= is carried out using a Lagrange multiplier test. The

The test of 9' = 9~ is carried out using a Lagrange multiplier test. The procedure is described in much more detail with an outline of optimality properties in Luukkonen et al. (l988a and b), Saikkonen and Luukkonen (1988), Granger and Terasvirta (1993) and Terasvirta (1994). This way of testing is optimal if it is used against a specific alternative (specific f) and it turns out that this particular alternative is in fact true. This seldom (never) happens in practice of course, and one could resort to a battery of tests for various alternatives. In this class of alternatives it must also be taken into account that the lag structure is unknown, and therefore it is important that such tests are fairly robust not only to a wrongly chosen f, but also to a wrongly specified lag structure.