A hybrid model of machine learning regression and swarm intelligence for stock price forecast in vietnam

Nội dung text: A hybrid model of machine learning regression and swarm intelligence for stock price forecast in vietnam

1. A HYBRID MODEL OF MACHINE LEARNING REGRESSION AND SWARM INTELLIGENCE FOR STOCK PRICE FORECAST IN VIETNAM Truong Thi Thu Ha*1, Ngo Ngoc Tri ABSTRACT: In recent years, financial time series forecasts have become a challenging issue and attracted many researchers. This study develops a novel hybrid model to forecast stock price in Vietnam Stock Exchange. The least squares support vector regression (LSSVR), a machine learning technique, is utilized as a forecast model. A swarm intelligence – firefly algorithm (FA), is applied to optimize hyperparameters of the LSSVR for improving forecast accuracy. Two daily closing stock price datasets are used to validate the predictive ability of the FA- LSSVR, which are Vietnam Dairy Products Joint Stock (VNM) and Joint Stock Commercial Bank for Foreign Trade of Vietnam (VCB). Experiment results confirmed that the proposed hybrid model is effective in forecasting stock prices. Comparison results show that the forecast performance of the proposed model is superior to that of the LSSVR and ARIMA (autoregressive integrated moving average) for both datasets. A finding of the study provides decision-makers with a potential and effective forecast tool in financial markets. Keywords: stock prices; financial forecast; least squares support vector regression; firefly algorithm. 1. INTRODUCTION The stock market plays a crucial role in an economic development of a nation and the world. It affects the capital raise for enterprises, the savings mobilization for investments, and the reallocation of wealth [1]. Decision-makers can take a distinct advantage if they have considerable business acumen and can predict the future status of stock market [2]. Stock price forecast has attracted increasing attention of researchers and practitioners over years. An accurate forecast of stock price values has been considered as one of the most challenging tasks since the intrinsic non-stationarity and non-linearity of financial data. Stock price forecast is the process of determining the future stock values of a company considering its historical values. Introduced by Box and Jenkins [2], an autoregressive integrated moving average model (ARIMA) has been one of the most popular time series forecast models. It assumes a linear relationship between the current value of the underlying variables and previous values of the variable and error terms [3]. Unlike ARIMA, neural networks are data-driven and non-parametric models. They are universal function approximators that can map any non-linear function without a priori assumptions about the properties of the data [4]. Neural networks has been successfully applied in financial time series data [5-7]. Panda et al. (2007) [5] utilized neural network, linear autoregressive, and random walk models to make one-step-ahead forecast of weekly Indian rupee/US dollar exchange rate. Experimental results indicated that the forecast performance of neural network model is superior to that of linear autoregressive, and random walk models in most of evaluation criteria. * Department of Civil Engineering, The University of Danang - University of Technology and Education, Danang city 550000, VietnamCorresponding author. Tel.: +84 905 476388.E-mail address: tttha@ute.udn.vn Faculty of Project Management, The University of Danang – University of Science and Technology, Danang city 550000, Vietnam.
