We introduce methods and theory for fractionally cointegrated curve time series. We develop a variance-ratio test to determine the dimensions associated with the nonstationary and stationary subspaces. For each subspace, we apply a local Whittle estimator to estimate the long-memory parameter and establish its consistency. A Monte Carlo study of finite-sample performance is included, along with two empirical applications.

翻译：本文提出了分数协整曲线时间序列的方法与理论。我们开发了一种方差比检验，用于确定与非平稳子空间和平稳子空间相关的维数。针对每个子空间，我们应用局部Whittle估计量来估计长记忆参数，并证明其一致性。文中还包含蒙特卡罗有限样本性能研究，以及两个实证应用。