Limit Theory of Local Polynomial Estimation in Functional Coefficient Regression

Ying Wang and Peter Phillips
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Ying Wang: Renmin University of China

No 2398, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: Limit theory for functional coefficient cointegrating regression was recently found to be considerably more complex than earlier understood. The issues were explained and correct limit theory derived for the kernel weighted local constant estimator in Phillips and Wang (2023b). The present paper provides complete limit theory for the general kernel weighted local p-th order polynomial estimator of the functional coefficient and the coefficient deriva-tives. Both stationary and nonstationary regressors are allowed. Implications for bandwidth selection are discussed. An adaptive procedure to select the fit order p is proposed and found to work well. A robust t-ratio is constructed following the new correct limit theory, which corrects and improves the usual t-ratio in the literature. Furthermore, the robust t-ratio is valid and works well regardless of the properties of the regressors, thereby providing a unified procedure to compute the t-ratio and facilitating practical inference. Testing constancy of the functional coefficient is also considered. Supportive finite sample studies are provided that corroborate the new asymptotic theory.

Keywords: bandwidth selection; functional-coefficient cointegration; local p-th order polyno-mial approximation; robust t-ratio (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Pages: 48 pages
Date: 2024-06
New Economics Papers: this item is included in nep-ecm and nep-ets
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