Detecting changepoints in functional data has become an important problem as interest in monitoring of climate phenomenon has increased, where the data is functional in nature. The observed data often contains both amplitude ($y$-axis) and phase ($x$-axis) variability. If not accounted for properly, true changepoints may be undetected, and the estimated underlying mean change functions will be incorrect. In this paper, an elastic functional changepoint method is developed which properly accounts for these types of variability. The method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly or can be computed via functional principal component analysis to ease the computational burden. We apply the method and its non-elastic competitors to both simulated data and observed data to show its efficiency in handling data with phase variation with both amplitude and phase changepoints. We use the method to evaluate potential changes in stratospheric temperature due to the eruption of Mt.\ Pinatubo in the Philippines in June 1991. Using an epidemic changepoint model, we find evidence of a increase in stratospheric temperature during a period that contains the immediate aftermath of Mt.\ Pinatubo, with most detected changepoints occurring in the tropics as expected.

翻译：随着对气候现象监测兴趣的增加，函数数据中的变点检测已成为一个重要问题，此类数据本质上具有函数特性。观测数据通常同时包含振幅（$y$轴）与相位（$x$轴）变异性。若未能正确处理这两种变异性，可能导致真实变点无法被检出，且估计的潜在均值变化函数也会出现偏差。本文提出一种弹性函数变点方法，可有效处理上述变异性。该方法能够检测目前文献中现有方法无法识别的振幅与相位变点——现有方法仅聚焦于振幅变点。本方法既可直接通过函数实现，也可通过函数主成分分析（FPCA）计算以降低计算负担。我们将该方法及其非弹性竞争方法应用于模拟数据与实测数据，验证了其在处理同时包含振幅与相位变点的相位变异数据时的有效性。基于该方法，我们评估了1991年6月菲律宾皮纳图博火山喷发可能引起的平流层温度变化。采用流行病变点模型分析发现，在皮纳图博火山喷发后的一段时期内，平流层温度存在上升迹象，且大部分检测到的变点如预期出现在热带地区。