Support vector regression with chaos-based firefly algorithm for stock market price forecasting

Due to the inherent non-linearity and non-stationary characteristics of financial stock market price time series, conventional modeling techniques such as the Box–Jenkins autoregressive integrated moving average (ARIMA) are not adequate for stock market price forecasting. In this paper, a forecasting model based on chaotic mapping, firefly algorithm, and support vector regression (SVR) is proposed to predict stock market price. The forecasting model has three stages. In the first stage, a delay coordinate embedding method is used to reconstruct unseen phase space dynamics. In the second stage, a chaotic firefly algorithm is employed to optimize SVR hyperparameters. Finally in the third stage, the optimized SVR is used to forecast stock market price. The significance of the proposed algorithm is 3-fold. First, it integrates both chaos theory and the firefly algorithm to optimize SVR hyperparameters, whereas previous studies employ a genetic algorithm (GA) to optimize these parameters. Second, it uses a delay coordinate embedding method to reconstruct phase space dynamics. Third, it has high prediction accuracy due to its implementation of structural risk minimization (SRM). To show the applicability and superiority of the proposed algorithm, we selected the three most challenging stock market time series data from NASDAQ historical quotes, namely Intel, National Bank shares and Microsoft daily closed (last) stock price, and applied the proposed algorithm to these data. Compared with genetic algorithm-based SVR (SVR-GA), chaotic genetic algorithm-based SVR (SVR-CGA), firefly-based SVR (SVR-FA), artificial neural networks (ANNs) and adaptive neuro-fuzzy inference systems (ANFIS), the proposed model performs best based on two error measures, namely mean squared error (MSE) and mean absolute percent error (MAPE).     

一种改进的组合SOFM-SVR股票价格预测模型

股票市场价格预测一直以来都被认为是金融时序预测领域的一项具有挑战性的工作。综合回归支持向量机SVR和自组织特征函数(SOFM)技术,并引入基于过滤的特征选择算法确定重要的输入变量,在SVR核函数的参数选择上采用粒子群优化算法(PSO)。SOFM算法将训练样本聚类,然后分别应用SVR来预测股票价格走势。最后应用上海A股的浦发银行日数据来做股票价格日预测,实验结果表明,经过改进的SOFM-SVR模型与之前的SOFM-SVR模型相比,在预测精度和训练时间上都有了较大的提高。     

Visualization and dynamic evaluation model of corporate financial structure with self-organizing map and support vector regression

Prediction of financial bankruptcy has been a focus of considerable attention among both practitioners and researchers. However, most research in this area has ignored the non-stationary nature of corporate financial structures. Specifically, financial structures do not always present consistent statistical tests at each point of time, resulting in dynamic relationships between financial structures and their predictors. This characteristic of financial bankruptcy presents a significant challenge for any single artificial prediction technique. Therefore, this paper will propose a multi-phased and dynamic evaluation model of the corporate financial structure integrating both the self-organizing map (SOM) and support vector regression (SVR) techniques. In the 1st phase, the inputs to the SOM are financial indicators derived from listed companies’ public financial statements adopting the principle component analysis (PCA) to extract useful indicators with a strong influence that each year determines the company's position on the SOM. In addition, we used the SOM to visualize and cluster each corporate in the 2D map. We also investigated each cluster and classified them into healthy and bankrupt-prone ones based on their regions in visualizing the 2D map. In the 2nd phase, we drew the trajectory for the healthy and the bankrupt-prone companies for consecutive years in a 2D map. Therefore, several visualized and dynamic patterns of corporate behavior could be recognized. In the 3rd phase, we used the SVR method to forecast the future trend for corporate financial structure. In addition, this research also compared the hybrid SOM–SVR architecture with single SOM, SVR, and Learning Vector Quantization (LVQ) algorithms. The results showed that the proposed methodology outperformed the other methods in both prediction accuracy and ease of use.     

