging markets in the
Prediction of the Indian stock index using neural networks 7611 world out of which India ranks in the second place. Currently, India is the 4th largest economic system in the world in terms of the purchasing power parity. In this research, we are basically focusing on the behavior of share prices which are governed by the various rational, emotional, economic, geographical and psychological factors. In this study, we are taking the S&P CNX Nifty as our national stock index for study, it is a stock market index and benchmark index for Indian equity market. The S&P CNX Nifty covers 22 sectors of the Indian economy and offers investment managers exposure to the Indian market in one portfolio. The S&P CNX Nifty stocks represent about 67.27% of the free float market capitalization of the stocks listed at National Stock Exchange (NSE) as on September 30, 2017. This study investigated the Indian stock market using feed forward back propagation neural networks. It aimed to find suitable neural network models for the prediction of the next day of the S&P CNX Nifty index by applying three time series data, expected to be the factors influencing the stock market, to the models created. The rest of the paper is organized as follows: Section 2 examines the literature review. Section 3 presents the objective of the study. Section 4 discusses the variables, data sources, research design & methodology, ANN & performances measures. Section 5 presents the data analysis & discussion and Section 6 summarizes and concludes. Artificial Neural Network According to Christos Stergiou and Dimitrios Siganos, Artificial neural network (ANN) is an information processing model where the constituents called neurons, process the information and is motivated by biological nervous system of human brain. The key element of this model is its unique method of information processing system. It is made up of several numbers of interconnected processing constituents working together to solve specific problems. As per Burgund and Marsolek (1997), in Advances in Psychology, any ANN can be thought of as a set of interconnected units broadly categorized into three layers of processing units. These three layers are the input layer, the hidden layer and the output layer. Inputs are fed into the input layer, and its weighted outputs are passed onto the hidden layer . The input signal passes through the network in the forward direction. These processing units can be referred as nodes. The directed graphs consists of nodes and each nodes are connected to perform some basic calculations and each connection carries a signal from one node to another labeled by some unique number termed as weight that modulate signal. Here in this paper, we are taking into account feed forward networks , in which connection is forwarded from layer 0 to layer 1 , layer 1 to layer 2 & layer 2 to layer 3. Each layer consists of nodes. The connection is represented by a
7612 Pandey & Samanta sequence of numbers indicating number of nodes in each layer. For example, 3-3-2-1 feed forward network; it indicates three nodes in the input layer (layer 0), three nodes in the first hidden layer (layer 1) , two nodes in second hidden layer (layer 2) , and two nodes in the output layer (layer 3). Here back propagation algorithm (Rumelhart, Hinton & McClellnad, 1986) is used in layered feed-forward ANNs. The network is a multi-layer perception that contains at least one hidden layer along with input and output layers. Review of literature Bashambu, Sikka & Negi (2018) in their paper applied machine learning techniques on the past data to predict the movement of the stock prices and found that although neural networks are not perfect in prediction but they are outperforming all other methods. Hafezi, Shahrabi & Hadavandi (2015) in their research proposed a new intelligent model in a multi-agent framework called bat-neural network multi-agent system (BNNMAS) to predict stock prices of DAX. The results have shown that BNNMAS is better than the genetic algorithm neural network (GANN) and some standard models like generalized regression neural network (GRNN), etc. Laboissiere, Fernandes & Lage (2015) through their research proposed a methodology that forecasts the maximum and minimum day stock prices of three Brazilian power distribution companies and actual prediction was carried out by ANNs whose performances were evaluated through MAE, MAPE & RMSE calculations and found results effective and helpful for investors. Adebiyi, Adewumi & Ayo (2014) in their paper “comparison of ARIMA and artificial neural networks models for stock price prediction” examined the forecasting performance of ARIMA and artificial neural networks model with data of NYSE and concluded superiority of neural networks model over ARIMA model. Al-Radaideh, Assaf, & Alnagi (2013) used data mining techniques for prediction of stock prices. In their study, they tried to help the investors in the stock market to decide the better timing for buying or selling stocks on the basis of information obtained from the historical prices of stocks. Their decisions based on decision tree classifier, which is based on CRISP-DM methodology, are used over real historical data of major companies listed in Amman Stock Exchange (ASE). Niaki & Hoseinzade (2013) have tried to forecast S&P 500 index using artificial neural networks and design of experiments. The results of employed methodology show that the ANN is able to forecast the daily direction of S&P 500 significantly better than the traditional logit
Prediction of the Indian stock index using neural networks 7613 model and ANN could significantly improve the trading profit as compared with the buy-and-hold strategy. Sureshkumar & Elango (2012) analyzed the performance of model of stock price prediction using artificial neural network. They found that multi layer perception (MLP) architecture with back propagation algorithm has the ability to predict with greater accuracy than other neural network algorithms. This would help the investor to analyze better in business decisions such as buy or sell a stock. Dase, Pawar & Daspute (2011) elaborated methodologies for prediction of stock market and focused on an artificial neural network and found that ANN model was more useful for stock market prediction. Artificial neural network, a computing system containing many simple non-linear computing units as neurons interconnected by links, is a well-tested method for financial analysis on the stock market. Dase & Pawar (2010) used artificial neural network model (ANN) for stock market predictions and found that prediction of stock index with ANN model is easier and more suitable than traditional time series analysis. A neural network has the ability to extract useful information from large set of data. Ahangar, Yahyazadehfar, & Pournaghshband (2010) in their research paper “The comparison of methods artificial neural network with linear regression using specific variables for prediction stock price in Tehran stock exchange” considered 10 macro economic variables and 30 financial variables to estimate the stock price using Independent components analysis (ICA) and later they found that artificial neural network method is more efficient than linear regression method. Ganatr & Kosta (2010) focused to build neural network for stock market predictions. Authors used R tool to implement the neural network with closing price, turnover, global indices, interest rate, and inflation as a neural network input. Authors also proposed to include other indicator like news, currency rate and crude price as input to the neural network. Subsequently, an attempt was made to build and evaluate a neural network with different network parameters and also with technical and fundamental data and found that the price prediction proves to be successful. Dutta, Jha, Laha & Mohan (2006) have used artificial neural network models for forecasting stock price index in the Bombay stock exchange. They study the efficacy of ANN in BSE Sensex weekly closing values. They had developed two networks with three hidden layers for the purpose of this study. The root mean square error (RMSE) and mean absolute error (MAE) are chosen as indicators of performance of the networks.
7614 Pandey & Samanta Thenmozhi (2006) has applied neural network models to predict the daily returns of the BSE (Bombay Stock Exchange) Sensex. Multilayer perception network is used to build the daily return’s model and the network is trained using Error Back Propagation algorithm. It was found that the predictive power of the network model is influenced by the previous day’s return than the first three-day’s inputs. The study showed that satisfactory results can be achieved when applying neural networks to predict the BSE Sensex. Objectives of the study The main objective of this study is to use neural networks prediction tool to predict stock prices with more accuracy and to use performance measures for their evaluation. The study makes an attempt to identify extent of impact of various factors on stock prices through neural networks. The study wants to help participants of the market to predict the prices more accurately by reducing error percentage. Data collection & methodology The actual problem discussed in this paper is to forecast the Nifty index of national stock exchange of India. For this purpose, we have used available daily data of Nifty from the NSE beginning from 01 –January- 2015 to 31- December- 2017. For this study, we have taken data of closing prices of three above mentioned years, Volume of Nifty, Data of exchange rates & Gold prices of said years. In order to predict the stock price, past data is necessary and it has been collected for the trading days from 01 –January-2015 to 31- December- 2017. The historical data was collected from different websites1,2,3. The main task is to predict whether the price of nifty index will be up or down tomorrow by using the historical values of the Nifty index. In this research we have chosen three important dependent variables which include gold prices, exchange rates of dollar-rupees & Nifty volumes. The result of any neural network is mostly dependent on the composition of the neural network. Intricacy of any neural network depends on the level of task and accordingly hidden layers can be added to the network to achieve the desired level of accuracy. The software chosen in this paper for creating, training and testing the networks is MATLAB Neural Network Toolbox, which has an extensive capability in terms of creating and training different types of networks. Input data variables & methodology The two types of input variables can be used for stock market index forecasting with neural networks. The first type of variables is related to macroeconomic indicators such as GDP rate, Inflation, FDI, Currency exchange rates, gold prices, developed market indicators etc, the other
Prediction of the Indian stock index using neural networks 7615 types of variables are market related indicators such as prices, dividends, trading volume, turnover, etc. In this study we have used exchange rates & gold prices as macroeconomic indicators and prices & volumes as market indicators. Input data was processed to achieve better predictive results in the application of neural networks on financial time series. In this study, data were collected and transformed through first differencing and logarithmic transformation of the return variable. As in the most other studies (Maciel & Ballini, 2010), in this study also for neural networks the time series data was partitioned into three different sets, first set for the training, second set for the testing and the third set for the validation of networks and it is the common practice to split dataset into three partitions with different quantum of data set in different partitions to make the network more robust. The training set is the largest set and it is used in the neural networks to learn the patterns present in the data. The testing set whose range vary up to 30% of the training set is used to figure out the generalization capacity of estimated trained network. At last, validation set should be of size that can evaluate a trained network efficiently and this set should consist of most recent observations. Although validation set uses past values to test the neural networks and to evaluate the generalization capability of the model. In this work we have partitioned data as follows: training set -70%, testing set -15% & validation set - 15%. The application of these three divided sets are as follows: Training set was used to adjust the network to make it error free. Validation set was used to measure network generalization and testing set was used to measure the network performance during and after training. In this model, random regression function was split to overcome over fit models. Neural Network Structure In neural network algorithm each independent variable that has been processed is represented by its own input neurons. A two-layer-feed- forward network, with sigmoid hidden and soft max output neurons, can classify vectors arbitrarily well, given enough neurons in its hidden layer. Tansig is used here as a neural transfer function. Transfer functions calculate a layer’s output from its net input. This is mathematically equivalent to tanh (N). N is the S-by-Q matrix of net input vectors. The network will be trained with scaled conjugate gradient back propagation. In the broadest sense, there are three main requirements for any successful ANN model: In-sample accuracy The ability of the model to perform with new data. Stability, consistency of the network output.
