Abstract: Grey incidence analysis is an important part of grey system theory which is used to ascertain the relationship grade between an inflential factor and the major behaviour factor. However, most of grey incidence models are mainly applied to the field in which the operational behaviour factor and relational factor are the cross-sectional data or time series data in a given system. Therefore, the grey model on pannel data is worth exploring that is the asscociated content in this paper.According to the basic idea of grey incidence of grey system theory, the degree of relative closeness of the development rate and growth rate indexes between the relative factor matrices and characteristic behavior matrix of the system is measured from two dimensions of individual and time on the basis of the definition of the matrix sequence of a discrete data sequence. With the measurement of grey incidence degree, the grey matrix similar incidence model of panel data is put forward from the traditional vector space to the matrix space and its properties are discussed. Finally, CO₂ emission is taken as an example where the data of carbon dioxide has been calculated for six provinces by the IPCC method in 2006 and the other data are from the Statistical Yearbook. And a grey matrix similar incidence model is established by measuring the CO₂ emission in 2005-2012 of six provinces in the central region in China. The real example shows its simplification and practicability. The empirical results show that people may take some main factors into account to abate carbon dioxide emission which are an effective way to implement energy saving and carbon emission reduction. For example, the central region can appropriately control the population scale but also put intensive economic development way that guide residents to live low carbon and improve the consciousness of energy conservation and carbon emission reduction.

Key words: degree of grey matrix similar incidence, development speed index, growth index, carbon emission