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. We show the proposed estimators are consistent and follow normal distributions in large samples under weak conditions. We also provide a precise characterisation of the leading bias term due to smoothing, which has not been done before. 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 autogressions with exogenous co--variates, to be normally distributed in large samples and characterise their leading biases. An empirical study of US corporate default counts demonstrates the applicability of the proposed local linear estimator for Poisson autoregression, shedding new light on the dynamic properties of US corporate defaults.