2. 190 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA Recently, support vector machines (SVMs) introduced by Vapnik [8], has widely applied in solving regression, classification tasks, and time series prediction. By minimizing an upper bound of the generalization error, SVMs achieves the better predicted results than neural networks that minimize the empirical error [9]. Kim (2003) [10] applied SVMs to predict a future direction of the daily Korea composite stock price index. The findings presented that SVMs had a better predictive ability than the back-propagation neural network and the case-based reasoning. Least squares support vector regression (LSSVR), developed by Suykens et at. [11], is an advanced regression variant of SVMs. The LSSVR solves linear equations instead of a quadratic programming problem solved by the standard support vector regression (SVR). The LSSVR, thus, reduces computational complexity while enhancing the efficiency of the standard SVR. The performance of SVR highly depends on its hyperparameters, which are the regularization parameter and the kernel function parameter [12]. An adequate selection of these hyperparameters is crucial to obtain good performance in handling forecasting tasks with the SVR. Recently, evolutionary algorithms such as genetic algorithm (GA), particle swarm optimization (PSO) have been adopted to optimize the hyperparameters of SVR. The firefly algorithm (FA), a swarm-based intelligent algorithm, has been proven effective in solving optimization problems [13, 14]. Introduced by Yang in 2008 [15], the FA mimics the social behavior of fireflies in the summer sky. Previous studies indicated the superiority of the FA against some metaheuristics including GA, PSO, differential evolution, ant colony optimization, and simulated annealing [16-18]. This study develops a forecast hybrid model of least squares support vector regression and the firefly algorithm (FA-LSSVR). Two real-world stock price datasets in Vietnam stock market including Vietnam Dairy Products Joint Stock (Vinamilk-VNM) and Joint Stock Commercial Bank for Foreign Trade of Vietnam (Vietcombank-VCB) are used to validate the performance of the FA-LSSVR. Vinamilk and Vietcombank are one of leading stock indices in Vietnam Stock Exchange. In 2017, the market capitalization of Vinamilk and Vietcombank respectively ranked in the first position (9.5 billion US dollars) and the third position (5.9 billion US dollars) among top ten entrepreneurs listed in Vietnam Stock Exchange [19]. Criteria including root mean square errot (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are used to evaluate the performance accuracy of predictive models. The remainder of this paper is organized as follows. Section 2 elucidates methodologies consisting of the LSSVR, the FA, and the FA-LSSVR forecast model. Section 3 presents data preparation and performance measures. Experimental results and discussion are presented in Section 4. Finally, Section 5 draws conclusions and future works. 2. MACHINE LEARNING REGRESSION OPTIMIZED BY SWARM INTELLIGENCE 2.1. Least squares support vector regression Machine learning techniques have been widely applied in predicting time series data [5, 10, 20]. The LSSVR, an advanced machine learning technique, was proposed by Suykens et al. [11]. For solving regression problem, the LSSVR maps nonlinearly the input space into a high-dimensional feature space, and then run linear regression in the feature space. The LSSVR finds the solution by solving a set of linear equations in the dual space rather than solving a quadratic programming problem with linear inequality constraints, as in the standard SVR. By this way, the LSSVR achieves a lower computational burden while enabling good generalization capacity [21]. Figure 1 shows a general structure of the support vector regression.
3. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 191 N In a function estimation of the LSSVR, given a training dataset , the optimization problem {}xykk, k =1 is formulated as N 112 2 minJ (ωω , e ) = + Ce∑ k (1 (ω ,,)be 22i=1 subject to yk=ωϕ, ( x kk ) ++ be , k = 1, , N where J(w,e) is the optimization function; w is the parameter of the linear approximator; ek R is error variables; C ≥ 0 is a regularization constant that represents the trade-off between the empirical error and the ∊ flatness of the function; xk is input patterns; yk is prediction labels; and N is the sample size. Since Eq. (1) is a typical optimization problem of a differentiable function with constraints, it can be solved by using Lagrange multipliers (αk ). The resulting LSSVR model for function estimation can be expressed as Eq. (2). N yx()= ∑αkk Kxx (, )+ b (2) k =1 where αk ,b are Lagrange multipliers and the bias term, respectively; and Kxx(,k ) is the kernel function. In the feature space, the kernel function can be described as Eq. (3). m Kxx(,k )= ∑ g k () xg kk ( x ) (3) k =1 Fig. 1. Architecture of support vector regression model. Typical examples of kernel function are polynomial kernel and radius basis function (RBF) kernels. In highly nonlinear spaces, the RBF kernel often yields better results than other proposed kernels [21]. The RBF function is mathematically expressed as 2 2 Kxx( ,kk )= exp( −− x x / 2σ (4) whereσ is the kernel parameter which controls the kernel width used to fit the training data. Despite the effectiveness of the LSSVR in solving prediction problem, it accuracy depends on the setting of hyperparameters. For enhanced prediction accuracy of time series data, parameter optimization in LSSVR should include a regularization parameter (C) and the RBF kernel function (σ).
