# Goodness-of-fit tests for functional data

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

*Econometrics Journal*, 2009, vol. 12, issue s1, S1-S18

**Abstract:**
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. Copyright (C) The Author(s). Journal compilation (C) Royal Economic Society 2009

**Date:** 2009

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