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Abstract
In this paper, we propose a nonparametric series estimation framework for a cointegrated system with coefficients that evolve smoothly over time. We first establish an asymptotic theory for the series-based OLS (SOLS) estimation method under nonstationary (unconditional) volatility of unknown form. Then, we develop an asymptotic efficiency theory for a broad class of series estimators. Building on this development, we further propose a series-based dynamic OLS estimator (SDOLS) that attains the efficiency bound and is easy to implement. Monte Carlo simulations show that the SDOLS estimator has satisfactory finite-sample performance and typically performs better than the existing alternatives. An empirical application to the consumption-wealth ratio shows that allowing for time variation in the cointegrating relationship often improves equity premium forecast accuracy relative to both the conventional fixed-coefficient specification and the historical-mean benchmark.