Forecasting functional time series (FTS) has arguably achieved tremendous success in recent years. Time series of curves, or functional time series, exist in many disciplines. Among the numerous existing contributions for forecasting time series, one-step-ahead functional time series forecasting, that is one-step-ahead prediction of a curve-valued time series, has been studied in several practical studies. Predominantly most traditional functional time series studies use functional (Hilbertian) autoregressive models for one-step-ahead forecast, but their application in real-world data remains a pertinent challenge due to a non-stationary behavior. Opposed to such models, several nonparametric approaches have been proposed in the recent literature for forecasting time series of curves. An analysis of the forecasting performances of such nonparametric approaches, validated empirically with a set of real experiments, is presented in this paper. While a complete understanding of these approaches remains elusive, we hope that our perspectives, discussions, and comparisons serve as a stimulus for new statistical research.

A key step to optimize the tests of semiconductors during the production process is to improve the prediction of the final yield from the defects detected on the wafers during the production process. This study investigates the link between the defects detected by a Scanning Electron Microscope (SEM) and the electrical failure of the final semiconductors, with two main objectives: (a) to identify the best layers to inspect by SEM; (b) to develop a model that predicts electrical failures of the semiconductors from the detected defects. The first objective has been reached by a model based on Odds Ratio that gave a (ranked) list of the layers that best predict the final yield. This allows process engineers to concentrate inspections on a few important layers. For the second objective, a regression/classification model based on Gradient Boosting has been developed. As a by-product, this latter model confirmed the results obtained by Odds Ratio analysis. Both models take account of the high lacunarity of the data and have been validated on two distinct datasets from STMicroelectronics.