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Inference on Co-integration Parameters in Heteroskedastic Vector Autoregressions

Author

Listed:
  • H. Peter Boswijk

    (University of Amsterdam)

  • Giuseppe Cavaliere

    (University of Bologna, Italy)

  • Anders Rahbek

    (University of Copenhagen, Denmark, and CREATES)

  • A. M. Robert Taylor

    (University of Essex, United Kingdom)

Abstract
It is well established that the shocks driving many key macro-economic and financial variables display time-varying volatility. In this paper we consider estimation and hypothesis testing on the coefficients of the co-integrating relations and the adjustment coefficients in vector autoregressions driven by both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the conventional results in Johansen (1996) for the maximum likelihood estimators and associated likelihood ratio tests derived under homoskedasticity do not in general hold in the presence of heteroskedasticity. As a consequence, standard confidence intervals and tests of hypothesis on these coefficients are potentially unreliable. Solutions to this inference problem based on Wald tests (using a "sandwich" estimator of the variance matrix) and on the use of the wild bootstrap are discussed. These do not require the practitioner to specify a parametric model for volatility, or to assume that the pattern of volatility is common to, or independent across, the vector of series under analysis. We formally establish the conditions under which these methods are asymptotically valid. A Monte Carlo simulation study demonstrates that significant improvements in finite sample size can be obtained by the bootstrap over the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments. An application to the term structure of interest rates in the US illustrates the difference between standard and bootstrap inferences regarding hypotheses on the co-integrating vectors and adjustment coefficients.

Suggested Citation

  • H. Peter Boswijk & Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2013. "Inference on Co-integration Parameters in Heteroskedastic Vector Autoregressions," Tinbergen Institute Discussion Papers 13-187/III, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20130187
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    2. H. Peter Boswijk & Yang Zu, 2022. "Adaptive Testing for Cointegration With Nonstationary Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 744-755, April.
    3. Rustam Ibragimov & Jihyun Kim & Anton Skrobotov, 2020. "New robust inference for predictive regressions," Papers 2006.01191, arXiv.org, revised Mar 2023.
    4. Popiel Michal Ksawery, 2017. "Interest rate pass-through: a nonlinear vector error-correction approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-20, December.
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    6. Marina Balboa & Paulo M. M. Rodrigues & Antonio Rubia & A. M. Robert Taylor, 2021. "Multivariate fractional integration tests allowing for conditional heteroskedasticity with an application to return volatility and trading volume," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(5), pages 544-565, August.
    7. H. Peter Boswijk & Giuseppe Cavaliere & Luca De Angelis & A. M. Robert Taylor, 2023. "Adaptive information-based methods for determining the co-integration rank in heteroskedastic VAR models," Econometric Reviews, Taylor & Francis Journals, vol. 42(9-10), pages 725-757, November.
    8. Giuseppe Cavaliere & Anton Skrobotov & A. M. Robert Taylor, 2019. "Wild bootstrap seasonal unit root tests for time series with periodic nonstationary volatility," Econometric Reviews, Taylor & Francis Journals, vol. 38(5), pages 509-532, May.
    9. Boldea, Otilia & Cornea-Madeira, Adriana & Hall, Alastair R., 2019. "Bootstrapping structural change tests," Journal of Econometrics, Elsevier, vol. 213(2), pages 359-397.
    10. Georgiev, Iliyan & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2018. "Testing for parameter instability in predictive regression models," Journal of Econometrics, Elsevier, vol. 204(1), pages 101-118.
    11. Graziano Moramarco, 2020. "Measuring Global Macroeconomic Uncertainty," Working Papers wp1148, Dipartimento Scienze Economiche, Universita' di Bologna.
    12. Boswijk, H. Peter & Cavaliere, Giuseppe & Georgiev, Iliyan & Rahbek, Anders, 2021. "Bootstrapping non-stationary stochastic volatility," Journal of Econometrics, Elsevier, vol. 224(1), pages 161-180.
    13. Shuping Shi & Peter C. B. Phillips & Stan Hurn, 2018. "Change Detection and the Causal Impact of the Yield Curve," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(6), pages 966-987, November.
    14. Motegi, Kaiji & Iitsuka, Yoshitaka, 2023. "Inter-regional dependence of J-REIT stock prices: A heteroscedasticity-robust time series approach," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    15. Demetrescu, Matei & Georgiev, Iliyan & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2022. "Testing for episodic predictability in stock returns," Journal of Econometrics, Elsevier, vol. 227(1), pages 85-113.
    16. Canepa Alessandra, 2022. "Small Sample Adjustment for Hypotheses Testing on Cointegrating Vectors," Journal of Time Series Econometrics, De Gruyter, vol. 14(1), pages 51-85, January.
    17. Takamitsu Kurita & Bent Nielsen, 2019. "Partial Cointegrated Vector Autoregressive Models with Structural Breaks in Deterministic Terms," Econometrics, MDPI, vol. 7(4), pages 1-35, October.
    18. Lukasz Gatarek & Soeren Johansen, 2017. "The role of cointegration for optimal hedging with heteroscedastic error term," Discussion Papers 17-03, University of Copenhagen. Department of Economics.
    19. Kemal Çag̃lar Gög̃ebakan & Burak Alparslan Eroglu, 2022. "Non-parametric seasonal unit root tests under periodic non-stationary volatility," Computational Statistics, Springer, vol. 37(5), pages 2581-2636, November.
    20. Takamitsu Kurita & B. Nielsen, 2018. "Partial cointegrated vector autoregressive models with structural breaks in deterministic terms," Economics Papers 2018-W03, Economics Group, Nuffield College, University of Oxford.

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    More about this item

    Keywords

    Co-integration; adjustment coefficients; (un)conditional heteroskedasticity; heteroskedasticity-robust inference; wild bootstrap;
    All these keywords.

    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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