This article presents a novel method for prediction of stationary functional time series, in particular for trajectories that share a similar pattern but display variable phases. The limitation of most of the existing prediction methodologies for functional time series is that they only consider vertical variation (amplitude, scale, or vertical shift). To overcome this limitation, we develop a shape-preserving (SP) prediction method that incorporates both vertical and horizontal variation. One major advantage of our proposed method is the ability to preserve the shape of functions. Moreover, our proposed SP method does not involve unnatural transformations and can be easily implemented using existing software packages. The utility of the SP method is demonstrated in the analysis of non-metanic hydrocarbons (NMHC) concentration. The analysis demonstrates that the prediction by the SP method captures the common pattern better than the existing prediction methods and also provides competitive prediction accuracy.
翻译:本条提出了预测固定功能时间序列的新方法,特别是预测具有类似模式但显示可变阶段的轨迹。功能时间序列大多数现有预测方法的局限性在于它们只考虑垂直变化(典型、规模或垂直变化)。为克服这一局限性,我们开发了一种包含纵向和横向差异的形状保护(SP)预测方法。我们拟议方法的一个主要优点是能够保持功能形状。此外,我们提议的SP方法并不涉及非自然变换,而且可以很容易地利用现有软件包加以实施。SP方法的效用在非甲基碳氢化合物浓度分析中得到了证明。分析表明,SP方法的预测所捕捉的常见模式比现有预测方法要好,并且提供了竞争性预测的准确性。