Forecasting binary longitudinal data by a functional PC-ARIMA model

The purpose of this paper is to forecast the time evolution of a binary response variable from an associated continuous time series observed only at discrete time points that usually are unequally spaced. In order to solve this problem we are going to use a functional logit model based on functional principal component analysis of the predictor time series that takes into account its continuous nature, close to classical ARIMA modelling of the associated discrete time series of principal components.