By Rituparna Sen, ISI Bangalore

Abstract 

Functional data analysis is the branch of statistics that deals with function valued random variables. We shall start with functional principal components analysis (FPCA) and illustrate the procedure with the example of daily volatility patterns. We shall then use this dimension reduction technique for a supervised learning task. We extend the FPCA methodology to a time series of functions and illustrate the method with the example of prediction of yield curves. We then discuss the problem of FPCA approach in hypothesis testing and describe an alternative Bayesian procedure for testing Granger causality in yield curves. We also illustrate the latter procedure with an example of pollution levels data.