Testing Hypotheses in an I(2) Model with Applications to the Persistent Long Swings in the Dmk/$ Rate

Table 2: Misspecification tests

(o.oo)

Univariate tests:

relation is indeed stationary. A graphical inspection of Figure 3 in Section 9 confirms
that the first three β relations look very stationary. Even though .⅛₂ = 1 would be
easier to discuss, .⅛₂ = 2 seems empirically more correct and we shall continue with the
case (r = 3, s₁ = 2, .⅛∙₂ = 2).

Altogether, the evidence of highly persistent behavior in the data seems compelling.

8 Testing non-identifying hypotheses

The ∏ matrix in Appendix C shows that the estimated coefficients in the row de-
scribing the nominal exchange rate and the US long-term bond rate are essentially all
insignificant, suggesting that there might be no long-run levels feed-back on these two
variables. This hypothesis, described in Section 4.1, was individually accepted with
y²(3) = 5.24 [0.15] for nominal exchange rate and y²(3) = 1.27 [0.74] for the US bond
rate, as well as jointly accepted based on χ²(6) = 6.578[0.362]. As FGJ points out,
this is exactly what one would expect to find given the temporal instability of market
participants’ forecasting strategies and the limited information set employed in this
study. Another hypothesis of interest is the unit vector in a, also described in Section
4.1, implying that a variable is purely adjusting, i.e., the opposite of the no long-run
feed-back hypothesis. We found that this hypothesis was accepted for the US inflation
rate based on y²(3) = 2.41 [0.66] . Thus, nominal exchange rates are pushing and goods
prices are adjusting, which is inconsistent with REH models of the exchange rate. This
result is, however, completely consistent with the FG model of swings. See FGJ for a
detailed discussion.

There are a number of interesting hypotheses that can be formulated as the same
restrictions on τ, described in Section 4.3, expressed either as τ = Hφ or R'τ = 0. We

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