Meta-Learning for Time Series Forecasting Ensemble

Amounts of historical data collected increase together with business intelligence applicability and demands for automatic forecasting of time series. While no single time series modeling method is universal to all types of dynamics, forecasting using ensemble of several methods is often seen as a compromise. Instead of fixing ensemble diversity and size we propose to adaptively predict these aspects using meta-learning. Meta-learning here considers two separate random forest regression models, built on 390 time series features, to rank 22 univariate forecasting methods and to recommend ensemble size. Forecasting ensemble is consequently formed from methods ranked as the best and forecasts are pooled using either simple or weighted average (with weight corresponding to reciprocal rank). Proposed approach was tested on 12561 micro-economic time series (expanded to 38633 for various forecasting horizons) of M4 competition where meta-learning outperformed Theta and Comb benchmarks by relative forecasting errors for all data types and horizons. Best overall results were achieved by weighted pooling with symmetric mean absolute percentage error of 9.21% versus 11.05% obtained using Theta method.