Luis A. Gil-Alana and Javier Hualde 45510.3.3.3 Applications to interest rates
This has not been a very popular application of fractional cointegration, but we
can mention at least two relevant works. First, Dueker and Startz (1998) proposed
an ARFIMA model and discussed its estimation, the main feature being to provide
joint estimates of the common integration order of the observables and cointegrat-
ing error. They illustrated their method by analyzing the relation between US and
Canadian bond rates (using monthly data for 1987–97). The authors suggested that
it is not desirable to rely on an assumed value for the order of integration of the
observables (usually one), as traditionally was done in previous empirical analyses
related to fractional cointegration. They provided evidence of fractional cointegra-
tion, their estimates of the memory of the observables and the cointegrating error
being 0.674 and 0.200, respectively, which could be evidence in favor of a weak
cointegration relation.
In a different setting, Barkoulas, Baum and Oguz (1996) analyzed cointegration
among long-term interest rates from five countries (the US, Canada, Germany,
the UK and Japan) using monthly data for the period 1967–90. They justified the
unit root condition of the series and examined the possibility of cointegration by
means of the GPH test applied to different sub-systems of observables, concluding
in favor of the existence of strong co-movements between Canadian and US interest
rates.
10.3.3.4 Applications to electricity prices
This is probably the most recent (and one of the most promising) application of
fractional integration and cointegration techniques. Haldrup and Nielsen (2006)
mention the possibility of cointegration in a regime-switching model which allows
for fractional cointegration in each of the regime states. They analyzed hourly
spot electricity prices (January 2000–October 2003) for the Nord Pool area (Mid
Norway, South Norway, West Denmark, East Denmark, Sweden and Finland). Two
different regimes are allowed, congestion (where prices differ across areas) and non-
congestion (where prices are identical for every area). Two main conclusions can
be drawn from their results. First, the memory properties of the individual series
seem to differ substantially across regimes (although, in all cases, series appear
to be stationary). Second, the use of a non-switching model could lead to wrong
conclusions regarding the cointegration of the series (which are analyzed in pairs),
which could be driven by the extreme type of cointegration which characterizes
the data when the series are in a non-congestion state.
10.3.3.5 Applications to political studies
There are different political issues which have been analyzed in recent times by frac-
tional integration and cointegration techniques. As Robinson (1978) and Granger
(1980) demonstrated, fractional integration could originate from aggregation of
data which exhibits heterogeneous dynamic behavior at the individual level. This
has an important appeal for political data, where series are obtained by aggre-
gating the opinions of possibly very heterogeneous individuals. The first topic