Goodness-of-fit tests for functional data

Federico A. Bugni*, Peter Hall, Joel L. Horowitz, George R. Neumann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Economic data are frequently generated by stochastic processes that can be modelled as occurring in continuous time. That is, the data are treated as realizations of a random function (functional data). Sometimes an economic theory model specifies the process up to a finite-dimensional parameter. This paper develops a test of the null hypothesis that a given functional data set was generated by a specified parametric model of a continuous-time process. The alternative hypothesis is non-parametric. A random function is a form of infinite-dimensional random variable, and the test presented here a generalization of the familiar Cramér-von Mises test to an infinite dimensional random variable. The test is illustrated by using it to test the hypothesis that a sample of wage paths was generated by a certain equilibrium job search model. Simulation studies show that the test has good finite-sample performance.

Original languageEnglish (US)
Pages (from-to)S1-S18
JournalEconometrics Journal
Issue numberSUPPL. 1
StatePublished - 2009


  • Bootstrap
  • Cramér-von Mises test
  • Equilibrium search model
  • Functional data analysis
  • Hypothesis testing

ASJC Scopus subject areas

  • Economics and Econometrics


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