Predicting Trading Signals of the All Share Price Index Using a Modified Neural Network Algorithm

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1 Predicting Trading Signals of the All Share Price Index Using a Modified eural etwork Algorithm C. D. Tilakaratne, J. H. D. S. P. Tissera, M. A. Mammadov 2 (cdt@stat.cmb.ac.lk, dspt@stat.cmb.ac.lk, m.mammadov@ballarat.edu.au ) Department of Statistics University of Colombo Colombo 3, Sri Lanka. 2 Center for Informatics and Applied Optimization School of Information Technology and Mathematical Sciences University of Ballarat, PO Box 663, Ballarat Victoria 3353, Australia. Abstract This study predicts whether it is best to buy, hold or sell shares (trading signals) of the All Share Price Index (ASPI) of the Colombo Stock Exchange, using a modified neural network () algorithm. Most commonly used classification techniques are not successful in predicting trading signals when the distribution of the actual trading signals, among these three classes, is imbalanced. The structure of this modified neural network is same as that of feedforward neural networks. This algorithm minimises a modified Ordinary Least Squares (OLS) error function. An adjustment relating to the contribution from the historical data used for training the networks, and penalisation of incorrectly classified trading signals were accounted for, when modifying the OLS function. A global optimization algorithm was employed to train these networks. Results obtained were satisfactory.. Introduction A number of previous studies have attempted to predict the price levels of stock market indices [-4]. However, in the last few decades, there have been a growing number of studies attempting to predict the direction or the trend movements of financial market indices [5-2]. Some studies have suggested that trading strategies guided by forecasts on the direction of price change may be more effective and may lead to higher profits [0]. Leung et al. [3] also found that the classification models based on the direction of stock return outperform those based on the level of stock return in terms of both predictability and profitability. Almost all of the above mentioned studies considered only two classes: the upward and the downward trend of the stock market movement, which were considered as buy and sell signals [5-7, 9, ]. It was noticed that the time series data used for these studies are approximately symmetrically distributed among these two classes. In practice, the traders do not participate in trading (either buy or sell shares) if there is no substantial change in the price level. Instead of buying/selling, they will hold the money/shares in hand. In such a case it is important to consider the additional class which represents a hold signal. For instance, the following criterion can be applied to define three trading signals: buy, hold and sell: Criterion A buy if Y(t+) l u hold if l l < Y(t+) < l u sell if Y(t+) l l

2 where Y(t+) is the relative return of the Close price of day (t+) of the stock market index of interest while l l and l u are thresholds. The values of l l and l u depend on the traders' choice. There is no standard criterion found in the literature how to decide the values of l l and l u and these values may vary from one stock index to another. A trader may decide the values for these thresholds according to his/her knowledge and experience. The most commonly used techniques to predict the trading signals of stock market indices are Feedforward neural networks (F) [9,, 2, 4], Probabilistic neural networks (P) [7, 3] and Support vector machines (SVM) [5, 6]. Due to the imbalance of data, the most classification techniques such as SVM and P produce less precise results [5-7]. F can be identified as a suitable alternative technique for classification when the data to be studied has an imbalanced distribution. However, a standard F itself shows some disadvantages: (a) use of local optimization methods which do not guarantee a deep local optimal solution; (b) because of (a), F needs to be trained many times with different initial weights and biases (multiple training results in more than one solution and having many solutions for network parameters prevent getting a clear picture about the influence of input variables); and (c) use of the ordinary least squares (OLS; see ()) as an error function to be minimised may not be suitable for classification problems. This study aims to predict whether it is best buy, hold or sell the shares (trading signals) of the All Share Price Index (APSI) of the Colombo Stock Exchange (CSE) by applying a modified neural network algorithm. This algorithm provided promising results when applied for similar study related to the Australian All Ordinary Index [8, 9]. In other words, the predictability as well as the profitability of this algorithm was higher compared to the standard F algorithm. There were only a few published studies (for example [20]) related to predicting the Sri Lankan stock markets and these studies aimed at value prediction. one of these studies attempted Pt () Pt ( ) where P(t) denotes the price at day t. Yt () = Pt () either predicting the direction or the trading signals. Therefore, it is worth to predict the trading signals of the ASPI, as the traders and investors can directly benefited from such predictions. The organisation of the paper is as follows: the next section explains the modified algorithm. The third section describes the network training, and the measures of evaluating the performance of the algorithms. Section four presents the results obtained from the proposed algorithms together with their interpretations. The last section is the conclusion of the study. 2. The modified neural network algorithm The structure of the modified algorithm is based on the F. F adopts backpropagation learning for weight modification. Backpropagation learning is an error minimising procedure and the network weights are changed according to an error function which compares the network output with the training targets [8]. The most commonly used error function is the Ordinary Least Squares function (OLS): ( ) 2 E OLS = ai oi () i= where is the total number of observations in the training set while a i and o i are the target and the output corresponding to the i th observation in the training set. The modified algorithm takes two matters into account: () use a global optimization algorithm for network training, and (2) modify the ordinary least squares error function. By using a global optimization algorithm (developed in [2, 22]) for network training, it is expected to find better solutions to the error function. Also it uses a modified OLS error function which is suitable for the classification problem of interest. 2. The modified error function ( E TCC ) As described in the Introduction (see Section ), in financial applications, it is more important to predict the direction of a time series rather than its value. Therefore, the minimisation of the absolute errors between the target and the output may not produce the desired accuracy of

