Inference on one-way effect and evidence in Japanese macroeconomic data

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Elimination of Third‐series Effect and Defining Partial Measures of Causality (2001, methodology): “For the cointegrated AR model, the Wald test approach was used for inference of the simple one-way effect measures in Yao and Hosoya (1998), based on Johansen's asymptotic theory of the maximum-likelihood estimator (Johansen, 1995).”
Testing for short- and long-run causality: A frequency-domain approach (2006, methodology): “On the other hand, leaving out the contemporaneous information of the variable y3t may give spurious inference on causality, as demonstrated by Hosoya (2000).”