The article establishes conditions for accurate estimation of data from changing processes. By using a stationary approximation and specific properties, the researchers ensure that estimators are consistent and normally distributed. For example, they show that a localized least squares estimator works well for certain types of data. Additionally, they demonstrate the effectiveness of a localized Whittle estimator and a maximum likelihood contrast-based estimator for different types of data sequences. Simulation studies confirm the practicality of these estimation methods.