Fig 1.
x = [x1,x2,···,xn] is n-dimensional input vector, Ci(i = 1,2,···,N) is the center of transformation function Φ(x), W = [W1,W2,···,WN] is the weight between the hidden layer and output layer.
Table 1.
Variables used as inputs.
Fig 2.
Diagram of (2D)2PCA+RBFNN forecasting model.
The model is divided five modules, including the database of stock market, variables calculated module, sliding window, dimension reduction module and RBFNN predictor.
Fig 3.
Diagram of building up the dataset.
Stock time series segmentation is made by 20 width sliding window. The gray block represents the input data which including 20 trading day’s data. The white block represents the target output data which is the next day's closing price.
Fig 4.
The closing price of raw data.
Shanghai stock market index collected from 4 Jan. 2000 to 31 Dec. 2004 includes 1200 trading days' data.
Table 2.
Measure indicators.
Fig 5.
Fitting curve of prediction results and the actual data.
The red and black colored curves indicate the prediction results and actual data, respectively. The top, middle and bottom row display the prediction results of ICA, PCA and (2D)2PCA associated with RBFNN (Dim = 7,50,128) and BPNN (Dim = 7), respectively.
Fig 6.
The red and black colored curves indicate the prediction return and actual return, respectively. The top, middle and bottom row display the returns of ICA, PCA and (2D)2PCA associated with RBFNN (Dim = 7,50,128) and BPNN (Dim = 7), respectively.
Fig 7.
The training process of the BP network.
(a)The (2D)2PCA+BPNN (DIM = 7×1 = 7) model converge after 461 epochs. (b)PCA+BPNN (DIM = 7) converges after 4627 epochs.
Table 3.
Nine measure indicators of ICA, PCA and (2D)2PCA associated with RBFNN and BPNN under different dimension.
Table 4.
The running time of ICA, PCA and (2D)2PCA associated with RBFNN and BPNN under different dimension.