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Abstract
In this paper, we derive the asymptotic properties of the Nadaraya-Watson type local level regression estimator of time–varying cointegrating coefficients when the regressors are either nearly or mildly integrated with autoregressive roots of the form $\rho_{ni}=1+c_i/n^{\alpha}$, where $\alpha \in (0,1]$ and $c_i <0$ are constant parameters. In nearly integrated case, it is shown that weighted signal matrix becomes asymptotically singular and a rotation decomposition is developed to restore the limit theory. In mildly integrated case, it is shown that the signal matrix is asymptotically well-behaved the estimator is consistent, so long as $n^{1-\alpha}h \rightarrow \infty$, where $h \vcentcolon =h_n$ is the bandwidth parameter. Achieving standard asymptotic normality, however, requires bias correction and stronger rate conditions. The theoretical findings are illustrated via an extensive Monte Carlo study.