Performance Comparison of Various Imputation Methods for Missing Data Mechanisms (MAR, MCAR, and MNAR) in a Nonstationary Time Series

Handling missing data in a time series is necessary for forecasting as they can significantly impact representation and pose serious problems such as loss of efficiency and unreliable results. The key to resolving this problem is data imputation, i.e., replacing the missing values with synthetic ones. The aim of this study is to understand the various missingness regimes and apply data imputation methods accordingly. To this end, the performances of several widely used data imputation methods for a nonstationary univariate time series having both trend and seasonality were assessed. The performances of four imputation methods: mean value, last observation carried forward (LOCF), Kalman smoothing, and multivariate imputation by a chained equation (MICE) based on whether 10%, 20%, 30%, or 40% of the data were missing at random (MAR), missing completely at random (MCAR), or missing not at random (MNAR), were compared in terms of the root mean squared error (RMSE) and the mean absolute percentage error (MAPE) values for each scenario tested. MICE performed the best in all of the test cases regardless of the whether the missing data were MAR, MCAR, or MNAR.