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Abstract:
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In a time-varying coefficient model, the regression coefficient is allowed to change over time as a nonparametric function to capture the time-varying feature. We consider the problem of semiparametric variable labeling and estimation for multi-output time-varying coefficient models in the time series setting, where a variable can be labeled as time-varying, time-constant, or irrelevant, in a nested structure. We first show that the natural approach of imposing separate penalties on the local linear estimator and its derivative will not work as intended for semiparametric labeling due to the lack of connection between the coefficient and derivative estimators in the popular local linear method. We then propose a stratified fix that borrows information from the coefficient estimator and puts together with the derivative into the same stratum that achieves successful labeling and estimation at the same time. Theoretical properties of the proposed method, including its estimation and labeling consistency, are established for a general class of nonstationary processes. A Monte Carlo simulation study and a real data application are presented to further illustrate the proposed method.
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