Model clarification by testing the dynamics of functional data using a score density

by Julia Polak, Maxwell L. King and Xibin Zhang

We propose a pattern characteristics testing (PCT) procedure for validating the predictive abilities of a functional model. With the growing interest in functional data analysis during the last several decades and with the expansion of the functional modeling in a diverse range of scientific disciplines, a procedure that clarifies the validity of the proposed functional model is a vital tool. Our approach involves generation of many potential paths from the proposed model and summarizing their characterizing dynamics using a density of the scores resulting from a functional principal component decomposition. Two sets of simulation experiments are presented to illustrate the size and power of the procedure. An example with involves testing the fertility rates forecasting method suggested by Hyndman and Ullah (2007), shows the application of the procedure to Australian fertility rates in years 1921 − 2002.

Keywords: Classification, Dimension reduction, Functional data analysis, Multivariate kernel density estimation, Non-parametric statistics, Prediction capability testing, Principal components analysis, P-value, Score density.