Genetic Programming (GP) has proved its applicability for time series forecasting in a number of studies. The Dynamic Forecasting Genetic Program (DyFor GP) model builds on the GP technique by adding features that are tailored for the forecasting of time series whose underlying data-generating processes are non-static. Such time series often appear for real-world forecasting concerns in which environmental conditions are constantly changing. In a previous study the DyFor GP model was shown to improve upon the performance of GP and other benchmark models for a set of simulated and real time series. The distinctive feature of DyFor GP is its adaptive data window adjustment. This feedback-driven window adjustment is designed to automatically hone in on the currently active process in an environment where the generating process varies over time. This study further investigates this adaptive windowing technique and provides an analysis of its dynamics for constructed time series with non-static data-generating processes. Results show that DyFor GP is able to capture the moving processes more accurately than standard GP and offer insight for further improvements to DyFor GP.