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

Table 7: The common stochastic trends and their loadings

Table 6. We also note that this adjustment explains a small part of the variation in
the nominal exchange rate.

Finally, Table 7 reports the weights with which the I(2) stochastic trends have
affected the variables of the system. We do not report the weights of the I(I) trends
as these are complicated functions of the estimated matrices. See Section 2.

We note that the first I(2) trend seems to have affected pp and s₁₂ with coefficients
of the same sign, but not the same magnitude, whereas the second I(2) trend appears
to influence these variables with coefficients of opposite signs. Interpreting the first
trend as the long-run downward sloping trend visible in both relative prices and nom-
inal exchange rates suggests that it is associated with twice cumulated shocks to the
bond spread and the German term spread. Interpreting the second trend as capturing
the long swings movements predominantly in nominal exchange rates suggests that it
is predominantly associated with the twice cumulated shocks to the US short- term
interest rate. Moreover, this second trend has affected relative prices with a fairly small
coefficient that is opposite in sign to the one on nominal exchange rates. This reflects,
of course, the tendency of the nominal exchange rate to move away from relative prices
for extended periods of time. Finally, it is notable that nominal interest rates seem to
have been affected in particular by the second I(2) trend which is consistent with the
FG model as discussed in FGJ.

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