A review on specification tests for models with functional data

Abstract

Nowadays, due to the progress in technological advances, massive amounts of data are generated. As a result, new statistical methodology is needed to properly manage this information. The functional data are an example of special importance. These are mainly obtained by means of high-frequency measurements (spectrometric curves, stock prices recording, etc.). Since the beginning of this century, this type of data has achieved great popularity. This fact has generated new distribution or regression models, among others, appropriate to the functional context. In the last 10 years, novel specification tests are proposed for those models. These are generalizations of methodologies developed for the vectorial framework over the last century. Besides, innovative procedures based on distance correlation ideas have been proposed as well. This article reviews the most notable developments in this context, providing some illustrations from real data sets.