4. 192 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA 2.2. Firefly algorithm The FA, developed by Yang (2008) [15], is one of the most successful swarm intelligence methods. For solving a number of optimization problems, the FA is proven to be more efficient than some algorithms, such as GA and PSO [16, 22]. The FA is based on the flashing patterns and behavior of tropical fireflies to find both global and local optima simultaneously effectively. It has three idealized rules: (i) a firefly is attracted to other fireflies because they are unisex; (ii) attractiveness is proportional to brightness and decreases as distance increases; a firefly moves randomly if nothing else is brighter; and (iii) the brightness of a firefly is determined by the landscape of the objective function. As a firefly’s attractiveness is proportional to the light intensity seen by adjacent fireflies, the attractiveness β of a firefly is defined as 2 ββ= −γ r 0e (5) in which β is the attractiveness of the firefly; βo is the attractiveness of the firefly at r = 0; r is the distance between the firefly of interest and any other, e is a constant coefficient, and γ is the absorption coefficient. The distance between any two firefliesi and j at xi and xj, respectively, is calculated as d 2 rij=−= x i x j ∑ (xi ,k − x j ,k ) (6) k =1 where rij is the distance between any two fireflies i and j at xi and xj, respectively; xi,k is the kth component of spatial coordinate xi of the ith firefly; xj,k is the kth component of spatial coordinate xj of the jth firefly, and d is the number of dimensions of the search space. The movement of the ith firefly when attracted to a brighter jth firefly is determined as −γ r2 xt+1 =+ x tβα eij ( xx tt −+ ) t [rand − 0.5] i i0 ji (7) t+1 t where xi is the coordinate of the ith firefly in the(t+1) th iteration; xi is the coordinate of the ith firefly t in the tth iteration; xj is the coordinate of the jth firefly in thet th iteration; γ is the absorption coefficient and was set to explore global optima, γ varies from 0 to 1. The best result obtained in the sensitivity analysis t of γ is γ = 1; βo = βmin (= 0.1) is the attractiveness at rij = 0; α denotes a trade-off constant to determine the r a n d o m b e h a v i o r o f m o v e m e n t ; r a n d i s a r a n d o m - n u m b e r g e n e r a t o r u n i f o r m l y d i s t r i b u t e d w i t h i n [ 0 , 1 ] . 2.3. The FA-LSSVR model This section elucidates the hybrid model of the FA and the LSSVR that is used to forecasting financial data. The FA is utilized to optimize the LSSVR parameters including the regularization parameter (C) and the RBF kernel function (σ). The proposed FA-LSSVR model was coded in the MATLAB programming language, and its flowchart is presented in Fig. 2. At first, the original historical data are separated into learning data and test data. With a particular embedding dimension or lag, a state reconstruction is made to generate an input matrix and an output matrix. The lag value significantly affects the prediction performance of a model. A technical explanation of the state reconstruction is presented at [23, 24]. The learning data are then divided into training data and validation data. The training data are used to train the FA-LSSVR model while the validation data are used to optimize the FA-LSSVR model. Herein, the FA is applied to simultaneously and automatically identify
5. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 193 the optimal values of LSSVR’s parameters (C and ơ). The objective function of the proposed model is established based on the validation data as shown in Eq. (8). The optimization process ends when the stopping condition is satisfied and the optimal values ofC and ơ are determined. Finally, test data are used to test the performance of the optimized FA-LSSVR forecast model. n 1 2 f(,) Cσ = RMSEVal =∑ ('y − y ) (8) i=1 n where RMSEVal is the root mean square error calculated according to the predicted (y’) and actual (y) values, respectively, based on the validation data; n is the sample size of validation data. Time series dataset State reconstruction Test data Learning data Validation Training data data FA operation Training LSSVR Automatic FA model parameters search Objective function value Satisfying No stopping condition? Yes Optimized LSSVR Optimized FA prediction model parameters (C, σ) Forecast Forecast accuracy results Fig. 2. Flow chart of the FA-LSSVR model. 