Skip to main content Accessibility help
×
Home
Hostname: page-component-99c86f546-vl2kb Total loading time: 0.205 Render date: 2021-12-02T04:42:43.866Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

A DATA-DRIVEN NONPARAMETRIC SPECIFICATION TEST FOR DYNAMIC REGRESSION MODELS

Published online by Cambridge University Press:  23 May 2006

Alain Guay
Affiliation:
Université du Québec à Montréal
Emmanuel Guerre
Affiliation:
LSTA, Université Paris 6

Abstract

The paper introduces a new nonparametric specification test for dynamic regression models. The test combines chi-square statistics based on Fourier series regression. A data-driven choice of the regression order, which uses the square root of the number of Fourier coefficients, is proposed. The benefits of the new test are (1) the selection procedure produces explicit and chi-square critical values that give a finite-sample size close to the nominal size; (2) the test is adaptive rate-optimal and detects local alternatives converging to the null with a rate that can be made arbitrarily close to the parametric rate. Simulation experiments illustrate the practical relevance of the new test.The first author acknowledges financial support from the Fonds Québécois de la Recherche sur la Société et la Culture (FQRSC). The second author acknowledges financial support from LSTA.

Type
Research Article
Copyright
© 2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aït-Sahalia, Y. (1996) Testing continuous-time models of the spot interest rate. Review of Financial Studies 9, 385426.Google Scholar
Aït-Sahalia, Y., P.J. Bickel, & T.M. Stocker (2001) Goodness of fit tests for kernel regression with an application to option-implied volatility. Journal of Econometrics 105, 363412.Google Scholar
Baraud, Y., S. Huet, & B. Laurent (2003) Adaptive tests of linear hypotheses by model selection. Annals of Statistics 31, 225251.Google Scholar
Bierens, H.J. (1984) Model specification testing of time series regressions. Journal of Econometrics 26, 323353.Google Scholar
Billingsley, P. (1968) Convergence of Probability Measures. Wiley.
Brown, L.D. & M.G. Low (1996) Asymptotic equivalence of nonparametric regression and white noise. Annals of Statistics 24, 23842398.Google Scholar
Chen, X. & Y. Fan (1999) Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series. Journal of Econometrics 91, 373401.Google Scholar
Chow, S.C. & H. Teicher (1988) Probability Theory: Independence, Interchangeability, Martingales. Springer.
Domowitz, I. & H. White (1982) Misspecified models with dependent observations. Journal of Econometrics 20, 3558.Google Scholar
Fan, J. (1996) Test of significance based on wavelet thresholding and Neyman's truncation. Journal of the American Statistical Association 91, 674688.Google Scholar
Fan, J. & L.S. Huang (2001) Goodness-of-fits test for parametric regression models. Journal of the American Statistical Association 96, 640652.Google Scholar
Fan, J. & Q. Yao (2003) Nonlinear Time Series: Nonparametric and Parametric Methods. Springer.
Fan, J., C. Zhang, & J. Zhang (2001) Generalized likelihood ratio statistics and Wilks phenomenon. Annals of Statistics 29, 153193.Google Scholar
Gao, J. & M. King (2001) Estimation and Model Specification Testing in Nonparametric and Semiparametric Regression. Working paper, School of Mathematics and Statistics, the University of Western Australia.
Gao, J. & M. King (2004) Adaptive testing in continuous-time diffusion models. Econometric Theory 20, 844883.Google Scholar
Gayraud, G. & C. Pouet (2005) Adaptive minimax testing in the discrete regression scheme. Probability Theory and Related Fields 133, 53158.Google Scholar
Gozalo, P.L. (1997) Nonparametric bootstrap analysis with applications to demographic effects in demand functions. Journal of Econometrics 81, 357393.Google Scholar
Guerre, E. & P. Lavergne (2002) Optimal minimax rates for nonparametric specification testing in regression models. Econometric Theory 18, 11391171.Google Scholar
Guerre, E. & P. Lavergne (2005) Data-driven rate-optimal specification testing in regression models. Annals of Statistics 33, 840870.Google Scholar
Hamilton, J.D. (2001) A parametric approach to flexible nonlinear inference. Econometrica 69, 537573.Google Scholar
Härdle, W. & E. Mammen (1993) Comparing nonparametric versus parametric regression fits. Annals of Statistics 21, 19261947.Google Scholar
Hart, J.D. (1997) Nonparametric Smoothing and Lack-of-fit Tests. Springer.
Hong, Y. & H. White (1995) Consistent specification testing via nonparametric series regression. Econometrica 63, 11331159.Google Scholar
Horowitz, J. & V.G. Spokoiny (2001) An adaptive, rate-optimal test of a parametric mean regression model against a nonparametric alternative. Econometrica 69, 599631.Google Scholar
Ingster, Y.I. (1992, 1993) Asymptotically minimax hypothesis testing for nonparametric alternatives, parts I, II, and III. Mathematical Methods of Statistics 2, 85–114, 171–189, and 249268.
Poo, J.R., S. Sperlich, & P. Vieu (2004) An Adaptive Specification Test for Semiparametric Models. Manuscript, Universidad de Zaragoza.
Rio, E. (2000) Théorie asymptotique des processus aléatoires faiblement dépendants. Mathématiques and Applications 31. Springer.
Robinson, P.M. (1989) Hypothesis testing in semiparametric and nonparametric models for econometric time series. Review of Economic Studies 56, 511534.Google Scholar
Shorack, G.R. & J.A. Wellner (1986) Empirical Processes with Applications to Statistics. Wiley.
Spokoiny, V.G. (1996) Adaptive hypothesis testing using wavelets. Annals of Statistics 24, 24772498.Google Scholar
Spokoiny, V.G. (2001) Data-driven testing the fit of linear models. Mathematical Methods of Statistics 10, 465497.Google Scholar
Timan, A.F. (1994) Theory of Approximation of Functions of a Real Variable. Dover.
Tjøstheim, D. (1994) Non-linear time series: A selective review. Scandinavian Journal of Statistics 21, 97130.Google Scholar
8
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

A DATA-DRIVEN NONPARAMETRIC SPECIFICATION TEST FOR DYNAMIC REGRESSION MODELS
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

A DATA-DRIVEN NONPARAMETRIC SPECIFICATION TEST FOR DYNAMIC REGRESSION MODELS
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

A DATA-DRIVEN NONPARAMETRIC SPECIFICATION TEST FOR DYNAMIC REGRESSION MODELS
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *