Title: Fully modified least square for multicointegrated systems
Authors: Igor Kheifets - ITAM (Mexico) [presenting]
Peter CB Phillips - Yale University (United States)
Abstract: Multicointegration is traditionally defined as a particular long run relationship among variables in a parametric vector autoregressive model. We depart from the parametric model. This allows us to provide the explicit relationship from which the multicointegration arises and reveal the leading role that the singularity of the long run conditional covariance matrix plays in determining multicointegration. Considering multicointegration in a semiparametric framework has an advantage that the short run dynamics of time series does not need to be modeled. We show that in a semiparametric triangular representation of cointegrated time series, multicointegration results in a singular long run covariance. We derive a convergence of fully modified regression estimator in case of singular long run covariance. We obtain faster rates of convergence along particular directions, these rates and asymptotic distribution depend on the conditional one-sided long run covariance estimator used after the first stage. We also show that in the presence of singularity the Wald test for restrictions on the regression coefficient has nonstandard distribution, depends on nuisance parameters and is conservative if restrictions isolate those directions and is invariant to singularity otherwise.