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Asymptotics for weighted periodic transformations of integrated time series

Chien-Ho Wang, Robert M. de Jong


This study establishes the analytical results of periodic transformations with weighted unit root processes. This study considers time series regression when the regressors are periodic transformations on a scaled I(1) process. When the transformation is a periodic function on a scaled I(1) process with a symmetric distribution, the convergence rate is slower than that of de Jong (2002). The proposed methods can be useful for developing the periodic transformation of nonlinear regression for nonstationary time series.


Asymptotic theory, Cointegration, integrated process, nonlinear time series, periodic transformation

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