Advanced Search

Determination of the Number of Common Stochastic Trends Under Conditional Heteroskedasticity/Determinación del número de tendencias estocásticas comunes bajo heteroscedasticidad condicional

Contents:

Author Info

  • CAVALIERE, GIUSEPPE

    () (Department of Statistical Sciences, University of Bologna. Italia.)

  • RAHBEK, ANDERS

    () (Department of Economics, University of Copenhagen. Suecia.)

  • TAYLOR, ROBERT

    () (School of Economics, University of Nottingham. Gran Bretaña.)

Abstract

business cycle frequencies strongly rely on the correct detection of the number of common stochastic trends (co-integration). Standard techniques for the determination of the number of common trends, such as the well-known sequential procedure proposed in Johansen (1996), are based on the assumption that shocks are homoskedastic. This contrasts with empirical evidence which documents that many of the key macro-economic and financial variables are driven by heteroskedastic shocks. In a recent paper, Cavaliere et al., (2010, Econometric Theory, forthcoming) demonstrate that Johansen's (LR) trace statistic for co-integration rank and both its i.i.d. and wild bootstrap analogues are asymptotically valid in non-stationary systems driven by heteroskedastic (martingale difference) innovations, but that the wild bootstrap performs substantially better than the other two tests in finite samples. In this paper we analyse the behaviour of sequential procedures to determine the number of common stochastic trends present based on these tests. Numerical evidence suggests that the procedure based on the wild bootstrap tests performs best in small samples under a variety of heteroskedastic innovation processes. Tanto las descomposiciones en componentes permanentes-transitorias de las series de tiempo como el análisis de las propiedades como tales de las variables económicas en las frecuencias del ciclo económico (business cycle) dependen fuertemente de la detección correcta del número de tendencias estocásticas comunes (cointegración). Las técnicas estándar para la determinación del número de tendencias comunes, como, por ejemplo, el conocido procedimiento secuencial propuesto en Johansen (1996), se basan en la hipótesis de que los shocks son homoscedásticos. Esto contradice la evidencia empírica que demuestra que muchas de las variables financieras y macroeconómicas más importantes se mueven por shocks heteroscedásticos. En un artículo reciente, Cavaliere y otros autores (2010, Econometric Theory, de próxima aparición) demuestran que el estadístico LR de la traza para el rango de la co-integración y sus análogos (tanto los i.i.d. como los “wild” bootstrap) son válidos asintóticamente en sistemas no estacionarios dirigidos por innovaciones heteroscedásticas (diferencia de martingalas) y que, además, “wild bootstrap” funciona sustancialmente mejor que los otros dos contrastes en muestras finitas. En este artículo, basándonos en esta prueba, analizaremos el comportamiento de procedimientos secuenciales para determinar, sobre la base de esos test, el número de tendencias estocásticas comunes presentes. La evidencia numérica sugiere que el procedimiento basado en los test “wild bootstrap” funciona mejor para pequeñas muestras y bajo una variedad de procesos de innovaciones heteroscedásticas.

Download Info

If 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.
File URL: http://www.revista-eea.net
Download Restriction: Access to full text is restricted to subscribers.

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 Info

Article provided by Estudios de Economía Aplicada in its journal Estudios de Economía Aplicada.

Volume (Year): 28 (2010)
Issue (Month): (Diciembre)
Pages: 519-552
Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Handle: RePEc:lrk:eeaart:28_3_2

Contact details of provider:
Postal: Beatriz Rodríguez Prado. Facultad de CC.EE. y EE. Avda. Valle del Esgueva. Valladolid 47011 SPAIN
Phone: (34) 983 423320
Fax: (34) 983 184568
Web page: http://www.revista-eea.net
More information through EDIRC

Order Information:
Email:
Web: http://www.revista-eea.net

For corrections or technical questions regarding this item, or to correct its listing, contact: (Beatriz Rodríguez Prado).

Related research

Keywords: Co-integration; maximum eigenvalue rank tests; conditional heteroskedasticity; i.i.d. bootstrap; wild bootstrap. ; Co-integration; maximum eigenvalue rank tests; conditional heteroskedasticity; i.i.d. bootstrap; wild bootstrap..;

Find related papers by JEL classification:

References

References listed on IDEAS
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.:
  1. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-77, Sept.-Oct.
  2. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  3. Kilian, Lutz & Gonçalves, Sílvia, 2002. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Discussion Paper Series 1: Economic Studies 2002,26, Deutsche Bundesbank, Research Centre.
  4. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2010. "Bootstrap co-integration rank testing: the role of deterministic variables and initial values in the bootstrap recursion," Discussion Papers 10/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  6. Giuseppe Cavaliere & A. M. Robert Taylor, 2008. "Time-Transformed Unit Root Tests for Models with Non-Stationary Volatility," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 300-330, 03.
  7. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, vol. 95(5), pages 1062-88, October.
  8. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(06), pages 1719-1760, December.
  9. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, vol. 114(2), pages 261-295, June.
  10. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2007. "Testing for unit roots in time series models with non-stationary volatility," Journal of Econometrics, Elsevier, vol. 140(2), pages 919-947, October.
  11. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor and Francis Journals, vol. 26(6), pages 609-641.
  12. Nielsen, Bent & Rahbek, Anders, 2000. " Similarity Issues in Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(1), pages 5-22, February.
  13. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Bootstrap Unit Root Tests For Time Series With Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 24(01), pages 43-71, February.
  14. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:lrk:eeaart:28_3_2

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Beatriz Rodríguez Prado).

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.