3 predictions [23, 24]. Having this idea in mind, some past studies aimed to modify the error function associated with the Fs (for instance [23-26]). These studies incorporated factors which represent the direction of the prediction (for example [23-25]) and the contribution from the historical data that used as inputs (for example [23, 24, 26]). The functions proposed in [26] and [23, 24] penalised the incorrectly predicted directions more heavily, than the correct predictions. In other words, higher penalty was applied if the predicted value o i is negative when the target a i is positive or vice-versa. However, we are interested in classifying trading signals into three classes: buy, hold and sell. The hold class includes both positive and negative values (refer Criterion A in Section ). Therefore, the least squares functions, in which the cases with incorrectly predicted directions (positive or negative) are penalised, will not give the desired prediction accuracy. Instead of the weighing schemes suggested by previous studies, this function adopts a different scheme of weighing. This novel scheme is based on the correctness of the classification of trading signals. If the predicted trading signal is correct, a very small (close to zero) weight is assigned, and otherwise, a weight equal to is assigned. The proposed weighing scheme is: δ if the predicted trading signal is correct w ds = Otherwise, where δ is a very small value. The value of δ needs to be decided according to the distribution of data. The contribution from the historical data of the data also plays an important role in the prediction accuracy of financial time series [26]. E considers The modified error function ( ) TCC the contribution from the historical data used for predictions, as well as the correctness of the trading signal predicted: ( ) 2 E TCC = wb wd ai oi (2) i= where w d (i) is defined above while, w b (i) is adjustment relating to the contribution of the i th observation and is described by the following equation [26]: w b = (3) 2 bi + exp b Discount rate b, denotes the contribution from the historical data and needs to be estimated from the historical data. 3. Training the algorithm and evaluating the predictions Many previous studies [5-7, 9,, 27-3] have used technical indicators of the local markets or economical variables to predict the stock market time series. Wijayanayake & Rupasinghe [20] suggested that environmental and political influences may have a significant impact on the behaviour of the ASPI. Following theses past studies, we also considered a set of variables, which represent the intermarket influence [27, 28], political and environmental factors, economic stability and macroeconomic factors, such as exchange rate (US$:SLRs) and interest rate, as the potential influential variables. A preliminary investigation done by authors suggested that the current day s (say day t) Close price of the ASPI is influenced by the previous day s (day t+) Close price of the same index, Interest rate, and news. The news indicates whether it has a negative impact on the ASPI or not. Therefore, the daily relative return of the Close price of day (t+) of the ASPI (RR Close (t+)) was taken as the output variable while the interest rate, news, and RR Close, of day t, were considered as the input variables. The study period was from ovember, 2002 to January, Since, influential patterns between markets are likely to vary with time [32], the whole study period was divided into three moving windows of a fixed length. Overlapping windows of length two and half trading years 2 were considered. A period of two and half trading years consists of enough data (638 daily relative returns) for neural network experiments. Also the chance that outdated data (which is not relevant for studying current behaviour of the market) being included in the training set is very low. 2 trading year 256 trading days

4 The most recent 0% of data (the last 58 trading days) in each window was accounted for out of sample predictions while the remaining 90% of data was allocated for training the algorithm. We called the part of the window which allocated for training the training window. Different number of neurons for the hidden layer was tested when training the algorithm with each input set. The minimum and the maximum values of the data (relative returns) used for network training are 0.23 and respectively. Therefore, we selected the value of δ (see Section 2.) as If the trading signals are correctly predicted, 0.00 is small enough to set the value of the modified error function, E, approximately zero. ( ) TCC As described in Section 2., the error function E TCC, consists of a parameter b (discount rate) which decides the contribution from the historical data of the observations in the time series. Refenes et al. [26] fixed b=6 for their experiments. However, the discount rate may vary from one stock market index to another. Therefore, this study tested different values for b when training the algorithm. Observing the results, the best value for b was selected as 5. The proper selection of the values for l l and l u (see Criterion A) was done by performing a sensitivity analysis. We experimented different pairs of values for l l and l u. The best prediction results were obtained when l l = and l u = Different numbers were tested as the number of hidden neurons. The best prediction results were obtained when the number of hidden neurons is equal to three. 3. Evaluation measures The algorithm outputs the (t+) th day relative returns of the Close price of the ASPI. Subsequently, the output was classified into trading signals according to Criterion A (see Section ). The performance of the networks was evaluated by the overall classification rate (r CA ) as well as by the overall misclassification rates (r E and r E2 ), which are defined as follows: r = 0 CA 00 (4) T where 0 and T are the number of test cases with correct predictions and the total number of cases in the test sample, respectively; r E = 00 (5) T 2 r E 2 = 00 (6) T where is the number of test cases where a buy/sell signal is misclassified as a hold signal or vice versa. 2 is the number of test cases where a sell signal is classified as a buy signal and vice versa. From a trader's point of view, the misclassification of a hold signal as a buy or sell signal is a more serious mistake than misclassifying a buy signal or a sell signal as a hold signal. The reason is in the former case a trader will lose the money by taking part in an unwise investment while in the later case he/she only lose the opportunity of making a profit, but no monetary loss. The most serious monetary loss occurs when a buy signal is misclassified as a sell signal and vice-versa. Because of the seriousness of the mistake, r E2 plays a more important role in performance evaluation than r E. 4. Prediction Results The values correspond to r CA, re and re 2 of the test set were 59.95, and 8.62, respectively. Results suggest that the overall prediction accuracy is satisfactory and the rate of more serious misclassification (that is misclassification of buy signals to sell signals and vice versa) is also relatively low. The prediction results can be elaborated as shown in Table. In this table, the classification rate indicates the proportion of correctly classified signals to a particular class out of the total number of actual signals in that class whereas, the misclassification rate indicates the proportion of incorrectly classified signals from a particular class to another class out of the total number of actual signals in the former class.

