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

Applications of Missing Data Imputation Methods in Wastewater Treatment Plants

“…These studies focused on various imputation methods, including the MSF-ARI approach (R2AU-Net) [20], univariate imputation methods (such as the SSD method and SVR model) [21], the SVM algorithm [16], coupling the expectation maximization (EM) algorithm with the Markov Chain Monte Carlo (MCMC) method (EM-MCMC) [22], Case-Based Reasoning (CBR) approach [18], Cubic Hermite interpolation method [14], Non-Linear decreasing inertia weight particle swarm algorithm (NLDIW-PSO) based optimal Support Vector Regression (SVR) [23], Daily average, auto-associative neural network (ANN) with a recursive minimization strategy [19], Multiple imputation (MI) [17], Linear interpolation [24], Two-directional exponential smoothing (TES) [9], PCA projection method [12], Kohonen self-organizing map (KSOM) [3], TES and TESWN [10].…”

“…The missing data points' ultimate replacement values are obtained by averaging the estimates derived from both the forward and backward exponential smoothing forecasts. The TESWN method shares similarities with the TES approach but includes a white noise term to handle random effects observed in the data, which might not be adequately addressed by the autocorrelation function [10].…”

“…Huo et al [10] showed that the TES and TESWN methods proposed in the article are effective in handling missing data challenges. The TES method is ideal when the objective is to minimize the average error linked to missing values, whereas the TESWN method is more suitable for quantifying the level of uncertainty associated with the missing values.…”

“…According to Huo et al [10], they observed that the TES and TESWN methods depend on time series models, which might not produce satisfactory outcomes when dealing with missing data unrelated to time. Furthermore, the TES method neglects the uncertainty associated with the missing value, resulting in an underestimation of the population variance for both influent data and simulated effluent concentrations.…”

“…Additionally, the TES method could erroneously introduce abrupt temporal changes in variables within the data record. In fact, the performance of TES and TESWN methods may be contingent on specific characteristics of the data being imputed, such as the degree of autocorrelation and the presence of outliers [10].…”