Smoothing a reference pathway based on discrete exogenous projections

In integrated assessment studies and scenario analysis, typically we need to calibrate a model to follow an exogenous pathway, e.g., the shared socioeconomic pathways. In these exogenous pathways, the data of key variables such as GDP and energy consumption are typically provided every five or ten years. In some cases, we need a yearly smooth pathway that is consistent with such an exogenous pathway with data of only every five years. Hence, this piece of study provides a method to obtain a smooth yearly pathway based on exogenous data of limited years.