“…Bruneau and Jondeau's (1999) definition can be seen as complementing the earlier concept of Gonzalo and Granger (1995) of common factors on which restrictions were tested for longrun noncausality. However, in contrast to Bruneau and Jondeau (1999) we avoid formulating nonlinear parameter restrictions to be tested by a Wald statistic. The econometric literature contains many warnings of the undesirable properties of the Wald statistic in the case of nonlinear parameter restrictions, see e.g., Dagenais andDufour (1991), Critchley, Marriott, andSalmon (1996), Gregory and Veall (1985), Lafontaine and White (1986), and, Philips and Park (1988).…”