Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models
AbstractIn this article we study a general class of goodness-of-fit tests for the conditional mean of a linear or nonlinear time series model. Among the properties of the proposed tests are that they are suitable when the conditioning set is infinite-dimensional; are consistent against a broad class of alternatives including Pitman's local alternatives converging at the parametric rate; and do not need to choose a lag order depending on the sample size or to smooth the data. It turns out that the asymptotic null distributions of the tests depend on the data generating process, so a new bootstrap procedure is proposed and theoretically justified. The proposed bootstrap tests are robust to higher order dependence, in particular to conditional heteroskedasticity of unknown form. A simulation study compares the finite sample performance of the proposed and competing tests and shows that our tests can play a valuable role in time series modeling. Finally, an application to an economic price series highlights the merits of our approach.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by American Statistical Association in its journal Journal of the American Statistical Association.
Volume (Year): 101 (2006)
Issue (Month): (June)
Contact details of provider:
Web page: http://www.amstat.org/publications/jasa/index.cfm?fuseaction=main
Other versions of this item:
- Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers 02/05, School of Economics and Business Administration, University of Navarra.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Juan Carlos Escanciano, 2004. "Model Checks Using Residual Marked Empirical Processes," Faculty Working Papers 13/04, School of Economics and Business Administration, University of Navarra.
- Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series /2005/482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June.
- Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, vol. 99(2), pages 291-315, December.
- repec:att:wimass:9520 is not listed on IDEAS
- J. Carlos Escanciano & Carlos Velasco, 2003.
"Generalized Spectral Tests For The Martingale Difference Hypothesis,"
Statistics and Econometrics Working Papers
ws035212, Universidad Carlos III, Departamento de Estadística y Econometría.
- Escanciano, J. Carlos & Velasco, Carlos, 2006. "Generalized spectral tests for the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 134(1), pages 151-185, September.
- Pena D. & Rodriguez J., 2002. "A Powerful Portmanteau Test of Lack of Fit for Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 601-610, June.
- Fan J. & Huang L-S., 2001. "Goodness-of-Fit Tests for Parametric Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 640-652, June.
- Hong, Yongmiao & Lee, Tae-Hwy, 2003. "Diagnostic Checking For The Adequacy Of Nonlinear Time Series Models," Econometric Theory, Cambridge University Press, vol. 19(06), pages 1065-1121, December.
- Efstathios Paparoditis, 2000. "Spectral Density Based Goodness-of-Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 27(1), pages 143-176.
- Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
- Escanciano, Juan Carlos & Mayoral, Silvia, 2010.
"Data-driven smooth tests for the martingale difference hypothesis,"
Computational Statistics & Data Analysis,
Elsevier, vol. 54(8), pages 1983-1998, August.
- Juan Carlos Escanciano & Silvia Mayoral, . "Data-Driven Smooth Tests for the Martingale Difference Hypothesis," Faculty Working Papers 01/07, School of Economics and Business Administration, University of Navarra.
- Landajo, Manuel & Presno, María José, 2010. "Nonparametric pseudo-Lagrange multiplier stationarity testing," MPRA Paper 25659, University Library of Munich, Germany.
- Escanciano, Juan Carlos & Velasco, Carlos, 2010.
"Specification tests of parametric dynamic conditional quantiles,"
Journal of Econometrics,
Elsevier, vol. 159(1), pages 209-221, November.
- Juan Carlos Escanciano & Carlos Velasco, 2008. "Specification Tests of Parametric Dynamic Conditional Quantiles," Caepr Working Papers 2008-021, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
- J. Carlos Escanciano & Carlos Velasco, 2010. "Specification tests of parametric dynamic conditional quantiles," Post-Print peer-00732534, HAL.
- Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
- Lavergne, Pascal & Patilea, Valentin, 2011.
"One for all and all for one: regression checks with many regressors,"
35779, University Library of Munich, Germany.
- Pascal Lavergne & Valentin Patilea, 2008. "One for All and All for One:Regression Checks With Many Regressors," Discussion Papers dp08-06, Department of Economics, Simon Fraser University.
- Pascal Lavergne & Valentin Patilea, 2007. "One for All and All for One : Regression Checks with Many Regressors”," Working Papers 2007-12, Centre de Recherche en Economie et Statistique.
- Zhu, Ke & Li, Wai-Keung, 2013. "A bootstrapped spectral test for adequacy in weak ARMA models," MPRA Paper 51224, University Library of Munich, Germany.
- Manuel Dominguez & Ignacio Lobato, 2010. "Consistent Inference in Models Defined by COnditional Moment Restrictions: an Alternative to GMM," Working Papers 1005, Centro de Investigacion Economica, ITAM.
- Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
- Leucht, Anne & Neumann, Michael H. & Kreiss, Jens-Peter, 2013. "A model specification test for GARCH(1,1) processes," Working Papers 13-11, University of Mannheim, Department of Economics.
- Escanciano, J. Carlos, 2006.
"A Consistent Diagnostic Test For Regression Models Using Projections,"
Cambridge University Press, vol. 22(06), pages 1030-1051, December.
- Juan Carlos Escanciano, 2005. "A Consistent Diagnostic Test for Regression Models Using Projections," Faculty Working Papers 09/05, School of Economics and Business Administration, University of Navarra.
- Manuel Landajo & María Presno, 2013. "Nonparametric pseudo-Lagrange multiplier stationarity testing," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(1), pages 125-147, February.
- Manuel A. Domínguez & Ignacio N. Lobato, 2006. "A Consistent Specification Test For Models Defined By Conditional Moment Restrictions," Economics Working Papers we064111, Universidad Carlos III, Departamento de Economía.
- Wasel Shadat, 2011. "On the Nonparametric Tests of Univariate GARCH Regression Models," The School of Economics Discussion Paper Series 1115, Economics, The University of Manchester.
- Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers 02/06, School of Economics and Business Administration, University of Navarra.
- Manuel Vega-Gordillo & José Luis Álvarez-Arce, 2005. "Heterogeneity In Economic Freedom: Free Clusters Or Free Countries," Faculty Working Papers 08/05, School of Economics and Business Administration, University of Navarra.
- Juan Carlos Escanciano, 2005. "On the Asymptotic Power Properties of Specification Tests for Dynamic Parametric Regressions," Faculty Working Papers 07/05, School of Economics and Business Administration, University of Navarra.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.