Estimation of Common Long-Memory Components in Cointegrated Systems

The study of cointegration in large systems requires a reduction of their dimensionality. To
achieve this, we propose to obtain the I(1)common factors in every subsystem and then analyze
cointegration among them. In this article, a new way of estimating common long-memory components
of a cointegrated system is proposed. The identification of these 1(1)common factors
is achieved by imposing that they be linear combinations of the original variables X,, and that
the error-correction terms do not cause the common factors at low frequencies. Estimation is
done from a fully specified error-correction model, which makes it possible to test hypotheses
on the common factors using standard chi-squared tests. Several empirical examples illustrate
the procedure.
KEY WORDS: Common factors; Cointegration; Error-correction model; Permanent-transitory
decomposition.