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

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1975            1980            1985            1990            1995            2000

2-Pdf

their heterogeneous exchange rate forecasts are assumed to follow random walks with
drift. With this assumption, revisions of market participants’ forecasting strategies
lead to temporally unstable drift terms in the processes driving the endogenous vari-
ables of the model. FGJ show that these broken-trends processes can be approximated
as I(2).

6 Specification of deterministic terms in the empir-
ical model

A proper specification of deterministic terms in the I(2) model is mandatory for the
model to yield statistically good estimates. From (8) we know that linear trends in the
data can originate from several sources: (l) E(∆x^_t) = 0 implying that some of the
variables have exhibited significant linear growth over the sample period, (2) E(β'x_t) =
p₀t = 0 implying that some of the cointegration relations are trend-stationary, (3) from
initial conditions. Even though one would expect a linear trend to be present in
nominal prices (reflecting the fact that average inflation rates have been nonzero in
most economies) it is less obvious that one should expect a linear trend in relative
prices and nominal exchange rates. Since deterministic trends in p₁,_t and p₂,_t are likely
to cancel in p_1jt— p₂,_t, one should generally expect the deterministic components to be
different in a model for p₁,_t, p₂,_t, and s₁₂,_t as compared to a model for pp_t = p₁,_t — p₂,_t
and s₁₂,_t. The graph in Figure l shows a downward sloping trend in relative prices

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