Forward and Backward Forecasting Ensembles for the Estimation of Time Series Missing Data

The presence of missing data in time series is big impediment to the successful performance of forecasting models, as it leads to a significant reduction of useful data. In this work we propose a multiple-imputation-type framework for estimating the missing values of a time series. This framework is based on iterative and successive forward and backward forecasting of the missing values, and constructing ensembles of these forecasts. The iterative nature of the algorithm allows progressive improvement of the forecast accuracy. In addition, the different forward and backward dynamics of the time series provide beneficial diversity for the ensemble. The developed framework is general, and can make use of any underlying machine learning or conventional forecasting model. We have tested the proposed approach on large data sets using linear, as well as nonlinear underlying forecasting models, and show its success.