1066 The Econometrics of Exchange Rates
anticipation of a change in policy regime has been an important focus of the analysis
of exchange rates are: (i) the possible anticipation of the return to gold of sterling prior
to April 1925 (e.g., Flood and Garber, 1983; Michaelet al., 1997), (ii) the anticipation of a
fixed exchange rate between the East and West German Mark following German monetary
union (Burda and Gerlach, 1993).- Similarly, chaotic behavior, which we do not have space to consider (see, e.g., De Grauwe
et al., 1993). - This would imply a half-life of around five years. Assumingyt∼AR(1), the half-life (h)of
a unit shock would be 0.5=βh, or taking logs, ln 0.5=hlnβ,h=ln 0.5lnβ. - Linear univariate autoregressive time series models for the real exchange rate have not
been restricted to integer orders of integration. Explosive as well as fractional processes
have been used to model real exchange rates. Bleaneyet al.(1999) fitted a stochastic unit
root process to the real exchange rate of high inflation countries (Argentina, Brazil, Chile,
and Israel). The real exchange rate process is as follows:
yt=( 1 +δt)yt− 1 +vt,
wherevt∼i.i.d.(0,σv^2 )δt∼i.i.d.(0,σδ^2 ). Leybourneet al.(1996) derive a test for the null
hypothesisH 0 :σδ^2 =0 againstH 1 :σδ^2 >0. It is worth mentioning that, even under the
null, PPP is assumed non-stationary in this model. A different order of integration for PPP
deviations is proposed by the fractional literature (see section 22.3.2: see, e.g., Diebold
et al., 1991; Pippenger and Goering, 1993; Tayloret al., 2001). These papers also show
that standard unit root tests may exhibit low power against the fractional alternative.
However, neither the stochastic unit root nor fractional process have clear theoretical
underpinnings.- Paya and Peel (2007a) also analyze the asymptotically efficient estimator for cointegration
regression introduced by Saikkonen (1991). Cointegration is then tested using the Shin
(1994) statistic, which is a residual-based test where the null hypothesis is that of co-
integration or stationary residuals in the Saikkonen regression. Using simulated data, Paya
and Peel (2007a) find that the Saikkonen estimator produces estimates of the cointegrating
weights which are much closer on average to their true values, and with much smaller
standard errors than the Johansen method. - The smooth adjustment process is suggested in the analysis of Dumas (1992), noted by
Teräsvirta (1994) and demonstrated by Berka (2002). - The other common form of STAR is the logistic STAR (LSTAR), where the transition
functionF(·)is logistic:
F(zt−d;γ,c)=[ 1 +exp(−γ(zt−d−c))]−^1.
The LSTAR transition function is asymmetric about (yt−d−c)and admits the limits:
F(·;γ)→1as(zt−d−c)→+∞,
F(·;γ)→0as(zt−d−c)→−∞.
LSTAR models have also been fitted to real exchange rates (see Sarantis, 1999; Copeland
and Heravi, 2007). Even though the theoretical argument is not as strongly supported as
with ESTAR, there are some attempts to rationalize the asymmetric adjustment in the real
exchange rate (see Campa and Goldberg, 2002).- The effect of nonlinearities on traditional cointegration techniques have been examined.
Paya and Peel (2007a) assume that the DGP is given by the ESTAR process. Using simulated
data from such a model, in which proportionality,(1,− 1 ), is imposed, they examine the
empirical results obtained when the Johansen method is employed to determine whether
the spot exchange rate is cointegrated with domestic and foreign prices and whether pro-
portionality can be rejected. Empirical results show that the Johansen method produces