Financial market forecasting using a two-step kernel learning method for the support vector regression

In this paper, we propose a two-step kernel learning method based on the support vector regression (SVR) for financial time series forecasting. Given a number of candidate kernels, our method learns a sparse linear combination of these kernels so that the resulting kernel can be used to predict well on future data. The L ₁-norm regularization approach is used to achieve kernel learning. Since the regularization parameter must be carefully selected, to facilitate parameter tuning, we develop an efficient solution path algorithm that solves the optimal solutions for all possible values of the regularization parameter. Our kernel learning method has been applied to forecast the S&P500 and the NASDAQ market indices and showed promising results.     

Estimating value at risk with semiparametric support vector quantile regression

Value at Risk (VaR) has been used as an important tool to measure the market risk under normal market. Usually the VaR of log returns is calculated by assuming a normal distribution. However, log returns are frequently found not normally distributed. This paper proposes the estimation approach of VaR using semiparametric support vector quantile regression (SSVQR) models which are functions of the one-step-ahead volatility forecast and the length of the holding period, and can be used regardless of the distribution. We find that the proposed models perform better overall than the variance-covariance and linear quantile regression approaches for return data on S&P 500, NIKEI 225 and KOSPI 200 indices.     

Rough support vector regression

This paper describes the relationship between support vector regression (SVR) and rough (or interval) patterns. SVR is the prediction component of the support vector techniques. Rough patterns are based on the notion of rough values, which consist of upper and lower bounds, and are used to effectively represent a range of variable values. Predictions of rough values in a variety of different forms within the context of interval algebra and fuzzy theory are attracting research interest. An extension of SVR, called rough support vector regression   (RSVR), is proposed to improve the modeling of rough patterns. In particular, it is argued that the upper and lower bounds should be modeled separately. The proposal is shown to be a more flexible version of lower possibilistic regression model using ?$?$-insensitivity. Experimental results on the Dow Jones Industrial Average demonstrate the suggested RSVR modeling technique.     

Relevance regression learning with support vector machines

We propose a variant of two SVM regression algorithms expressly tailored in order to exploit additional information summarizing the relevance of each data item, as a measure of its relative importance w.r.t. the remaining examples. These variants, enclosing the original formulations when all data items have the same relevance, are preliminary tested on synthetic and real-world data sets. The obtained results outperform standard SVM approaches to regression if evaluated in light of the above mentioned additional information about data quality.     

Support vector regression for warranty claim forecasting

Forecasting the number of warranty claims is vitally important for manufacturers/warranty providers in preparing fiscal plans. In existing literature, a number of techniques such as log-linear Poisson models, Kalman filter, time series models, and artificial neural network models have been developed. Nevertheless, one might find two weaknesses existing in these approaches: (1) they do not consider the fact that warranty claims reported in the recent months might be more important in forecasting future warranty claims than those reported in the earlier months, and (2) they are developed based on repair rates (i.e., the total number of claims divided by the total number of products in service), which can cause information loss through such an arithmetic-mean operation.To overcome the above two weaknesses, this paper introduces two different approaches to forecasting warranty claims: the first is a weighted support vector regression (SVR) model and the second is a weighted SVR-based time series model. These two approaches can be applied to two scenarios: when only claim rate data are available and when original claim data are available. Two case studies are conducted to validate the two modelling approaches. On the basis of model evaluation over six months ahead forecasting, the results show that the proposed models exhibit superior performance compared to that of multilayer perceptrons, radial basis function networks and ordinary support vector regression models.     

Some evidence on forecasting time-series with support vector machines

The importance of predicting future values of a time-series transcends a range of disciplines. Economic and business time-series are typically characterized by trend, cycle, seasonal, and random components. Powerful methods have been developed to capture these components by specifying and estimating statistical models. These methods include exponential smoothing, autoregressive integrated moving average (ARIMA), and partially adaptive estimated ARIMA models. New research in pattern recognition through machine learning offers innovative methodologies that can improve forecasting performance. This paper presents a study of the comparative results of time-series analysis on nine problem domains, each of which exhibits differing time-series characteristics. Comparative analyses use ARIMA selection employing an intelligent agent, ARIMA estimation through partially adaptive methods, and support vector machines. The results find that support vector machines weakly dominate the other methods and achieve the best results in eight of nine different data sets.     

