出版社：Suntory Toyota International Centres for Economics and Related Disciplines
摘要：A semiparametric bivariate fractionally cointegrated system is considered,
integration orders possibly being unknown and I (0) unobservable inputs having
nonparametric spectral density. Two kinds of estimate of the cointegrating
parameter ν are considered, one involving inverse spectral weighting and the
other, unweighted statistics with a spectral estimate at frequency zero. We
establish under quite general conditions the asymptotic distributional
properties of the estimates of ν, both in case of “strong cointegration” (when
the difference between integration orders of observables and cointegrating
errors exceeds 1/2) and in case of “weak cointegration” (when that difference is
less than 1/2), which includes the case of (asymptotically) stationary
observables. Across both cases, the same Wald test statistic has the same
standard null χ2 limit distribution, irrespective of whether integration orders
are known or estimated. The regularity conditions include unprimitive ones on
the integration orders and spectral density estimates, but we check these under
more primitive conditions on particular estimates. Finite-sample properties are
examined in a Monte Carlo study.