5 Table : Classification of predicted trading signals of test sets (Average (over 3 windows) classification/misclassification rates are shown within brackets) Actual Class Predicted Class Total Buy (.67%) Hold 3 (4.76%) Sell 4 (7.84%) Buy Hold Sell 59 (98.30%) 60 (95.23%) 46 (90.9%) 0 (0.00%) 0 (0.00%) (.96%) Table shows that there is a tendency that more signals are predicted as hold signals. However, the possibility of misclassifying buy signals as sell signals and vice versa is very low. According to these results, one can guess that the traders/investors can make money by responding to the predictions produced by the algorithm of interest. However, the profit margin may not be high. More experiments needs to be carried out to assess the profitability. 5. Conclusions Results suggest that the modified algorithm produce satisfactory predictions in the sense that it does not make serious misclassifications. Therefore, the traders will not lose their money, although the profit margin is less. Sri Lankan stock market is highly volatile, and that may be the reason that the algorithm did not show the level of performance that expected. Further experiments need to be carried out by extending the study period and using a better set of input features. References. Egeli B, Ozturan M, Badur B (2003) Stock Market Prediction Using Artificial eural etworks. In: Proceeding of the Hawaii International Conference on Business 2. Gencay R, Stengos T (998) Moving Average Rules, Volume and the Predictability of Security Returns with Feedforward etworks. Jour of Forecasting 7: Qi M (999) onlinear Predictability of Stock Returns Using Financial and Economic Variables Journal of Business & Economic Statistics 7: Safer A M (2003) A comparison of two data mining techniques to predict abnormal stock market returns. Intell Data Analy 7: Cao L, Tay F E H (200) Financial forecasting using support vector machines. eu Comp & Appl 0: Huang W, akamori Y, Wang S Y (2005) Forecasting stock market movement direction with support vector machine. Comp and Opera Research 32:-0 7. Kim S H, Chun S H (998) Graded forecasting using an array of bipolar predictions: Application of probabilistic neural networks to a stock market index. Inter Jour of Forecasting 4: Pan H, Tilakaratne C, Yearwood J (2005) Predicting the Australian Stock Market Index Using eural networks Exploiting Dynamical Swings and Intermarket Influences. Journal of Research and Practice in Information Technology 37: Qi M, Maddala G S (999) Economic factors and the stock market: A new perspective. Journal of Forecasting 8: Wu Y, Zhang H (997) Forward Premiums as Unbiased Predictors of Future Currency Depreciation: A on-parametric Analysis. Journal of International Money and Finance 6: Yao J, Tan C L, Poh H L (999) eural etworks for Technical Analysis: A Study on KLCI. International Journal of Theoretical and Applied Finance 2: Tilakaratne C D, Mammadov M A, Hurst C P (2006) Quantification of Intermarket Influence Based on the Global Optimization and Its Application for Stock Market Prediction. In: Proceedings of the International Workshop on Integrating AI and Data Mining (AIDM'06) Leung M T, Daouk H, Chen A S (2000) Forecasting stock indices: a comparison of classification and level estimation models. International Journal of Forecasting 6: K, Fukuhara Y, akamura Y (996) Selective Presentation for eural etwork Forecasting of Stock Markets. eu Comp & Appl 4: Akbani R, Kwek S, Japkowwicz (2004) Applying Support Vector Machines to Imbalanced Datasets. In: Proceedings of the 5th European Conference on Machine Learning (ECML'04), 33-50, Springer-Verlag Heidelberg Berlin. 6. Chawla V, Bowyer K W, Hall L O, Kegelmeyer W P (2002) SMOTE: Synthetic Minority Over- Sampling Technique. Journal of Artificial Intelligence Research 6: Tilakaratne C D, Morris S A, Mammadov M A, Hurst C P (2007) Predicting Stock Market Index

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