We develop a statistical testing procedure to examine whether the curve-valued time series of interest is integrated of order d for an integer d. The proposed procedure can distinguish between integer-integrated time series and fractionally-integrated ones, and it has broad applicability in practice. Monte Carlo simulation experiments show that the proposed testing procedure performs reasonably well. We apply our methodology to Canadian yield curve data and French sub-national age-specific mortality data. We find evidence that these time series are mostly integrated of order one, while some have fractional orders exceeding or falling below one.

翻译：我们开发了一种统计检验程序，用于检验感兴趣的曲线值时间序列是否具有整数阶d的积分特性。所提出的程序能够区分整数阶积分时间序列与分数阶积分时间序列，在实践中具有广泛适用性。蒙特卡洛模拟实验表明，该检验程序表现良好。我们将该方法应用于加拿大收益率曲线数据和法国次国家级年龄别死亡率数据。研究发现，这些时间序列大多具有一阶积分特性，而部分序列的分数阶积分阶数则高于或低于一阶。