New approaches to prediction using functional data analysis

Abstract

In this paper we address the problem of prediction with functional data. We discuss several new methods for predicting the future values of a partially observed curve when it can be assumed that the data is coming from an underlying Gaussian Process. When the underlying process can be assumed to be stationary with powered exponential covariance function we suggest two new predictors and compare their performance. In some real life situations the data may come from a mixture of two stationary Gaussian Processes. We introduce three new methods of prediction in this case and compare their performance. In case the data comes from a non-stationary process we propose a modifi cation of the powered exponential covariance function and study the performance of the three predictors mentioned above using three real-life data sets. The results indicate that the KM-Predictor in which the training data is clustered using the K-Means algorithm before prediction can be used in several real life situations.