We propose a novel framework for modeling time-varying persistence in economic time series, allowing for smoothly evolving heterogeneity in shock dynamics. We leverage localized regression techniques to flexibly identify changes in persistence over time, offering a data-driven alternative to traditional parametric models. We applied this methodology to U.S. inflation and stock market volatility data and found substantial persistence variations that align with key macroeconomic events and market conditions. The results reveal previously undetected pockets of predictability and provide significant increases in out-of-sample forecast accuracy. These findings have important implications for economic modeling, forecasting, and policy analysis.

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