1070 The Econometrics of Exchange Rates- Whenstandftare integrated variables, a regression ofst+nonftwill give the same
coefficient as one ofstonft, at least asymptotically. Maynard and Phillips (2001) show
that in small samples the overlapping errors induced by employingst+nin the regressions
can give rise to different estimates. - See Minford and Peel (2002) for a textbook derivation.
- However, we note that the properties of regressions withft−stas the dependent variable
and the conditional variance as a regressor would be of interest in this context. They would
determine whether the estimates of the conditional variance have predictive content for
the forward premium. - An alternative economic explanation of the anomaly that might be relevant for particular
periods is the one advanced by McCallum (1994). He suggests that the negative co-
efficient may be the result of simultaneity induced by the existence of a policy reaction
function where the interest rate differential is set in order to stabilize current exchange rate
movements. Another important possibility is set out by Evans and Lewis (1995) and Spag-
nolaet al.(2005). They show that if the “long” swings in exchange rate regimes between
depreciating and appreciating periods haveex antepredictability, then in small samples
a peso problem occurs. They assume that the exchange rate regimes can be captured by
a Markov-switching process (see, e.g., Hamilton, 1990). Again, whilst the peso problem
is undoubtedly important to some policy periods, the systematic nature of the forward
anomaly over different time periods and different numeraire currencies suggests there are
other factors at work. - At the one extreme,d=0 represents the short memory case. Ifd>0.5, the process
is not wide-sense stationary, having infinite variance. And at the other extreme,d= 1
corresponds to the ordinary integrated process, familiarly known as an RW, which is well
known not to revert to the mean, but eventually to wander arbitrarily far from the starting
point. The autocorrelations of a fractional process dissipate but at a slow hyperbolic rate
rather than the geometric rate of a standard ARMA process (see Granger, 1980; Granger
and Joyeux, 1980). (see Granger , 1980; Granger and Joyeux, 1980). - Peel and Davidson (1998) fit a nonlinear error correction mechanism to the spot-forward
relationship based on the idea of nonlinearities in the unobserved risk-premium which
might be captured by a bilinear process. - Baillie and Kiliç (2006) prefer the logistic function as the transition function. This implies
asymmetric behavior of the deviations as to whether they are positive or negative. Given
this, their results have the same qualitative implications as those of Sarnoet al.(2006), even
though the symmetric transition function appears to be better economically motivated. - The standard ESTAR model exhibits a maximum expected deviation from equilibrium.
Note that if the dataset does not actually include a maximum or minimum then the value
ofγestimated has to be such, i.e., smaller, to ensure that a max or min occurs outside of
the range of estimated data. An economic rationale for the maxima or minima is unclear.
This line of reasoning suggests a simple modification of the ESTAR model, which is to
assume that the variable forcing the process towards its equilibrium value is not observed
from past deviations but from the expected deviation at timet. - They employ survey data to measure anticipated excess returns.
- See also Van Dijket al.(2002) for an earlier application to unemployment rates, and Tsay
and Härdle (2007), who set out a general class of Markov-switching ARFIMA processes. - Baillie and Kapetanios (2005) consider a test based on neural networks.
- The FI-STAR model is clearly of interest. If it is the case that forward premia (or PPP) are
parsimoniously described by such a process then it seems to pose a challenge for theoretical
work. - We note that numerous studies have been conducted to determine the empirical relation-
ship between real interest rates and the real exchange rate. From the uncovered parity
conditions, ignoring any time-varying risk-premia for simplicity:
it−Etpt+n+pt=i∗t−Etp∗t+n+p∗t+Etyt+n−yt, (22.55)