3. DATA PREPARATION AND PERFORMANCE MEASURES In this study, the performance of the FA-LSSVR is validated by two financial datasets collected from Ho Chi Minh Stock Exchange: Vietnam Dairy Products Joint Stock (VNM) and Joint Stock Commercial Bank for Foreign Trade of Vietnam (VCB) [25]. Each dataset includes daily closing observations from January 2015 to December 2017. In each year, the first ten months are used to train the model and the remaining two
6. 194 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA months are used to test the model. Actual values of the VNM and VCB datasets are visualized in Figs. 3 and 4, respectively. The statistical characteristics of two datasets are described in Table 1. 220 55 Learning data Learning data 200 Test data 50 Test data 180 45 160 40 140 35 120 30 100 Daily closing price (1000 VN dong) VN (1000 price closing Daily 80 dong) VN (1000 price closing Daily 25 60 20 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 Data points (Jan 2015 - Dec 2017) Data points (Jan 2015 - Dec 2017) Fig. 3. Daily closing prices of VNM. Fig. 4. Daily closing prices of VCB. Table 1. Statistical characteristics of two stock price datasets. VNM VCB Dataset 2015 2016 2017 2015 2016 2017 Data samples No. of total data 248 250 250 248 251 250 Period of learning data January - October January - October No. of learning data 204 206 207 204 207 207 Period of test data November - December November - December No. of test data 44 44 43 44 44 43 Statistical values of stock price (Unit: 1000 VN dong) Max 116.667 156.000 208.600 40.370 42.593 54.300 Mean 82.991 124.527 151.916 31.390 35.004 39.347 Min 66.667 95.000 126.000 23.630 28.593 34.850 Standard deviation 12.015 14.563 19.166 3.803 3.280 3.796 To assess forecast accuracy of predictive models, criteria are used including RMSE, MAE, and MAPE. The lower values of these criteria indicate the better forecast accuracy. Their corresponding equations are shown as follows. N 1 2 RMSE=∑ (yy − ') (9) N i=1 1 n MAE =∑ yy − ' (10) n i=1 1'n yy− MAPE = ∑ (11) nyi=1 where y is the actual value; y’ is the predicted value; and n is the number of test data. 4. EXPERIMENTAL RESULTS AND DISCUSSION
7. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 195 In this section, the performances of the ARIMA, LSSVR, and FA-LSSVR models are compared with each other using the VNM and VCB datasets. The initial settings of the proposed FA-LSSVR is presented in Table 2. Two hyperparameters of the LSSVR model are set to their default values (i.e., C = 10 and ơ = 0.1). Table 2. Parameter settings of the FA-LSSVR. Components Name Settings Learning data Training data 70% Validation data 30% LSSVR’s parameters C [10-3; 1012] ơ [10-3; 1012] FA’s parameters Number of fireflies 60 Max. of generation 30 As mentioned in Section 2.3, the embedding dimension or lag must be defined before the prediction is made. In this study, the optimal lag is determined by a sensitivity analysis. In each dataset, a subset in the year 2017 is used to validate the FA-LSSVR model when lag ranges from 3 to 10 days. The result indicates that the optimal lag of VNM dataset and VCB dataset is 3 days and 4 days, respectively. The performance of predictive models are then compared by adopting the optimal lag. Table 3 and 4 respectively compare the performance of predictive models in forecasting daily closing stock prices of VNM and VCB. The average performance measures and improvement rates are showed in Table 5. Table 3. Performance measures of predictive models using the VNM dataset. ARIMA LSSVR FA-LSSVR RMSE MAE MAPE RMSE MAE MAPE RMSE MAE MAPE 1000 1000 VN 1000 VN 1000 VN 1000 VN 1000 VN (%) (%) VN (%) dong dong dong dong dong dong 2015 6.552 4.952 4.60 23.399 23.117 21.87 2.081 1.552 1.46 2016 11.877 9.927 7.64 3.162 2.424 1.84 2.193 1.747 1.32 2017 38.252 35.101 18.17 45.462 41.578 21.50 4.395 3.292 1.75 Table 4. Performance measures of predictive models using the VCB dataset. ARIMA LSSVR FA-LSSVR RMSE MAE MAPE RMSE MAE MAPE RMSE MAE MAPE 1000 1000 1000 1000 VN 1000 VN 1000 VN VN (%) VN (%) VN (%) dong dong dong dong dong dong 2015 2.193 1.858 5.81 0.972 0.720 2.23 0.653 0.423 1.31 2016 0.872 0.741 2.11 0.436 0.348 0.98 0.357 0.263 0.74 2017 7.560 6.613 13.69 9.176 8.574 17.96 1.116 0.856 1.80 Table 5. Average performance measures and error rates improvement by the FA-LSSVR. Average performance measures Improved by the FA-LSSVR RMSE MAE MAPE RMSE MAE MAPE 1000 VN dong 1000 VN dong (%) (%) (%) (%) VNM dataset ARIMA 18.894 16.660 10.14 84.71 86.81 85.11 LSSVR 24.008 22.373 15.07 87.96 90.18 89.98 FA-LSSVR 2.890 2.197 1.51 - - -
