Nonparametric Kernel Estimation of Evolutionary Autoregressive Processes

Woocheol Kim

Assistant Professor, Department of Taxation, University of Seoul, 163 Siripdaero, Dongdaemun-gu, Seoul 130-743, Korea, Tel: +82-2-6490-6799, Fax: +82-2-6490-6794 sunrise@uos.ac.kr

JEL Classification: C14

Abstract

This paper develops a new econometric tool for evolutionary autoregressive 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.

Keywords:

Autoregressive models, Evolutionary linear processes, Local linear fits, Locally stationary processes, Phillips and Solo device, Time-varying coefficients

Acknowledgments

I would like to thank Rainer Dahlhaus, Oliver Linton, Michael Neuman, Peter Phillips, Donald Andrews, and Wolfgang Härdle for helpful discussions and comments.

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