Goodness-of-Fit Tests for Functional Data

18 Pages Posted: 4 Jul 2009

See all articles by Federico Bugni

Federico Bugni

Northwestern University - Department of Economics

Peter Hall

University of Melbourne

Joel L. Horowitz

Northwestern University

George R. Neumann

University of Iowa - Henry B. Tippie College of Business - Department of Economics

Date Written: 2008-08

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.

Suggested Citation

Bugni, Federico and Hall, Peter and Horowitz, Joel L. and Neumann, George R., Goodness-of-Fit Tests for Functional Data (2008-08). Econometrics Journal, Vol. 12, Issue s1, pp. S1-S18, January 2009. Available at SSRN: https://ssrn.com/abstract=1429070 or http://dx.doi.org/10.1111/j.1368-423X.2008.00266.x

Federico Bugni

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States

Peter Hall

University of Melbourne ( email )

185 Pelham Street
Carlton, Victoria 3053
Australia

Joel L. Horowitz

Northwestern University ( email )

2001 Sheridan Road
Evanston, IL 60208
United States

George R. Neumann

University of Iowa - Henry B. Tippie College of Business - Department of Economics ( email )

108 Pappajohn Building
Iowa City, IA 52242
United States
319-335-0850 (Phone)
319-356-1956 (Fax)

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