Nonparametric Kernel Estimation of Evolutionary Autoregressive Processes

This paper develops a new econometric tool for evolutionary auto- regressive models, where the AR coefficients change smoothly over time. To estimate the unknown functional form of time-varying coefficients, we propose a modified local linear smoother. The asymptotic normality and variance of the new estimator are derived by extending the Phillips and Solo device to the case of evolutionary linear processes. As an application for statistical inference, we show how Wald tests for stationarity and misspecification could be formulated based on the finite-dimensional distributions of kernel estimates. We also examine the finite sample performance of the method via numerical simulations