The properties and methods for computation of exponentially-mapped-past statistical variables

The exponentially-mapped-past (emp) statistical variables represent an approach to the statistical analysis of a process when the interest is focused on the recent behavior of the process. An exponential weighting function, decreasing into the past, in the case of continuously observed processes, and a geometric ratio, in the case of discrete data, are utilized. This approach is the simplest from the point of view of ease of computation, and at the same time it possesses the advantage of some simple theoretical relationships, which are discussed. Analog computer circuits and digital computer flow diagrams which serve to compute the exponentially-mapped-past statistical variables are presented.