基于HP-LSTM模型的股指价格预测方法

股指价格时间序列受到长期和短期不同因素的影响,且具有非平稳、非线性等特点,传统计量模型的预测精度较低。为提高预测精度,一些研究将人工神经网络模型用于金融时间序列预测,取得了比传统计量模型更好的效果。提出了一种融合了HP滤波（Hodrick-Prescott Filter）和LSTM神经网络模型的股指价格预测模型,模型使用HP滤波将股指价格时间序列分解为长期趋势和短期波动,利用LSTM神经网络模型分别学习长期趋势和短期波动序列的特征,并分别进行长期趋势和短期波动预测,将预测结果融合得出股指价格预测结果。实验结果表明,提出的HP-LSTM混合模型不仅可以有效捕捉到股指价格时间序列的长期趋势和短期波动的变化规律,提高了股指价格预测精度,并且长期趋势和短期波动都具有相应的经济含义,提高了模型的可解释性。     

Short term forecasting with support vector machines and application to stock price prediction

Forecasting a stock price movement is one of the most difficult problems in finance. The reason is that financial time series are complex, non stationary. Furthermore, it is also very difficult to predict this movement with parametric models. Instead of parametric models, we propose two techniques, which are data driven and non parametric. Based on the idea that excess returns would be possible with publicly available information, we developed two models in order to forecast the short term price movements by using technical indicators. Our assumption is that the future value of a stock price depends on the financial indicators although there is no parametric model to explain this relationship. This relationship comes from the technical analysis. Comparison shows that support vector regression (SVR) out performs the multi layer perceptron (MLP) networks for a short term prediction in terms of the mean square error. If the risk premium is used as a comparison criterion, then the SVR technique is as good as the MLP method or better.     

自组织映射算法与基于专家系统的支持向量回归的结合

A new approach is proposed to model nonlinear dynamic systems by combining SOM (self-organizing feature map) with support vector regression (SVR) based on expert system. The whole system has a two-stage neural network architecture. In the first stage SOM is used as a clustering algorithm to partition the whole input space into several disjointed regions. A hierarchical architecture is adopted in the partition to avoid the problem of predetermining the number of partitioned regions. Then, in the second stage, multiple SVR, also called SVR experts, that best fit each partitioned region by the combination of different kernel function of SVR and promote the configuration and tuning of SVR. Finally, to apply this new approach to time-series prediction problems based on the Mackey-Glass differential equation and Santa Fe data, the results show that SVR experts has effective improvement in the generalization performance in comparison with the single SVR model.     

A Bayesian regularized artificial neural network for stock market forecasting

In this paper a Bayesian regularized artificial neural network is proposed as a novel method to forecast financial market behavior. Daily market prices and financial technical indicators are utilized as inputs to predict the one day future closing price of individual stocks. The prediction of stock price movement is generally considered to be a challenging and important task for financial time series analysis. The accurate prediction of stock price movements could play an important role in helping investors improve stock returns. The complexity in predicting these trends lies in the inherent noise and volatility in daily stock price movement. The Bayesian regularized network assigns a probabilistic nature to the network weights, allowing the network to automatically and optimally penalize excessively complex models. The proposed technique reduces the potential for overfitting and overtraining, improving the prediction quality and generalization of the network. Experiments were performed with Microsoft Corp. and Goldman Sachs Group Inc. stock to determine the effectiveness of the model. The results indicate that the proposed model performs as well as the more advanced models without the need for preprocessing of data, seasonality testing, or cycle analysis.     

Stock trend prediction based on a new status box method and AdaBoost probabilistic support vector machine

