Abstract

Functional data analysis is concerned with observations that are random functions defined on a set $\tau$ . For example, $X(t)$ could denote the observation of temperature
(pollution level) at a given location at time $t$. Stock prices, exchange rates are also modeled
as continues curves in economics and finance. Many of such continuous time phenomena are studied, although they are measured only at discrete time points. We provide
examples when the observations can be modeled as curves. We discuss how inference
on the mean of random curves is performed. There are two popular techniques for this
task: principal component analysis and fully functional approach. The principal component analysis transforms the data into a finite dimensional vector (dimension reduction)
while the fully functional approach uses the whole sample paths directly. We compare the advantages and drawbacks of both methods.