A novel imputation methodology for time series based on pattern sequence forecasting.

The Pattern Sequence Forecasting (PSF) algorithm is a previously described algorithm that identifies patterns in time series data and forecasts values using periodic characteristics of the observations. A new method for univariate time series is introduced that modifies the PSF algorithm to simultaneously forecast and backcast missing values for imputation. The imputePSF method extends PSF by characterizing repeating patterns of existing observations to provide a more precise estimate of missing values compared to more conventional methods, such as replacement with means or last observation carried forward. The imputation accuracy of imputePSF was evaluated by simulating varying amounts of missing observations with three univariate datasets. Comparisons of imputePSF with well-established methods using the same simulations demonstrated an overall reduction in error estimates. The imputePSF algorithm can produce more precise imputations on appropriate datasets, particularly those with periodic and repeating patterns.

R Package imputeTestbench to Compare Imputation Methods for Univariate Time Series.

Missing observations are common in time series data and several methods are available to impute these values prior to analysis. Variation in statistical characteristics of univariate time series can have a profound effect on characteristics of missing observations and, therefore, the accuracy of different imputation methods. The imputeTestbench package can be used to compare the prediction accuracy of different methods as related to the amount and type of missing data for a user-supplied dataset. Missing data are simulated by removing observations completely at random or in blocks of different sizes depending on characteristics of the data. Several imputation algorithms are included with the package that vary from simple replacement with means to more complex interpolation methods. The testbench is not limited to the default functions and users can add or remove methods as needed. Plotting functions also allow comparative visualization of the behavior and effectiveness of different algorithms. We present example applications that demonstrate how the package can be used to understand differences in prediction accuracy between methods as affected by characteristics of a dataset and the nature of missing data.