Stock trend prediction is regarded as one of the most challenging tasks of financial time series prediction. Conventional statistical modeling techniques are not adequate for stock trend forecasting because of the non-stationarity and non-linearity of the stock market. With this regard, many machine learning approaches are used to improve the prediction results. These approaches mainly focus on two aspects: regression problem of the stock price and prediction problem of the turning points of stock price. In this paper, we concentrate on the evaluation of the current trend of stock price and the prediction of the change orientation of the stock price in future. Then, a new approach named status box method is proposed. Different from the prediction issue of the turning points, the status box method packages some stock points into three categories of boxes which indicate different stock status. And then, some machine learning techniques are used to classify these boxes so as to measure whether the states of each box coincides with the stock price trend and forecast the stock price trend based on the states of the box. These results would support us to make buying or selling strategies. Comparing with the turning points prediction that only considered the features of one day, each status box contains a certain amount of points which represent the stock price trend in a certain period of time. So, the status box reflects more information of stock market. To solve the classification problem of the status box, a special features construction approach is presented. Moreover, a new ensemble method integrated with the AdaBoost algorithm, probabilistic support vector machine (PSVM), and genetic algorithm (GA) is constructed to perform the status boxes classification. To verify the applicability and superiority of the proposed methods, 20 shares chosen from Shenzhen Stock Exchange (SZSE) and 16 shares from National Association of Securities Dealers Automated Quotations (NASDAQ) are applied to perform stock trend prediction. The results show that the status box method not only have the better classification accuracy but also effectively solve the unbalance problem of the stock turning points classification. In addition, the new ensemble classifier achieves preferable profitability in simulation of stock investment and remarkably improves the classification performance compared with the approach that only uses the PSVM or back-propagation artificial neural network (BPN).     

A Takagi–Sugeno fuzzy model combined with a support vector regression for stock trading forecasting

The turning points prediction scheme for future time series analysis based on past and present information is widely employed in the field of financial applications. In this research, a novel approach to identify turning points of the trading signal using a fuzzy rule-based model is presented. The Takagi–Sugeno fuzzy rule-based model (the TS model) can accurately identify daily stock trading from sets of technical indicators according to the trading signals learned by a support vector regression (SVR) technique. In addition, when new trading points are created, the structure and parameters of the TS model are constantly inherited and updated. To verify the effectiveness of the proposed TS fuzzy rule-based modeling approach, we have acquired the stock trading data in the US stock market. The TS fuzzy approach with dynamic threshold control is compared with a conventional linear regression model and artificial neural networks. Our result indicates that the TS fuzzy model not only yields more profit than other approaches but also enables stable dynamic identification of the complexities of the stock forecasting system.     

MTICA-AEO-SVR股票价格预测模型

为了改善传统Fast ICA算法的稳定性和分离效率,基于Tukey M估计构造了一种新的非线性函数,提出了MTICA算法;并在此基础上结合SVR算法,建立了一种新的MTICA-AEO-SVR股票价格预测模型。用MTICA算法将原始股票数据分解为独立分量进行排序去噪,选择不同的SVR模型分别对各独立分量和股票价格进行预测。在SVR算法中引入了人工生态系统优化算法（AEO）选参,提高了模型的预测精度。通过对上证B股指数的实证分析,结果表明,MTICA-AEO-SVR模型比ICA-AEO-SVR模型和ICA-SVR模型更准确和高效。     

A hybrid procedure for stock price prediction by integrating self-organizing map and genetic programming

Stock price prediction is a very important financial topic, and is considered a challenging task and worthy of the considerable attention received from both researchers and practitioners. Stock price series have properties of high volatility, complexity, dynamics and turbulence, thus the implicit relationship between the stock price and predictors is quite dynamic. Hence, it is difficult to tackle the stock price prediction problems effectively by using only single soft computing technique. This study hybridizes a self-organizing map (SOM) neural network and genetic programming (GP) to develop an integrated procedure, namely, the SOM-GP procedure, in order to resolve problems inherent in stock price predictions. The SOM neural network is utilized to divide the sample data into several clusters, in such a manner that the objects within each cluster possess similar properties to each other, but differ from the objects in other clusters. The GP technique is applied to construct a mathematical prediction model that describes the functional relationship between technical indicators and the closing price of each cluster formed in the SOM neural network. The feasibility and effectiveness of the proposed hybrid SOM-GP prediction procedure are demonstrated through experiments aimed at predicting the finance and insurance sub-index of TAIEX (Taiwan stock exchange capitalization weighted stock index). Experimental results show that the proposed SOM-GP prediction procedure can be considered a feasible and effective tool for stock price predictions, as based on the overall prediction performance indices. Furthermore, it is found that the frequent and alternating rise and fall, as well as the range of daily closing prices during the period, significantly increase the difficulties of predicting.     

