Title: Prediction of missing functional data with memory
Authors: Lauri Viitasaari - Aalto University (Finland) [presenting]
Pauliina Ilmonen - Aalto University School of Science (Finland)
Germain Van Bever - Universite de Namur (Belgium)
Tommi Sottinen - University of Vaasa (Finland)
Nourhan Shafik - Aalto University (Finland)
Abstract: Functional observations $X^i$ that are realisations of some Gaussian process are considered. We assume that parts of the paths are unobservable, and the aim is to fill in the missing information as accurately as possible. One natural approach is to predict some missing value $X_s^k$ by using the information provided by $X_s^i,i\neq k$ of those functions $X^i$ for which $X_s^i$ is observed. However, under memory the unobserved $X_s^k$ relies heavily on that particular observation $X^k$ directly, and thus applying other observations $X^i$ may be misleading, even if they are drawn from the same underlying process. We present a novel approach for accurate prediction of missing information $X_s^k$ that is based on applying combined information provided by the observed part of the path $X^k$ and the observed values $X_s^i,i\neq k$. Extensions beyond the Gaussianity assumption are discussed.