Testing for Integer Integration in Functional Time Series
提出一种统计检验方法，判断曲线值时间序列是否为非负整数阶d的积分过程，并能区分整数积分与分数积分，应用于加拿大收益率曲线和法国地区死亡率数据，发现多数序列为一阶积分。
We develop a statistical testing procedure to examine whether the curve-valued time series of interest is integrated of order d for a nonnegative 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.