  Multicointegration is traditionally defined as a particular long run
relationship among variables in a parametric vector autoregressive model that
introduces additional cointegrating links between these variables and partial
sums of the equilibrium errors. This paper departs from the parametric model,
using a semiparametric formulation that reveals the explicit role that
singularity of the long run conditional covariance matrix plays in determining
multicointegration. The semiparametric framework has the advantage that short
run dynamics do not need to be modeled and estimation by standard techniques
such as fully modified least squares (FM-OLS) on the original I(1) system is
straightforward. The paper derives FM-OLS limit theory in the multicointegrated
setting, showing how faster rates of convergence are achieved in the direction
of singularity and that the limit distribution depends on the distribution of
the conditional one-sided long run covariance estimator used in FM-OLS
estimation. Wald tests of restrictions on the regression coefficients have
nonstandard limit theory which depends on nuisance parameters in general. The
usual tests are shown to be conservative when the restrictions are isolated to
the directions of singularity and, under certain conditions, are invariant to
singularity otherwise. Simulations show that approximations derived in the
paper work well in finite samples. The findings are illustrated empirically in
an analysis of fiscal sustainability of the US government over the post-war
period.