基于模糊近似支持向量回归的股价预测研究

股价预测是投资策略形成和风险管理模型发展的基础。为了降低股价变化趋势中的噪声信息和投资者关于两种股价预测误差的不同偏好对股价预测的影响,提出了基于信噪比的模糊近似支持向量回归(FPSVR)的股价预测模型。首先构建信噪比输入变量,然后引入模糊隶属度和双边权重测量方法对支持向量回归(SVR)模型进行改进,最后借助沪深300成份股2008至2019年的股票时间序列日数据,按照股市的波动情况将其分为三个阶段(牛市、熊市、震荡市),并建立三个基准模型进行对比分析。研究结果表明:与三个基准模型相比,所提出的股价预测模型的预测误差最低;与原有的SVR模型相比,FPSVR模型可以更好地对处于牛市和震荡市阶段的股票时间序列进行股价预测。     

A generalized model for financial time series representation and prediction

Traditional financial analysis systems utilize low-level price data as their analytical basis. For example, a decision-making system for stock predictions regards raw price data as the training set for classifications or rule inductions. However, the financial market is a complex and dynamic system with noisy, non-stationary and chaotic data series. Raw price data are too random to characterize determinants in the market, preventing us from reliable predictions. On the other hand, high-level representation models which represent data on the basis of human knowledge of the problem domain can reduce the randomness in the raw data. In this paper, we present a high-level representation model easy to translate from low-level data into the machine representation. It is a generalized model in that it can accommodate multiple financial analytical techniques and intelligent trading systems. To demonstrate this, we further combine the representation with a probabilistic model for automatic stock trades and provide promising results. An erratum to this article can be found at     

Integration of genetic fuzzy systems and artificial neural networks for stock price forecasting

Stock market prediction is regarded as a challenging task in financial time-series forecasting. The central idea to successful stock market prediction is achieving best results using minimum required input data and the least complex stock market model. To achieve these purposes this article presents an integrated approach based on genetic fuzzy systems (GFS) and artificial neural networks (ANN) for constructing a stock price forecasting expert system. At first, we use stepwise regression analysis (SRA) to determine factors which have most influence on stock prices. At the next stage we divide our raw data into k clusters by means of self-organizing map (SOM) neural networks. Finally, all clusters will be fed into independent GFS models with the ability of rule base extraction and data base tuning. We evaluate capability of the proposed approach by applying it on stock price data gathered from IT and Airlines sectors, and compare the outcomes with previous stock price forecasting methods using mean absolute percentage error (MAPE). Results show that the proposed approach outperforms all previous methods, so it can be considered as a suitable tool for stock price forecasting problems.     

Evolutional RBFNs prediction systems generation in the applications of financial time series data

An artificial neural prediction system is automatically developed with the combinations of step wise regression analysis (SRA), dynamic learning and recursive-based particle swarm optimization (RPSO) learning algorithms. In the first stage, the SRA can be considered like a data filtering machine to choose two primary factors from 20 channel technical indexes as input variables of the RBFNs system. Then, an efficient dynamic learning algorithm is applied to sequentially generate RBFs functions from training data set, where it can efficiently determine the proper number of RBFs’ centers and their associated positions. It can be exploited to forecast appropriate behaviors of the wanted identified financial time series data. While characteristics of training data set are automatically mined and generated by the proposed dynamic learning algorithm, architecture of the RBFNs prediction system is initially represented with collected information. Moreover, the RPSO learning scheme with the hybrid particle swarm optimization (PSO) and recursive least-squares (RLS) learning methods are applied to extract those appropriate parameters of the RBFNs prediction system.The RBFNs prediction systems are implemented in data analysis, module generation and price trend of the financial time series data. It not only automatically determines proper RBFs number but also fast approach the desired target in actual trading of Taiwan stock index (TAIEX). Computer simulations in training and testing phases of historic TAIEX are compared with other learning methods, which illustrate our great performance not only increases the accuracy of the stock price prediction but also improves the win rate in the trend of TAIEX.     

