Time Series Smoothing and OWA Aggregation

In this paper, an overview of the time series smoothing problem is provided and the role of data aggregation is described using a weighted average of the past observations. Two important features associated with this smoothing process are introduced. One is the average age of the data and other is the expected variance. It is noted how both of these are defined in terms of the associated weights. We show the fundamental conflict between trying to keep the variance small while simultaneously using the freshest data. We study the moving average and exponential smoothing methods. Focusing on the aggregation aspect of the data smoothing problem allows us to draw upon the work done with the ordered weighted averaging aggregation operators to suggest new methods for developing smoothing techniques. A new class of smoothing operators based on the use of linearly decaying weights is introduced and is shown to have some better features than either exponential smoothing or the moving average. Other classes of smoothing operators are introduced. We introduce the idea of an operational estimate that involves adjusting a smoothed value by other considerations.