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Nonparametric kernel estimation of evolutionary autoregressive processes

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  • Kim, Woocheol

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 mdified local linear smoother. The asymptotic normality and variance of the new estimator are derived by extending 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 finite-dimensional distributions of the kernel estimates. We also examine the finite sample performance of the method via numerical simulations. As an empirical illustration, the method is applied to the real data of US stock returns.

Suggested Citation

  • Kim, Woocheol, 2001. "Nonparametric kernel estimation of evolutionary autoregressive processes," SFB 373 Discussion Papers 2001,103, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:2001103
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    Cited by:

    1. Dahlhaus, Rainer, 2009. "Local inference for locally stationary time series based on the empirical spectral measure," Journal of Econometrics, Elsevier, vol. 151(2), pages 101-112, August.
    2. Xiangjin B. Chen & Jiti Gao & Degui Li & Param Silvapulle, 2013. "Nonparametric Estimation and Parametric Calibration of Time-Varying Coefficient Realized Volatility Models," Monash Econometrics and Business Statistics Working Papers 21/13, Monash University, Department of Econometrics and Business Statistics.
    3. Cai, Zongwu, 2003. "Trending Time-Varying Coefficient Models With Serially Correlated Errors," SFB 373 Discussion Papers 2003,7, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.

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