LOCAL POLYNOMIAL ESTIMATION OF TIME-VARYING PARAMETERS IN NONLINEAR MODELS

We develop a novel asymptotic theory for local polynomial extremum estimators of time-varying parameters in a broad class of nonlinear time-series models, including discrete-valued ones. We show that the proposed estimators are asymptotically normally distributed under weak conditions. We also provide a precise characterization of the leading bias term due to smoothing. We demonstrate the usefulness of our general results by establishing primitive conditions for local (quasi-)maximum-likelihood estimators of time-varying models threshold autoregressions, ARCH models and Poisson autoregressions with exogenous covariates, to be normally distributed in large samples and characterize their leading biases. An empirical study of U.S. corporate default counts demonstrates the applicability of the proposed local linear estimator for Poisson autoregressions, shedding new light on the dynamic properties of U.S. corporate defaults.