8. 196 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA VCB dataset ARIMA 3.542 3.071 7.20 79.99 83.26 82.18 LSSVR 3.528 3.214 7.06 79.91 84.01 81.81 FA-LSSVR 0.709 0.514 1.28 - - - Table 3 shows that the FA-LSSVR outperformed the LSSVR and ARIMA models in predicting the daily closing price of the VNM. The FA-LSSVR obtained the significant lower values of RMSE, MAE, and MAPE over a period of 3 years compared to the ARIMA and the LSSVR. The lowest MAPE obtained by the proposed MFA-LSSVR was 1.32% while those of the ARIMA and the LSSVR were 4.6% (in 2015) and 1.84% (in 2016), respectively. In addition, the ARIMA showed a better predictive ability than the LSSVR. Table 5 shows that the error rates of the proposed model were 84.71-86.81% and 87.96-90.18% lower than those of the ARIMA and the LSSVR, respectively. Table 4 and 5 indicates that performance measures of the FA-LSSVR were superior to those of other models when using VCB dataset. The average MAE value yielded by the FA-LSSVR was 514 VND which was significantly lower than that yielded by the ARIMA (3,071 VND) and the LSSVR (3,214 VND). Similar to the VNM dataset, prediction errors obtained by all models in 2017 were higher than those obtained in 2015 and in 2016. This confirmed a strong fluctuation of Vietnam stock market in 2017. Comparing to the ARIMA, the LSSVR had lower values of RMSE, MAE, and MAPE, indicating its better predictive ability. The overall percentage improvement in error rates for the FA-LSSVR were 79.99-83.26% and 79.91-84.01% better than those of the ARIMA and the LSSVR, respectively. 37 120 Actual value Actual value 36 Predicted value by ARIMA 115 Predicted value by ARIMA Predicted value by LSSVR Predicted value by LSSVR 35 Predicted value by FA-LSSVR 110 Predicted value by FA-LSSVR 34 105 33 100 32 95 31 90 VND) (1000 price closing Daily Daily closing price (1000 VND) (1000 price closing Daily 30 85 29 80 10 20 30 40 45 10 20 30 40 45 Number of observations Number of observations (a) VNM dataset - 2015 (d) VCB dataset - 2015 150 37 145 36.5 140 36 135 35.5 130 35 Daily closing price (1000 VND) (1000 price closing Daily Daily closing price (1000 VND) (1000 price closing Daily Actual value Actual value 125 Predicted value by ARIMA 34.5 Predicted value by ARIMA Predicted value by LSSVR Predicted value by LSSVR Predicted value by FA-LSSVR Predicted value by FA-LSSVR 34 120 10 20 30 40 45 10 20 30 40 45 Number of observations Number of observations (b) VNM dataset - 2016 (e) VCB dataset - 2016
9. INTERNATIONAL CONFERENCE STARTUP AND INNOVATION NATION 197 56 210 Actual value Actual value 54 Predicted value by ARIMA 200 Predicted value by ARIMA Predicted value by LSSVR Predicted value by LSSVR 52 Predicted value by FA-LSSVR Predicted value by FA-LSSVR 190 50 48 180 46 170 44 Daily closing price (1000 VND) (1000 price closing Daily 160 42 Daily closing price (1000 VND) (1000 price closing Daily 40 150 38 10 20 30 40 45 140 Number of observations 10 20 30 40 45 Number of observations (c) VNM - 2017 (f) VCB dataset - 2017 Fig. 5. The comparison of actual values and predicted values of the VNM and VCB datasets. Fig. 5 displays actual values and predicted values when using VNM dataset and VCB dataset, respectively. It is clear that predicted values achieved by the FA-LSSVR model were closer to actual values than those achieved by the ARIMA and the LSSVR models. This confirmed the efficiency of the proposed model in predicting stock prices. CONCLUSIONS This study proposes a hybrid model of least squares support vector regression and a firefly algorithm to forecast financial time series data. The FA was utilized to automatically optimize the LSSVR’s parameters, which is aimed to