Luis A. Gil-Alana and Javier Hualde 453Still concerning the forward premium, much effort has also been devoted to
explanations of the so-called “forward premium anomaly.” This refers to surprising
negative estimates from regressions of the change in the log of the spot exchange
rate on the forward premium, where theory predicts a value of 1 for that slope
(see, for example, Bekaert, 1996; Bekaert, Hodrick and Marshall, 1997). Baillie and
Bollerslev (2000) consider this issue to be a statistical problem caused by the dif-
ferent integration orders of the dependent variable and regressor in the equation
mentioned above. They indicate that the spot exchange rate is approximately a unit
root, whereas there seems to be evidence in favor of a mean-reverting (but non-
stationary) forward premium. Under these circumstances, Maynard and Phillips
(2001) showed that the slope coefficient of such a regression (with a short memory
dependent variable and a non-stationary but mean-reverting regressor) converges
in probability to zero, the long left tail of the asymptotic distribution of this estima-
tor giving further support to the puzzling negative values obtained in the literature.
Baillie, Han and Koul (2002) provided further evidence regarding the imbalance
of the forward premium regression equation with high-frequency data, so that
the forward premium anomaly seems to be an intrinsic property of exchange rates,
and they conjectured that the phenomenon is not due to regime shifts or structural
breaks.
Finally, there is a more recent literature trying to explain, by means of fractional
cointegration, the connection between exchange rates and fundamentals. Caporale
and Gil-Alana (2004a) examined the issue of whether real exchange rates were
cointegrated with real interest rates and labor productivity differentials in the DM–
US$, Yen–US$ relations using quarterly data (1975–98). They provided evidence of
unit roots in the observables and also, by estimating parametrically the memory
of the cointegrating error from cointegrating residuals, conjectured the existence
of fractional cointegration, with the estimated integration order of the residuals
fluctuating between 0 and 0.5 in the case of Germany and between 0.1 and 0.6 in
the case of Japan.
Dufrénotet al.(2006) explored the real exchange rate misalignments of five Euro-
pean countries during the period 1979–99. They posited an equilibrium relation
between real exchange rates and macroeconomic fundamentals (terms of trade,
prices, foreign assets, fiscal wedge, interest rate differential), with each variable
representing the value in a particular country related to a weighted average of the
same variable for other countries. They estimated the memory of the cointegrating
residuals by means of the modified R/S statistic of Lo (1991), the GPH estimator
and the exact ML estimator of Sowell (1992a). In view of their results, there seems
to be strong evidence of fractional cointegration for the Netherlands, with mixed
evidence for France and the UK.
10.3.3.2 Applications to financial series
Within this area of research, the main focus has been the study of the volatil-
ity of financial series, providing evidence of long memory covariance stationary
observables with weakly dependent cointegrating errors. The first explicit reference