A canonical decomposition (CD) method that includes building a multi-variate linear autoregressive ("MLAR") model from an original data set or from a reduced set derived by data reduction methods from the original data set. The MLAR analysis is followed by seeking a coordinate transformation of the MLAR model to obtain the best possible match with one or more canonical forms representing relationships among components. For multi-variate data with a truly hierarchical structure, CD accurately extracts the underlying sources of the system.