Composite support vector quantile regression estimation

In this paper we propose a new nonparametric regression method called composite support vector quantile regression (CSVQR) that combines the formulations of support vector regression and composite quantile regression. First the CSVQR using the quadratic programming (QP) is proposed and then the CSVQR utilizing the iteratively reweighted least squares (IRWLS) procedure is proposed to overcome weakness of the QP based method in terms of computation time. The IRWLS procedure based method enables us to derive a generalized cross validation (GCV) function that is easier and faster than the conventional cross validation function. The GCV function facilitates choosing the hyperparameters that affect the performance of the CSVQR and saving computation time. Numerical experiment results are presented to illustrate the performance of the proposed method     

Electric load forecasting by support vector model

Accurately electric load forecasting has become the most important management goal, however, electric load often presents nonlinear data patterns. Therefore, a rigid forecasting approach with strong general nonlinear mapping capabilities is essential. Support vector regression (SVR) applies the structural risk minimization principle to minimize an upper bound of the generalization errors, rather than minimizing the training errors which are used by ANNs. The purpose of this paper is to present a SVR model with immune algorithm (IA) to forecast the electric loads, IA is applied to the parameter determine of SVR model. The empirical results indicate that the SVR model with IA (SVRIA) results in better forecasting performance than the other methods, namely SVMG, regression model, and ANN model.     

Multiphase support vector regression for function approximation with break-points

In this paper, we propose a novel multiphase support vector regression (mp-SVR) technique to approximate a true relationship for the case where the effect of input on output changes abruptly at some break-points. A new formulation for mp-SVR is presented to allow such structural changes in regression function. And then, we present a new hybrid-encoding scheme in genetic algorithms to select the best combination of the kernel functions and to determine both break-points and hyperparameters of mp-SVR. The proposed method has a major advantage over the conventional ones that different kernel functions can be possibly adapted to different regions of the data domain. Computational results in two examples including a real-life data demonstrate its capability in capturing the local characteristics of the data more effectively. Consequently, the mp-SVR has a high potential value in a wide range of applications for function approximations.     

System reliability forecasting by support vector machines with genetic algorithms

Support vector machines (SVMs) have been used successfully to deal with nonlinear regression and time series problems. However, SVMs have rarely been applied to forecasting reliability. This investigation elucidates the feasibility of SVMs to forecast reliability. In addition, genetic algorithms (GAs) are applied to select the parameters of an SVM model. Numerical examples taken from the previous literature are used to demonstrate the performance of reliability forecasting. The experimental results reveal that the SVM model with genetic algorithms (SVMG) results in better predictions than the other methods. Hence, the proposed model is a proper alternative for forecasting system reliability.     

Predictive modeling in a steelmaking process using optimized relevance vector regression and support vector regression

Annals of Operations Research - The existence of contaminants in metal alloys products is the main problem affecting the product quality, which is an important requirement for competitiveness in...     

Global sensitivity analysis using support vector regression

Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on response variables. In this paper, a new kernel function derived from orthogonal polynomials is proposed for support vector regression (SVR). Based on this new kernel function, the Sobol’ global sensitivity indices can be computed analytically by the coefficients of the surrogate model built by SVR. In order to improve the performance of the SVR model, a kernel function iteration scheme is introduced further. Due to the excellent generalization performance and structural risk minimization principle, the SVR possesses the advantages of solving non-linear prediction problems with small samples. Thus, the proposed method is capable of computing the Sobol’ indices with a relatively limited number of model evaluations. The proposed method is examined by several examples, and the sensitivity analysis results are compared with the sparse polynomial chaos expansion (PCE), high dimensional model representation (HDMR) and Gaussian radial basis (RBF) SVR model. The examined examples show that the proposed method is an efficient approach for GSA of complex models.     

Learning errors of linear programming support vector regression

In this paper, we give several results of learning errors for linear programming support vector regression. The corresponding theorems are proved in the reproducing kernel Hilbert space. With the covering number, the approximation property and the capacity of the reproducing kernel Hilbert space are measured. The obtained result (Theorem 2.1) shows that the learning error can be controlled by the sample error and regularization error. The mentioned sample error is summarized by the errors of learning regression function and regularizing function in the reproducing kernel Hilbert space. After estimating the generalization error of learning regression function (Theorem 2.2), the upper bound (Theorem 2.3) of the regularized learning algorithm associated with linear programming support vector regression is estimated.     

