Application of Two-Directional Time Series Models to Replace Missing Data

Abstract

Missing data commonly exist in operational records of wastewater treatment plants, such as influent and effluent water quality data. To deal with missing data, time series models that characterize trend, lag, and seasonality may be applied. In this paper, two-time series model-based methods, i.e., the two-directional exponential smoothing (TES) and TES with white noise (TESWN) added methods, are developed to replace missing data. Comparisons with traditional missing-data-replacement methods are also evaluated in the context of predicting missing values from influent data and the subsequent effect when the resulting influent time series are used as an input to process simulation models. The TES method is shown to be most appropriate when the goal is to minimize the average error associated with the missing value. The TESWN method is shown to be better suited for characterizing the amount of uncertainty that may be associated with the missing values.