7616 Pandey & Samanta To ensure the above points are successfully met, a large number of considerations need to be taken into account. Our tests included data pre-processing techniques, the number of layers, the choice of activation function, learning rate, training time and the number of hidden neurons. After several combinations of experiments, the architecture was finalized for all the main experiments. The goal is to use the least amount of neurons which generate the best results for out-of-sample. A simple approach was used in this paper based on starting with very small number of neurons and training and testing the networks to a fixed number of iterations. The hidden neurons are increased gradually until the optimal number of neurons is found. There is no any rule of thumb to find optimal number of neurons required in hidden layers. Here, it was found through trial and error method for the minimum squared error (MSE) and through test set. Every time a new input (or lagged value of the same variable) was added, we started with 1 hidden neuron and added one each time up to 10. Performance measures The ultimate goal of this study is to forecast the direction of the price, since it is very difficult to correctly predict the magnitude of the price for financial data. Hence, prediction of direction of nifty index is sufficient to fulfill this goal. The success ratio for direction prediction (or the hit rate) was considered. h= (1) z =1 if , > 0, and 0 otherwise. Where: n is the sample size, +1 , +1 , are the value of the target and the output at time t+1 consecutively. The MSE (Mean squared error) is by far the most used metric for ANN performance regardless of the network goal. Furthermore, the correlation coefficient R and 2 was also used; as a measure of the linear correlation between the forecasted value and the actual one. Mean squared error was calculated. Finally, the information coefficient given by equation 2 was used. ∑ =1( − )2 IC = (2) ∑ =1( − −1 )2 Where: y is the predicted value, and x is the actual value. This ratio provides an indication of the prediction compared to the trivial predictor based on the random walk, whereas IC >1 indicates poor prediction, and IC < 1 means the prediction is better than the random walk. The different neural network models were constructed by using
Prediction of the Indian stock index using neural networks 7617 the three input nodes in an input layer. Some models are shown in table 1, where the first number is the number of nodes in the input layer, the second number is the number of nodes in the first hidden layer and so on. The last number is the node of the output layer, which is 1. Results & analysis Starting from one lag up to 20 lagged value of the spot price was tested. The results obtained from input transformed by equation (3) were very poor and the hit rate was 46% for out-of-sample. − −1 =( ) (3) − −2 −1 + =( −2 ) (4) − While the results generated by equation (4) was much better around 60% (equation 4 contains 2 step differencing) the combination of eq (3) & eq (4) as input with eq (4) alone as output seems to produce much better results. For different combinations of data and parameters, this performance curve varies. Training of the model stops either when it reaches to the stated number of epochs (fig.1) or when Mean Squared Error (MSE) is almost not improving after certain epochs. The circle in the performance curve shows the best validation performance. The following networks were trained to identify the best performing networks. The networks trained and retrained using levenberg-marquardt and scaled conjugate gradient. The first network is 3-3-1-1 which is trained and retrained using levenberg-marquardt and scaled conjugate gradient. Fig-1. Performance curve of Primary Working Set Data of network 3-3-1-1 Source : Matlab
7618 Pandey & Samanta Next network is 3-7-1-1 which is also trained using above method. Fig-2 : Performance curve of Primary Working Set Data of network 3-7-1-1 Source : Matlab The other network is 3-10-1-1 trained as above. Fig-3 : Performance curve of Primary Working Set Data of network 3-10-1-1 Source : Matlab
Prediction of the Indian stock index using neural networks 7619 Next network is 3-13-1-1 which is also trained by the same procedure. Fig-4 : Performance curve of Primary Working Set Data of network 3-13-1-1 Source : Matlab The best model for four layered neural networks was 3-7-1-1. The summary of performance measures of the nifty Index through the network 3-7-1-1. Metrics Samples MSE R2 Training 521 0.0002 0.21 Validation 111 0.0005 0.23 Testing 111 0.0007 0.19 Source : Matlab The network structure for the benchmark consisted of four layers feed forward with 7 hidden neurons and 0.01 learning rate. The network was trained with Levenberg-Marquardt algorithm & scaled conjugate gradient. Conclusions The study has presented the prediction of the Nifty index using multi layer feed forward back propagation neural networks. The most suitable network model for the Nifty index production is 3-7-1-1 but their prediction performance measured by MSE is nil and correlation is also found as nil. Thus this study supports that movement of Nifty index is insensitive to gold prices’ fluctuations & dollar exchange rate fluctuations.
