Brunnermeier, Nagel and Pedersen (2009) and Jordà and Taylor (2009) in addition investigate nonlinear alternatives. Their approach is to allow for threshold effects under the view that when UIP deviations are small (or volatility is low as will be our case), then exchange rates are difficult to predict and closer in behavior to a random walk. However, outside this “tranquility” band, it may be expected that exchange rates will revert to their equilibrium levels. For this purpose, we tested our data for evidence of nonlinearity with a general test as suggested in Granger and Teräsvirta (1993). The results of these tests are reported in table 4 and provide firm evidence against the null of linearity.
Consequently, we expand our medley of linear models with a threshold model based on deviations of VX from its median. There is no way to formally ascertain whether this choice of nonlinearity is best, however, we find that this particular form lends itself to easier interpretation and full-sample estimates reported in table 5 suggest that it is a very viable alternative. In fact, as we will demonstrate shortly, this is our preferred specification.
Table 5 – Estimates of the Threshold Model
VX < θ
(e j ,t −3
VX ≥ θ
Notes: Sample: December 2000 to March 2009, monthly.