On the theory of moving average graduation

Abstract

In this paper a new criterion for judging the properties of moving averages is given, and moving averages which are optimal according to this criterion under general assumptions are derived. For the standard case where the observations are uncorrelated and have equal variance, our optimal moving averages generalize two well-known optimal moving averages: The minimum-variance and the minimum-R_z moving averages. This case is given some particular attention in the theoretical discussion, and some Monte Carlo experiments throw further light on it. These investigations indicate that our generalization is of practical as well as theoretical interest. The paper also contains the result that Spencer's 21-term moving average is approximately equal to the corresponding minimum-R ₅ moving average.