THE NONSTATIONARY FRACTIONAL UNIT ROOT
研究标量分数阶积分过程I(d)的渐近性质，提出d的检验和估计方法，适用于任意实数d，检验渐近一致最优无偏，极大似然估计渐近有效。
This paper deals with a scalar I ( d ) process { y j }, where the integration order d is any real number. Under this setting, we first explore asymptotic properties of various statistics associated with { y j }, assuming that d is known and is greater than or equal to ½. Note that { y j } becomes stationary when d < ½, whose case is not our concern here. It turns out that the case of d = ½ needs a separate treatment from d > ½. We then consider, under the normality assumption, testing and estimation for d , allowing for any value of d . The tests suggested here are asymptotically uniformly most powerful invariant, whereas the maximum likelihood estimator is asymptotically efficient. The asymptotic theory for these results will not assume normality. Unlike in the usual unit root problem based on autoregressive models, standard asymptotic results hold for test statistics and estimators, where d need not be restricted to d ≥ ½. Simulation experiments are conducted to examine the finite sample performance of both the tests and estimators.