رتبه های رابطه ای گری در رگرسیون بردار پشتیبانی محلی برای پیش بینی سری های زمانی مالی

Support vector regression (SVR) has often been applied in the prediction of financial time series with many characteristics. On account of much time consumption of global SVR, local machines are carried out to accelerate the computation. In this paper, we introduce local grey SVR (LG-SVR) integrated grey relational grade with local SVR for financial time series forecasting. Pattern search method and leave-one-out errors are adopted for model selection. Experimental results of three real financial time series prediction demonstrate that LG-SVR can speed up computing speed and improve prediction accuracy.

On the grounds that some financial time series contain several specific characteristics: large sample sizes, high noise, non-stationary, non-linearity, and varying associated risk, we are inclined to find some comparatively precise methods to forecast their future values. Namely, given financial time series data set {(x1, y1), (x2, y2), … , (xn, yn)}, we usually use a learned model to make accurate predictions of y for future values of x. Recently, due to both the better performance of generalization and the good empirical results ( Cristianini and Shawe-Taylor, 2000, Evgeniou et al., 2000, Smola and Schölkopf, 2004 and Vapnik, 1998), kernel machines, including support vector regression machines, have been introduced for financial time series forecasting ( Kim, 2003, Tay and Cao, 2002 and Yang et al., 2002). However, the costly computation of global machines becomes an obstacle to apply them to some problems. Despite consideration of model selection, the total computation cost is still large because of repeated SVR algorithm. In order to solve these problems, some experts introduced lazy learning methods which defer the processing of training data until a query needs to be answered (Kobayashi, Konishi, & Ishigaki, 2007). In addition, experts also proposed some modified local support vector regression models and optimized methods. He and Wang (2007) introduced local kernel machines in which models optimized based on leave-one-out errors, and multiple-kernels are adopted for model selecting and performance improvement. Huang et al. proposed a novel local support vector regression model demonstrated to provide a systematic and automatic scheme to adopt the margin locally and flexibly. This method not only captures the local information in data, but establishes connection with several models (Huang, Yang, King, & Lyu, 2006). Inspired by these literatures, based on the popular grey system theory (Deng, 1982), we introduce a local support vector regression combined with grey relational analysis (GRA). GRA is an important component of grey system theory. In the uncertain and incomplete system, this method is used to find out not only the key factors affecting a selected object, but also the basic relationship between an influential factor and the selected object. This method compares variation trends of influential factors with that of a selected object. A more similar trend means a closer relationship. Meanwhile, the similarity can be measured in grey relational grade. The greater the grade, the closer the similarity. In addition, GRA does not require strict compliance with certain statistical laws or linear relationships among objects, and is thus widely applied in artificial intelligence (He & Hwang, 2007), hydrology (Wong, Hu, IP, & Xia, 2006), laser technology (Cayda & Hascalik, 2008), material science (Chan & Tong, 2007), mathematics (Xu, Tian, Qian, & Zhang, 2007) and other fields (Liu et al., 2009 and Moran et al., 2006). In practice, to some financial time series in SVR, training data are seldom distributed evenly in input space regarded as an uncertain and incomplete system because they are affected by many unknown factors. If we only consider the part of training examples close to the test point, the GRA can be adopted here based on that it is a kind of measurement approach that describes the relationship between a test point and the other in an uncertain and incomplete grey space (Deng, 1989). With its great significance in the GRA, the grey relational grade between two points is a measurement of their relationship in a certain data set. Where financial time series data are concerned, we learn the model by choosing a certain fixed number of the nearest former points of the query as the training data, and query point has been matched with every candidate to calculate grey relational grade as the weight of punishment parameter C in SVR. Because the nearest points capture the main information of the query, the accuracy can be improved. In the meantime, the size of training data or computation cost can be changed according to the fixed number. The smaller the number, the faster the computation. In addition, leave-one-out errors and pattern search method can be adopted for model selection. Experimental results demonstrate the good performance of our methods. The rest of this paper is organized as follows. Local grey support vector regression (LG-SVR) including standard SVR, grey relational grade weighting function (GRF), local support vector regression integrated with GRF and LD-SVR have been provided in Section 2, model optimization methods in Section 3, the experimental results of three real financial time series forecasting in Section 4, conclusion in the last section.

Prediction to future values of the financial time series plays a very important role in our life. So learning machines are introduced in this field. In practice we often expect a fast and accurate forecasting and hope to find an efficient way to train the machines. For these reasons above, in this paper, we have proposed the local grey support vector regression (LG-SVR) in order to improve the performance of support vector regression (SVR) for some financial time series prediction. There are many advantages to the proposed approach. In contrast to the global SVR, LG-SVR offers local strategy and grey relational grade as weighting function to adapt every test point locally and flexibly. Therefore, it can reduce the computation cost and capture the local information of test data. Experimental results demonstrate that LG-SVR can improve the prediction accuracy in three financial time series and accelerate the computation in median and large size sample data. In contrast to the LD-SVR, LG-SVR is different from the weighting function. Experimental results of three real financial time series forecasting also demonstrate that LG-SVR outperforms the LD-SVR. Clearly, the disadvantages of LG-SVR are the unsteadiness of training set and the uncertainty of optimum k. We leave the latter as our future work. Three main issues need to be pointed out in the experimental section. First, we obtained the optimum parameters based on the fixed lag. The best parameters in different lag should be achieved by further experiments. Second, different types of Gaussian Kernel, such as Gaussian RGF network, maybe impact our regression results. We leave it as future work. Finally, we adopt PS algorithm and optimized programs developed by Steve Gunn. Exploiting other algorithms to accelerate the computation and improve performance will be a highly challenging yet interesting topic.