7620 Pandey & Samanta REFERENCES Adebiyi, A. A., Adewumi, A. O., & Ayo, C. K. (2014). Comparison of ARIMA and artificial neural networks models for stock price prediction. Journal of Applied Mathematics. Retrieved from file:///C:/Users/Welcome/Downloads/ 614342.pdf Ahangar, R. G., Yahyazadehfar, M., & Pournaghshband, H. (2010). The comparison of methods artificial neural network with linear regression using specific variables for prediction stock price in Tehran stock exchange. International Journal of Computer Science and Information Security, IJCSIS, 7(2), 038- 046. Al-Radaideh, Q. A., Assaf, A. A., & Alnagi, E. (2013). Predicting stock prices using data mining technique s. In The Inter national Ar ab Confere nce on Information Technology (ACIT’2013). Retrieved from http://acit2k.org/ACIT/ 2013Proceedings/163.pdf Bashambu, S., Sikka, A., & Negi, P. (2018). Stock price prediction using neural networks. International Journal of Advance Research, Ideas and Innovations in Technology, 4(1), 603-606. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31(3), 307-327. Burgund, E. D., & Marsolek, C. J. (1997). Case-specific priming in the right cerebral hemisphere with a form-specific perceptual identification task. Brain and Cognition, 35(2), 239-258. Dase, R. K., & Pawar, D. D. (2010). Application of artificial neural network for stock market predictions: A review of literature. International Journal of Machine Intelligence, 2(2), 14-17. Dase, R.K., Pawar, D. D., & Daspute, D.S. (2011). Methodologies for Prediction of Stock Market: An Artificial Neural Network. International Journal of Statistika and Mathematika, 1(1), 08-15. Dutta, G., Jha, P., Laha, A. K., & Mohan, N. (2006). Artificial neural network mo dels for for ecasting sto ck price index in the Bo mbay sto ck exchange. Journal of Emerging Market Finance, 5(3), 283-295. Ganatr, A., & Kosta, Y. P. (2010). Spiking back propagation multilayer neural network design for predicting unpredictable stock market prices with time ser ies analysis. Internatio nal Jour nal of Computer Theo ry and Engineering, 2(6), 963. Hafezi, R., Shahrabi, J., & Hadavandi, E. (2015). A bat-neural network multi-agent system (BNNMAS) for stock price prediction: Case study of DAX stock price. Applied Soft Computing, 29, 196-210. Laboissiere, L. A., Fernandes, R. A., & Lage, G. G. (2015). Maximum and minimum stock price forecasting of Brazilian power distribution companies based on artificial neural networks. Applied Soft Computing, 35, 66-74. Maciel, L.S., & Ballini, R.(2010). Neural networks applied to stock market forecasting: An empirical analysis. Journal of the Brazilian Neural Network Society, 8(1), 3-22. Niaki, S. T. A., & Hoseinzade, S. (2013). Forecasting S&P 500 index using artificial neural networks and design o f experiments. Jo urnal o f Indus trial Engineering International, 9(1), 1. Rumelhart, D. E., Hinton, G. E., & McClelland, J. L. (1986). A general framework for parallel distributed processing. In Jerome A. Feldman, Patrick J. Hayes & David E. Rumelhart (Eds.), Parallel distributed processing: Explorations in the mic rost ruct ure of cognitio n, 1(pp. 45-76). MA, USA: MIT Press Cambridge.
Prediction of the Indian stock index using neural networks 7621 Sureshkumar, K. K., & Elango, N. M. (2012). Performance analysis of stock price prediction using artificial neural network. Global Journal of Computer Science and Technology, 2(1). Retrieved from file:///C:/Users/Welcome/ Downloads/426-1-426-1-10-20150122.pdf Thenmozhi, M. (2006). Forecasting stock index returns using neural networks. Delhi Business Review, 7(2), 59-69. Websites 1 https://www.nseindia.com/products/content/equities/indices/ historical_index_data.htm, retrieved on 20/01/2018 2 https://in.investing.com/commodities/gold-historical-data, retrieved on 20/01/2018 3 https://in.investing.com/currencies/usd-inr-historical-data, retrieved on 20/01/2018
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