improve the forecast accuracy. The proposed FA-LSSVR model was validated using two daily stock price datasets namely VNM and VCB. The performance of the FA-LSSVR was compared with that of ARIMA and the LSSVR. Experimental results show that the predictive ability of the FA-LSSVR was superior to that of the ARIMA and the LSSVR in both datasets. In practice, the stock price is affected by some factors like rates, political events that were not considered in this study. Thus, a novel model which predicts multivariate time series data should be developed. In addition, the proposed model needs to be confirmed by using other financial datasets like exchange rates. REFERENCES H.N. Nhu, S. Nitsuwat, M. Sodanil, Prediction of Stock Price Using An Adaptive Neuro-Fuzzy Inference System Trained by Firefly Algorithm International Computer Science and Engineering Conference, IEEE, 2013. George Box, G. Jenkins, Time series analysis, forecasting and control, CA:Holden-Day, San Francisco, 1970. H. Ince, T.B. Trafalis, A hybrid model for exchange rate prediction, Decision Support Systems 42 (2006) 1054–1062. S. Haykin, Neural networks: a comprehensive foundation, Englewood CliKs, NJ: Prentice Hall, 1999. C. Panda, V. Narasimhan, Forecasting exchange rate better with artificial neural network, Journal of Policy Modeling 29(2) (2007) 227-236. F. Shen, J. Chao, J. Zhao, Forecasting exchange rate using deep belief networks and conjugate gradient method, Neurocomputing 167 (2015) 243-253. M. Rehman, G.M. Khan, S.A. Mahmud, Foreign Currency Exchange Rates Prediction Using CGP and Recurrent Neural Network, IERI Procedia 10 (2014) 239-244. V.N. Vapnik, The nature of statistical learning theory, Springer-Verlag, New York, 1995. P.-F. Pai, C.-S. Lin, A hybrid ARIMA and support vector machines model in stock price forecasting, Omega 33(6) (2005) 497-505.
10. 198 HỘI THẢO KHOA HỌC QUỐC TẾ KHỞI NGHIỆP ĐỔI MỚI SÁNG TẠO QUỐC GIA K.-j. Kim, Financial time series forecasting using support vector machines, Neurocomputing 55(1–2) (2003) 307-319. J.A.K. Suykens, T.V. Gestel, J.D. Brabanter, Least squares support vector machines, Singapore: World Scientific2002. O. Chapelle, V. Vapnik, O. Bousquet, S. Mukherjee, Choosing Multiple Parameters for Support Vector Machines, Machine Learning 46(1-3) (2002) 131–159. C.-Y. Yeh, C.-W. Huang, S.-J. Lee, A multiple-kernel support vector regression approach for stock market price forecasting, Expert Systems with Applications 38(3) (2011) 2177-2186. T. Xiong, Y. Bao, Z. Hu, Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting, Knowledge-Based Systems 55 (2014) 87-100. X.-S. Yang, Firefly algorithm, Luniver Press, Bristol, U.K, 2008. I. Fister, I. Fister Jr, X.-S. Yang, J. Brest, A comprehensive review of firefly algorithms, Swarm and Evolutionary Computation 13 (2013) 34-46. S.K. Pal, C.S. Rai, A.P. Singh, Comparative Study of Firefly Algorithm and Particle Swarm Optimization for Noisy Non-Linear Optimization Problems, International Journal of Intelligent Systems and Applications 4 (2012). H. Banati, M. Bajaj, Fire Fly Based Feature Selection Approach, International Journal of Computer Science Issues 8(4) (2011). M. Hanh, Top 10 Giants in Vietnam Stock Exchange, 2017. exchange-20170823164608368.htm. (Accessed August 2018). W.-C. Hong, Hybrid evolutionary algorithms in a SVR-based electric load forecasting model, International Journal of Electrical Power & Energy Systems 31(7–8) (2009) 409-417. H. Wang, D. Hu, Comparison of SVM and LS-SVM for regression, International Conference on Neural Networks and Brain, IEEE, 2005, pp. 279-283. L.d.S. Coelho, V.C. Mariani, Improved firefly algorithm approach applied to chiller loading for energy conservation, Energy and Buildings 59 (2013) 273-278. Z. Min, T. Huanq, Short Term Load Forecasting with Least Square Support Vector Regression and PSO, in: J. Zhang (Ed.), Communications in Computer and Information Science, Springer Heidelberg Dordrecht London NewYork2011, pp. 124-132. N.-T. Ngo, T.T.H. Truong, Time Series Analysis for Improving Accuracy of Stock Price Forecasts Using Least Squares Support Vector Regression, International Conference for Young Researchers in Economics and Business, Da Nang, Vietnam, 2017, pp. 637-643. C.t.T.F. Media, 2018).