A robust support vector regression with a linear-log concave loss function

Support vector regression (SVR) is one of the most popular nonlinear regression techniques with the aim to approximate a nonlinear system with a good generalization capability. However, SVR has a major drawback in that it is sensitive to the presence of outliers. The ramp loss function for robust SVR has been introduced to resolve this problem, but SVR with ramp loss function has a non-differentiable and non-convex formulation, which is not easy to solve. Consequently, SVR with the ramp loss function requires smoothing and Concave-Convex Procedure techniques, which transform the non-differentiable and non-convex optimization to a differentiable and convex one. We present a robust SVR with linear-log concave loss function (RSLL), which does not require the transformation technique, where the linear-log concave loss function has a similar effect as the ramp loss function. The zero norm approximation and the difference of convex functions problem are employed for solving the optimization problem. The proposed RSLL approach is used to develop a robust and stable virtual metrology (VM) prediction model, which utilizes the status variables of process equipment to predict the process quality of wafer level in semiconductor manufacturing. We also compare the proposed approach to existing SVR-based methods in terms of the root mean squared error of prediction using both synthetic and real data sets. Our experimental results show that the proposed approach performs better than existing SVR-based methods regardless of the data set and type of outliers (ie, X-space and Y-space outliers), implying that it can be used as a useful alternative when the regression data contain outliers.     

Selecting rows and columns for training support vector regression models with large retail datasets

Although support vector regression models are being used successfully in various applications, the size of the business datasets with millions of observations and thousands of variables makes training them difficult, if not impossible to solve. This paper introduces the Row and Column Selection Algorithm (ROCSA) to select a small but informative dataset for training support vector regression models with standard SVM tools. ROCSA uses ε-SVR models with L₁-norm regularization of the dual and primal variables for the row and column selection steps, respectively. The first step involves parallel processing of data chunks and selects a fraction of the original observations that are either representative of the pattern identified in the chunk, or represent those observations that do not fit the identified pattern. The column selection step dramatically reduces the number of variables and the multicolinearity in the dataset, increasing the interpretability of the resulting models and their ease of maintenance. Evaluated on six retail datasets from two countries and a publicly available research dataset, the reduced ROCSA training data improves the predictive accuracy on average by 39% compared with the original dataset when trained with standard SVM tools. Comparison with the ε SSVR method using reduced kernel technique shows similar performance improvement. Training a standard SVM tool with the ROCSA selected observations improves the predictive accuracy on average by 21% compared to the practical approach of random sampling.     

Forecasting concentrations of air pollutants by logarithm support vector regression with immune algorithms

The need to minimize the potential impact of air pollutants on humans has made the accurate prediction of concentrations of air pollutants a crucial subject in environmental research. Support vector regression (SVR) models have been successfully employed to solve time series problems in many fields. The use of SVR models for forecasting concentrations of air pollutants has not been widely investigated. Data preprocessing procedures and the parameter selection of SVR models can radically influence forecasting performance. This study proposes a support vector regression with logarithm preprocessing procedure and immune algorithms (SVRLIA) model which takes advantage of the structural risk minimization of SVR models, the data smoothing of preprocessing procedures, and the optimization of immune algorithms, in order to more accurately forecast concentrations of air pollutants. Three pollutants, namely particulate matter (PM₁₀), nitrogen oxide, (NO_x), and nitrogen dioxide (NO₂), are collected and examined to determine the feasibility of the developed SVRLIA model. Experimental results reveal that the SVRLIA model can accurately forecast concentrations of air pollutants.     

An application of support vector machines to sales forecasting under promotions

This paper deals with sales forecasting of a given commodity in a retail store of large distribution. For many years statistical methods such as ARIMA and Exponential Smoothing have been used to this aim. However the statistical methods could fail if high irregularity of sales are present, as happens for instance in case of promotions, because they are not well suited to model the nonlinear behaviors of the sales process. In recent years new methods based on machine learning are being employed for forecasting applications. A preliminary investigation indicates that methods based on the support vector machine (SVM) are more promising than other machine learning methods for the case considered. The paper assesses the application of SVM to sales forecasting under promotion impacts, compares SVM with other statistical methods, and tackles two real case studies.