Recently, increasing interest in the issue of fractional cointegration
has emerged from theoretical and empirical viewpoints. Here, as opposed to
the traditional prescription of unit root observables with weak dependent
cointegrating errors, the orders of integration of these series are
allowed to take real values, but, as in the traditional framework,
equality of the orders of at least two observable series is necessary for
cointegration. This assumption, in view of the real-valued nature of these
orders, could pose some difficulties, and in the present paper we explore
some ideas related to this issue in a simple bivariate framework. First,
in a situation of “near-cointegration,” where the only
difference with respect to the “usual” fractional
cointegration is that the orders of the two observable series differ in an
asymptotically negligible way, we analyze properties of standard estimates
of the cointegrating parameter. Second, we discuss the estimation of the
cointegrating parameter in a situation where the orders of integration of
the two observables are truly different but their corresponding balanced
versions (with same order of integration) are cointegrated in the usual
sense. A Monte Carlo study of finite-sample performance and simulated
series is included.I thank Adrian Pagan,
James Davidson, and seminar participants at the 2004 Econometric Society
European Meeting and the 2004 Simposio de Análisis Económico
for helpful comments. I also thank two referees and a co-editor whose
comments led to improvements of the paper. This research was supported by
the Spanish Ministerio de Educación y Ciencia through a contract
Juan de la Cierva and ref. SEJ2005-07657/ECON, and also by the
Universidad de Navarra, ref. 16037001.