Analyzing Data Which are Curves-Functional Data Analysis

In many areas of application, the data comes in the form of a curve or in other words a function. Consider a hotel having a fixed number of rooms. Suppose the hotel starts accepting booking for one year in advance. The information about the number of rooms booked for a particular date (say for 1^st April, 2016) would be available for every day in the period 1^st April, 2015 to 31^st March, 2016. If the number of rooms booked 't' days prior to 1^st April 2016 is denoted by b(t) then the curve {b(t) : 0≤ t ≤ 365} is called the booking curve for 1^st April 2016. Similar curves would be available for the number of rooms booked for 2^nd April, 3^rd April etc. Thus we would have the data in the form of curves {b₁, b₂,..., b_n}. Statistical analysis of this kind of data is referred to as functional data analysis. One of the simplest questions to ask with booking curves data is about the shape of the average booking curve.