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

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  • 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.

Suggested Citation

  • Cavaliere, Giuseppe & Rahbek, Anders & Taylor, Robert, 2010. "Determination of the Number of Common Stochastic Trends Under Conditional Heteroskedasticity/Determinación del número de tendencias estocásticas comunes bajo heteroscedasticidad condicional," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 28, pages 519-552, Diciembre.
  • Handle: RePEc:lrk:eeaart:28_3_2
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    References listed on IDEAS

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    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 563-577, Sept.-Oct.
    2. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, vol. 74(6), pages 1699-1714, November.
    3. Giese, Julia V., 2008. "Level, Slope, Curvature: Characterising the Yield Curve in a Cointegrated VAR Model," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 2, pages 1-20.
    4. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    5. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    6. Giuseppe Cavaliere & A. M. Robert Taylor & Carsten Trenkler, 2013. "Bootstrap Cointegration Rank Testing: The Role of Deterministic Variables and Initial Values in the Bootstrap Recursion," Econometric Reviews, Taylor & Francis Journals, pages 814-847.
    7. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    8. 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 1062-1088, October.
    9. ANDERSEN, Torben G. & BOLLERSLEV, Tim & MEDDAHI, Nour, 2002. "Correcting the Errors : A Note on Volatility Forecast Evaluation Based on High-Frequency Data and Realized Volatilities," Cahiers de recherche 2002-21, Universite de Montreal, Departement de sciences economiques.
    10. 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.
    11. 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.
    12. Silvia Goncalves & Lutz Kilian, 2007. "Asymptotic and Bootstrap Inference for AR(∞) Processes with Conditional Heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, pages 609-641.
    13. Hansen, Peter Reinhard, 2003. "Structural changes in the cointegrated vector autoregressive model," Journal of Econometrics, Elsevier, pages 261-295.
    14. Gonçalves, Sílvia & Kilian, Lutz, 2002. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Working Paper Series 0196, European Central Bank.
    15. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    16. 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.
    17. 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, March.
    18. 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.
    19. 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, pages 116-126.
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    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..;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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