INFERENCE ON COMMON TRENDS IN FUNCTIONAL TIME SERIES
研究了Hilbert空间中时间序列的单位根与协整推断，提出估计非平稳子空间维数并检验子空间假设的方法，适用于高维协整序列、因子模型和函数型时间序列等场景。
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, that is, 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 cointegrated vector time series that are either high-dimensional or of finite dimension, to high-dimensional factor models that include a finite number of nonstationary factors, to cointegrated curve-valued (or function-valued) time series, and to nonstationary dynamic functional factor models. To illustrate our methods, we include two empirical examples.