On unified framework for discrete-time grey models: Extensions and applications

Grey theory-based time series models are widely used in various fields and disciplines. While most of the research is focused on the development and improvement of novel discrete-time models, very limited attention has been paid to the relationships among diverse models. The current paper proposes a methodological and practical framework to unify the single-variable, multi-variable, and multi-output discrete-time grey models, making it easier for practitioners to select an appropriate model for a given time-series forecasting problem. The recursive extrapolation strategy is present to generate multi-step ahead forecasts and four model families are deduced within the universal framework. Large-scale simulation studies are conducted to evaluate the finite-sample fitting and multi-step ahead forecasting performance. The proposed approach is illustrated using application examples from the indirect measurement of the tensile strength of materials.