440 Fractional Integration and Cointegration
Other variables, such as consumption and income, have been analyzed from
a fractional viewpoint in Diebold and Rudebusch (1991), Haubrich (1993) and
Dolado and Marmol (2004). Finally, Crato and Rothman (1994a) and Gil-Alana
and Robinson (1997) analyzed updated versions of Nelson and Plosser’s (1982)
dataset, which has 14 US macroeconomic series, and found evidence of fractional
integration in practically all series.
10.2.2.2 Applications to exchange rates
The theory of purchasing power parity (PPP) occupies a central place in interna-
tional economics, being a key building block in monetary models of exchange rate
determination. In a flexible-price monetary model, PPP is assumed to hold contin-
uously. In a sticky-price model, PPP does not hold, but is a maintained assumption
for the long run. The question of interest is to determine if deviations from PPP
are transitory or permanent. Applying R/S techniques to daily rates for the British
pound, French franc and Deutsche mark, Booth, Kaen and Koveos (1982) found
positive memory during the flexible exchange rate period (1973–79) but negative
memory (that is, anti-persistence) during the fixed exchange rate period (1965–
71). Later, Cheung (1993) also found evidence of long memory behavior in foreign
exchange markets during the managed floating regime. On the other hand, Baum,
Barkoulas and Caglayan (1999) estimated ARFIMA models for real exchange rates in
the post-Bretton Woods era and found almost no evidence to support long-run PPP.
Additional papers on exchange rate dynamics using fractional integration are Fang,
Lai and Lai (1994), Crato and Ray (2000) and Wang (2004). The volatility dynam-
ics in foreign exchange rates with fractional integration has been examined with
the FIGARCH-model, introduced by Baillie, Bollerslev and Mikkelsen (1996), and
subsequent papers using this approach are Andersen and Bollerslev (1997, 1998),
Tse (1998), Baillie, Cecen and Han (2000), Kihc (2004) and Morana and Beltratti
(2004).
10.2.2.3 Applications to interest rates
Shea (1991) investigated the consequences of long memory in interest rates for
tests of the expectations hypothesis of the term structure. He found that allowing
for the possibility of long memory significantly improves the performance of the
model, even though the expectations hypothesis cannot be fully resurrected. In
related work, Backus and Zin (1993) observed that the volatility of bond yields
does not decline exponentially when the maturity of the bond increases; in fact,
they noticed that the decline was hyperbolic, consistent with the fractionally inte-
grated specification. Lai (1997) and Phillips (1998) provided evidence, based on
semiparametric methods, thatex anteandex postUS real interest rates are fraction-
ally integrated. Tsay (2000) employs an ARFIMA model to provide evidence that
the US real interest rate can be described as anI(d)process. Further evidence can
be found in Barkoulas and Baum (1997), Meade and Maier (2003) and Gil-Alana
(2004a, 2004b). Couchman, Gounder and Su (2006) estimated ARFIMA models for
ex postandex anteinterest rates from 16 countries. Their results suggest that, for