标题： 函数时间序列中共同趋势的推断 显示英文标题

标题： Inference on common trends in functional time series

摘要： 我们研究在希尔伯特空间中的时间序列的单位根和协整的统计推断。 我们发展了对时间序列中嵌入的共同随机趋势数量的统计推断，即非平稳子空间的维数。 我们还考虑了对非平稳和平稳子空间本身的假设检验。 希尔伯特空间可以是任意大的维度，即使感兴趣的时间序列取值于可能维数未知的子空间，我们的方法仍然渐近有效。 这在实践中具有广泛的应用性；例如，应用于高维或有限维的协整向量时间序列，应用于包含有限个非平稳因子的高维因子模型，应用于协整曲线值（或函数值）时间序列，以及应用于非平稳动态函数因子模型。 我们分别对利率期限结构和劳动力市场指数进行了两个实证说明。 显示英文摘要

摘要： We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the nonstationary subspace. We also consider tests of hypotheses on the nonstationary and stationary subspaces themselves. The Hilbert space can be of an arbitrarily large dimension, and our methods remain asymptotically valid even when the time series of interest takes values in a subspace of possibly unknown dimension. This has wide applicability in practice; for example, to the case of cointegrated vector time series that are either high-dimensional or of finite dimension, to high-dimensional factor model that includes a finite number of nonstationary factors, to cointegrated curve-valued (or function-valued) time series, and to nonstationary dynamic functional factor models. We include two empirical illustrations to the term structure of interest rates and labor market indices, respectively.