Research On Multivariate Time Series Prediction Based On Partial Least Squares And Grey Relational Analysis

Multivariate time series is a hot research topic,and it has widely existed in the fields of hydrology,meteorology,medicine and so on.For multivariate time series,it can contain more system information,but the correlations between the variables are more complicated and changeable.In order to reasonably use the system information,it is necessary to analyze the correlations between the variables,eliminate the irrelevant information and redundant information and reduce the dimensions of input variables.Therefore,in this paper,we try to analyze the correlations between the time series by feature extraction and variable selection.For extreme learning machine,the optimum number of hidden layer nodes is difficult to determine.Moreover,the multicollinearity problem always exists in the hidden layer output matrix.Therefore,in this paper,we proposed an improved extreme learning machine based on partial least squares,where the partial least squares is used to optimize the hidden layer output of extreme learning machine and build the regression model.Compared with the traditional extreme learning machine,the proposed method can effectively improve the stability and reliability of extreme learning machine.The prediction result based on Lorenz time series,San Francisco river runoff datasets and sunspots-Yellow River runoff dataset verify the effectiveness of the proposed method.For similitude degree of grey incidence and absolute degree of grey incidence which based on the area,the sum of positive and negative areas may counteract each other in the integral process.Therefore,in this paper,an improved grey relational analysis model is proposed based on relative area change in order to overcome the problem above.Based on the relative change area of the sequence curve,the improved grey relational analysis model is defined by comparing the relative change area between the different time series.At the same time,according to the results of correlation analysis,a variable selection and prediction model is also proposed based on the thinking of set.Then the variable selection and prediction model is used into the prediction of Friedman dataset and Dalian atmosphere dataset.Moreover,for Deng's grey relational analysis model which based on the distance between the point to point,it may be not accurate in sometime.Therefore,in order to improve the prediction accuracy of grey relational analysis,another improved grey relational analysis model is proposed based on vector.By constructing a vector set,the projection length of the vector is used as a basis for judging the correlation degree between the different sequences.And then the grey relational analysis model is defined.We also apply the improved grey relational analysis model into the prediction of Gas furnace datasets and San Francisco river runoff datasets.