Research Of Grey Canonical Correlation Analysis And It's Application On Multivariable Time Series

Canonical correlation analysis is one of the methods of multivariate statistical analysis. It converts the correlation between two sets of variables to the correlation of a few pairs of linear combinations of the variables by selecting some representative linear combinations from each of the two sets of the variables with the theory of principal components analysis. Canonical correlation analysis is widely used in areas of natural science and social science because of its ability to represent the linear correlation between two sets of variables.But canonical correlation analysis has localizations. Multivariate statistical analysis can only provide the measure of the spread or variation in the numbers by mathematical expectation while it is on the basis of the four numeric characters named mathematical expectation, variance, covariance and correlation coefficient. Canonical correlation analysis treats the samples equally without discrimination and is not applicable to the issues involve time series as it can not reflect the time character and development trend of systems promptly.Grey system theory has a tight relationship with time series, the cumulative plus of which is the basis of grey modeling and forecasting. We put forward the idea of grey statistics by introducing grey system theory into multivariate statistical analysis and present the model of grey canonical correlation analysis on the basis of the numerical character of grey series, which is redefined with grey degree. The new model put the importance of the newest data in time series to the foregrounding position and gets a much better statistical effect on time significance problems.We build a platform named grey statistical analysis system (GSAS) with the methods of canonical correlation analysis and grey canonical correlation analysis as theoretical foundation. The platform presents the realization of the two methods mentioned above and meets different needs of users by providing a better choice for statistical analysis for problems that involve higher requirements of time character.In order to validate the time effectiveness of grey canonical correlation analysis, we apply this method to research of the relationship between social ethics and economic development and the relationship between gross domestic product and fiscal spending on pension and social welfare and contrast the results with classical canonical correlation analysis. It is revealed that grey canonical correlation analysis has its superiority on solving time series problems, the result can provide more potent theoretical gist for the decision-making of relevant function departments.