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Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes

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  • Jentsch, Carsten
  • Paparoditis, Efstathios
  • Politis, Dimitris N.

Abstract

We develop some asymptotic theory for applications of block bootstrap resampling schemes to multivariate integrated and cointegrated time series. It is proved that a multivariate, continuous-path block bootstrap scheme applied to a full rank integrated process, succeeds in estimating consistently the distribution of the least squares estimators in both, the regression and the spurious regression case. Furthermore, it is shown that the same block resampling scheme does not succeed in estimating the distribution of the parameter estimators in the case of cointegrated time series. For this situation, a modified block resampling scheme, the so-called residual based block bootstrap, is investigated and its validity for approximating the distribution of the regression parameters is established. The performance of the proposed block bootstrap procedures is illustrated in a short simulation study.

Suggested Citation

  • Jentsch, Carsten & Paparoditis, Efstathios & Politis, Dimitris N., 2014. "Block Bootstrap Theory for Multivariate Integrated and Cointegrated Processes," Working Papers 14-18, University of Mannheim, Department of Economics.
    • Handle: RePEc:mnh:wpaper:36668
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    Cited by:

    1. Brüggemann, Ralf & Jentsch, Carsten & Trenkler, Carsten, 2016. "Inference in VARs with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 191(1), pages 69-85.
    2. Zhu, Ke & Li, Wai Keung, 2015. "A bootstrapped spectral test for adequacy in weak ARMA models," Journal of Econometrics, Elsevier, vol. 187(1), pages 113-130.
    3. Helmut Herwartz & Simone Maxand & Hannes Rohloff, 2022. "The Link between Monetary Policy, Stock Prices, and House Prices—Evidence from a Statistical Identification Approach," International Journal of Central Banking, International Journal of Central Banking, vol. 18(5), pages 1-53, December.

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    More about this item

    Keywords

    Block bootstrap ; bootstrap consistency ; spurious regression ; functional limit theorem ; continuous-path block bootstrap ; model-based block bootstrap;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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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