A hybrid ANFIS model based on empirical mode decomposition for stock time series forecasting

Time series forecasting is an important and widely popular topic in the research of system modeling, and stock index forecasting is an important issue in time series forecasting. Accurate stock price forecasting is a challenging task in predicting financial time series. Time series methods have been applied successfully to forecasting models in many domains, including the stock market. Unfortunately, there are 3 major drawbacks of using time series methods for the stock market: (1) some models can not be applied to datasets that do not follow statistical assumptions; (2) most time series models that use stock data with a significant amount of noise involutedly (caused by changes in market conditions and environments) have worse forecasting performance; and (3) the rules that are mined from artificial neural networks (ANNs) are not easily understandable.To address these problems and improve the forecasting performance of time series models, this paper proposes a hybrid time series adaptive network-based fuzzy inference system (ANFIS) model that is centered around empirical mode decomposition (EMD) to forecast stock prices in the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) and Hang Seng Stock Index (HSI). To measure its forecasting performance, the proposed model is compared with Chen's model, Yu's model, the autoregressive (AR) model, the ANFIS model, and the support vector regression (SVR) model. The results show that our model is superior to the other models, based on root mean squared error (RMSE) values.     

基于改进GA参数优化的SVR股价预测模型

针对股票价格的动态性及非线性等特点, 提出了基于改进遗传算法(Genetic Algorithm, GA)优化参数的支持向量回归机(Support Vector Regression, SVR)股价预测模型. 首先将选取的股票价格样本进行小波去噪处理, 然后将经过改进GA优化参数的SVR模型对去噪后的数据进行预测及评价. 结果证明, 改进小波-GA-SVR模型具有良好的预测效果, 对股票价格的预测研究具有一定的意义.     

基于ATLG混合模型的股票价格预测

股市是金融市场的重要组成部分,对股票价格预测有着重要的意义.同时,深度学习具有强大的数据处理能力,可以解决金融时间序列的复杂性所带来的问题.对此,本文提出一种结合自注意力机制的混合神经网络模型(ATLG).该模型由长短期记忆网络(LSTM)、门控递归单元(GRU)、自注意力机制构建而成,用于对股票价格的预测.实验结果表明:(1)与LSTM、GRU、RNN-LSTM、RNN-GRU等模型相比, ATLG模型的准确率更高;(2)引入自注意力机制使模型更能聚焦于重要时间点的股票特征信息;(3)通过对比,双层神经网络起到的效果更为明显.(4)通过MACD (moving average convergence and divergence)指标进行回测检验,获得了53%的收益,高于同期沪深300的收益.结果证明了该模型在股票价格预测中的有效性和实用性.     

A novel model by evolving partially connected neural network for stock price trend forecasting

This paper proposes a novel model by evolving partially connected neural networks (EPCNNs) to predict the stock price trend using technical indicators as inputs. The proposed architecture has provided some new features different from the features of artificial neural networks: (1) connection between neurons is random; (2) there can be more than one hidden layer; (3) evolutionary algorithm is employed to improve the learning algorithm and training weights. In order to improve the expressive ability of neural networks, EPCNN utilizes random connection between neurons and more hidden layers to learn the knowledge stored within the historic time series data. The genetically evolved weights mitigate the well-known limitations of gradient descent algorithm. In addition, the activation function is defined using sin(x) function instead of sigmoid function. Three experiments were conducted which are explained as follows. In the first experiment, we compared the predicted value of the trained EPCNN model with the actual value to evaluate the prediction accuracy of the model. Second experiment studied the over fitting problem which occurred in neural network training by taking different number of neurons and layers. The third experiment compared the performance of the proposed EPCNN model with other models like BPN, TSK fuzzy system, multiple regression analysis and showed that EPCNN can provide a very accurate prediction of the stock price index for most of the data. Therefore, it is a very promising tool in forecasting of the financial time series data.     

Forecasting stock indices with back propagation neural network

Stock prices as time series are non-stationary and highly-noisy due to the fact that stock markets are affected by a variety of factors. Predicting stock price or index with the noisy data directly is usually subject to large errors. In this paper, we propose a new approach to forecasting the stock prices via the Wavelet De-noising-based Back Propagation (WDBP) neural network. An effective algorithm for predicting the stock prices is developed. The monthly closing price data with the Shanghai Composite Index from January 1993 to December 2009 are used to illustrate the application of the WDBP neural network based algorithm in predicting the stock index. To show the advantage of this new approach for stock index forecast, the WDBP neural network is compared with the single Back Propagation (BP) neural network using the real data set.