Abstract
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.
Highlights
When continuous-time records are separated into natural consecutive time intervals, such as days, weeks, or years, for which a reasonably similar behavior is expected, the resulting functions can be described as a functional time series, where one unit of observation is an observed trajectory
An immediate result is that, the predicted curve may not show the common underlying pattern. To overcome this serious limitation, we develop a novel method for stationary functional time series, where trajectories share a common pattern
We develop a new prediction method for stationary functional time series that display a common pattern
Summary
When continuous-time records are separated into natural consecutive time intervals, such as days, weeks, or years, for which a reasonably similar behavior is expected, the resulting functions can be described as a functional time series, where one unit of observation is an observed trajectory. The variation of the occurrence time of the peaks can be viewed as phase variation. An immediate result is that, the predicted curve may not show the common underlying pattern. To overcome this serious limitation, we develop a novel method for stationary functional time series, where trajectories share a common pattern. Our goal is to obtain competitive prediction from the past data by some stationary functional time series model, such as functional auto-regressive model, in terms of mean squared error, and to preserve the underlying pattern for the predicted curves
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