Research On Financial Time Series Prediction Based On Tensor Model

Stock markets are the main entity of financial market and the issuance and transaction of stocks play an important role in promoting the development of market economy.If the characteristics and trends of the stocks can be reasonably grasped,it can provide effective reference and basis for the decision-making of the relevant government departments.So the government has able to advance the supervision and control of stock market and strength the prevention and avoidance of financial risk.As an integrated embodiment of the macroeconomic,stock market index reflects the national economic situation,thus its research and forecast have great influence on the healthy development of macroeconomy.Therefore,it's of great importance to forecast the time series of stock market index.Since algorithm based on the tensor feature extraction can keep the temporal and spatial characteristics of the samples in the process of feature extraction,tensor analysis has become a hot research field of pattern recognition and feature extraction.The tensor form of financial time series is more in line with the characteristics of financial time series.Based on tensor model,this paper studies how to extract better features to improve the prediction accuracy of financial time series.The main studies are as follows:(1)Aiming at the problem that the feature dimension extracted using(2D)~2PCA algorithm is still too high,by combining(2D)~2PCA and PCA algorithms,this paper studies and designs a feature extraction algorithm based on(2D)~2PCA+PCA.After building a second-order tensor model by using the multivariate time series of single stock market,feature extraction method of second-order tensor is conducted.For the tensor model,(2D)~2PCA algorithm is carried out to extract features and then further feature extraction is implemented by using PCA algorithm to reduce the dimension of feature matrices.The algorithm is experimentally compared with(2D)~2PCA algorithm and PCA algorithm.(2)For the problem that the vector-based algorithm cannot keep the internal structure information of three-dimensional data,the multilinear principal component analysis(MPCA)algorithm is introduced to extract the features.By using the correlation between various stock markets and collecting time series data of the relevant technical indexes of them,a third-order tensor model is constructed.In order to preserve the data space structure information,MPCA algorithm is introduced,which extracts features directly in all the pattern directions of the tensor model.Through experiments,MPCA algorithm is compared with the vector-based algorithms.(3)Aiming at the problem that the MPCA algorithm cannot distinguish the contributions of different eigenvectors on the prediction of financial time series,a eigenvalue normalization weighted multilinear principal component analysis(ENW-MPCA)algorithm is designed and implemented.For the eigenvectors,obtained by MPCA algorithm,which compose the projection matrices,uses the normalized eigenvalues as the weights of the corresponding eigenvectors.The ENW-MPCA algorithm is compared with MPCA algorithm to verify the effectiveness of the ENW-MPCA algorithm.