出版社：Suntory Toyota International Centres for Economics and Related Disciplines
摘要：Empirical evidence has emerged of the possibility of fractional cointegration
such that the gap, β, between the integration order δ of observable time series,
and the integration order γ of cointegrating errors, is less than 0.5. This
includes circumstances when observables are stationary or asymptotically
stationary with long memory (so δ < 1/2), and when they are nonstationary (so
δ 1/2). This “weak cointegration” contrasts strongly with the traditional
econometric prescription of unit root observables and short memory cointegrating
errors, where β = 1. Asymptotic inferential theory also differs from this case,
and from other members of the class β > 1/2, in particular ≥ consistent - n
and asymptotically normal estimation of the cointegrating vector ν is possible
when β < 1/2, as we explore in a simple bivariate model. The estimate depends
on γ and δ or, more realistically, on estimates of unknown γ and δ. These latter
estimates need to be consistent - n , and the asymptotic distribution of the
estimate of ν is sensitive to their precise form. We propose estimates of γ and
δ that are computationally relatively convenient, relying on only univariate
nonlinear optimization. Finite sample performance of the methods is examined by
means of Monte Carlo simulations, and several applications to empirical data
included.
