Aggregation operators with moving averages

Abstract

A moving average is an average that aggregates a subset of variables from the set and moves across the sample. It is widely used in time-series forecasting. This paper studies the use of moving averages in some representative aggregation operators. The ordered weighted averaging weighted moving averaging (OWAWMA) operator is introduced. It is a new approach based on the use of the moving average in a unified model between the weighted average and the ordered weighted average. Its main advantage is that it provides a parameterized family of moving aggregation operators between the moving minimum and the moving maximum. Moreover, it also includes the weighted moving average and the ordered weighted moving average as particular cases. This approach is further extended by using generalized aggregation operators, obtaining the generalized OWAWMA operator. The construction of interval and fuzzy numbers with these operators obtaining the concept of moving interval number and moving fuzzy number is also studied. The paper ends analyzing the applicability of this new approach in some key statistical concepts such as the variance and the covariance and with a numerical example regarding sales forecasting.