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Local Polynomial Estimation of Time-Varying Parameters in Nonlinear Models

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Document pages: 48 pages

Abstract: We develop a novel asymptotic theory for local polynomial (quasi-)maximum-likelihood estimators of time-varying parameters in a broad class ofnonlinear time series models. Under weak regularity conditions, we show theproposed estimators are consistent and follow normal distributions in largesamples. Our conditions impose weaker smoothness and moment conditions on thedata-generating process and its likelihood compared to existing theories.Furthermore, the bias terms of the estimators take a simpler form. Wedemonstrate the usefulness of our general results by applying our theory tolocal (quasi-)maximum-likelihood estimators of a time-varying VAR s, ARCH andGARCH, and Poisson autogressions. For the first three models, we are able tosubstantially weaken the conditions found in the existing literature. For thePoisson autogression, existing theories cannot be be applied while our novelapproach allows us to analyze it.

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