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Estimating Time-Varying Parameters of Various Smoothness in Linear Models via Kernel Regression

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  • Mikihito Nishi

Abstract

We consider estimating nonparametric time-varying parameters in linear models using kernel regression. Our contributions are twofold. First, We consider a broad class of time-varying parameters including deterministic smooth functions, the rescaled random walk, structural breaks, the threshold model and their mixtures. We show that those time-varying parameters can be consistently estimated by kernel regression. Our analysis exploits the smoothness of the time-varying parameter, which is quantified by a single parameter. The second contribution is to reveal that the bandwidth used in kernel regression determines the trade-off between the rate of convergence and the size of the class of time-varying parameters that can be estimated. We demonstrate that an improper choice of the bandwidth yields biased estimation and provide a guide on the bandwidth selection. An empirical application shows that the kernel-based estimator with a particular bandwidth choice can capture the random-walk dynamics in time-varying parameters.

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  • Mikihito Nishi, 2024. "Estimating Time-Varying Parameters of Various Smoothness in Linear Models via Kernel Regression," Papers 2406.14046, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2406.14046
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