Multiresolution Forecasting for Industrial Applications

Abstract

The forecasting of univariate time series poses challenges in industrial applications if the seasonality varies. Typically, a non-varying seasonality of a time series is treated with a model based on Fourier theory or the aggregation of forecasts from multiple resolution levels. If the seasonality changes with time, various wavelet approaches for univariate forecasting are proposed with promising potential but without accessible software or a systematic evaluation of different wavelet models compared to state-of-the-art methods. In contrast, the advantage of the specific multiresolution forecasting proposed here is the convenience of a swiftly accessible implementation in R and Python combined with coefficient selection through evolutionary optimization which is evaluated in four different applications: scheduling of a call center, planning electricity demand, and predicting stocks and prices. The systematic benchmarking is based on out-of-sample forecasts resulting from multiple cross-validations with the error measure MASE and SMAPE for which the error distribution of each method and dataset is estimated and visualized with the mirrored density plot. The multiresolution forecasting performs equal to or better than twelve comparable state-of-the-art methods but does not require users to set parameters contrary to prior wavelet forecasting frameworks. This makes the method suitable for industrial applications.