G. Antille Descriptive Analysis of Matrix-Valued Time-Series In this article we present a technique of data analysis applied to three-dimensional tables as, for instance, matrix-valued time-series. <...> Moreover, our technique points out similar statistical units provided by a classification of their trajectories. 1. <...> Analysing each data matrix to get an idea of the data structure at time t,tT; matrix whose rows contain the means or medians {} 1,. , 2. <...> Constructing and analysing theTp of each data matrix to get an idea of the global evolution of the process under study; and, finally, 3. <...> Finding a common space to describe the evolution of statistical units and relationships between variables with respect to time. <...> In the article we have mainly developed the third point with techniques based on Principal Component Analysis (PCA). <...> PCA is also a way to perform the above mentioned first and second steps. <...> In Section 3we present a descriptive method of analysis of matrix valued time series which consists in projections, with respect to time, of statistical units or variables on principal directions of thecommonspace. <...> In Section 4we apply our method to a 26 8 26 matrix: 26 years of observations of 8 variables of rates of mortality in 26 Swiss cantons. <...> We define a data set as a three-dimensional matrix denoted byua aa a where xijt represents the value of the j th () , ., ;11 T xijt i variable for the i th Another way to define such a data set is given by ua aXt 1,. ,T , where Xt{}| statistical unit at time t. t matrix of observations at time t. The first step in the analysis of our data sets is to perform PCA on the T matrices Xt n j , ., ;p t 1, ., is thenp to explore the structure of each matrix in order to point out important changes in the structure of the data. <...> In this article we do not discuss this type of question. 45 Российскошвейцарский семинар по эконометрике и статистике , units, whicht th The second step consists in applying PCA to Xu , theTp x jt j In the third step, PCA is conducted onXxij perties of the Rayleigh quotient rV () to X. () . a (), thenp matrix of the means <...>