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Generating Univariate Fractional Integration within a Large VAR(1)

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Abstract

This paper shows that a large dimensional vector autoregressive model (VAR) of finite order can generate fractional integration in the marginalized univariate series. We derive high-level assumptions under which the final equation representation of a VAR(1) leads to univariate fractional white noises and verify the validity of these assumptions for two specific models.

Suggested Citation

  • Guillaume Chevillon & Alain Hecq & Sébastien Laurent, 2018. "Generating Univariate Fractional Integration within a Large VAR(1)," AMSE Working Papers 1844, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:1844
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    Cited by:

    1. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    2. Bauwens, Luc & Chevillon, Guillaume & Laurent, Sébastien, 2023. "We modeled long memory with just one lag!," Journal of Econometrics, Elsevier, vol. 236(1).
    3. Javier Haulde & Morten Ørregaard Nielsen, 2022. "Fractional integration and cointegration," CREATES Research Papers 2022-02, Department of Economics and Business Economics, Aarhus University.
    4. Anna Mikusheva & Mikkel Sølvsten, 2025. "Linear regression with weak exogeneity," Quantitative Economics, Econometric Society, vol. 16(2), pages 367-403, May.
    5. Gianluca Cubadda & Alain Hecq & Antonio Riccardo, 2018. "Forecasting Realized Volatility Measures with Multivariate and Univariate Models: The Case of The US Banking Sector," CEIS Research Paper 445, Tor Vergata University, CEIS, revised 30 Oct 2018.
    6. Wilms, Ines & Rombouts, Jeroen & Croux, Christophe, 2021. "Multivariate volatility forecasts for stock market indices," International Journal of Forecasting, Elsevier, vol. 37(2), pages 484-499.
    7. Castro, Tomas del Barrio & Escribano, Alvaro & Sibbertsen, Philipp, 2025. "Modeling and forecasting the long memory of Cyclical Trends in paleoclimate data," Energy Economics, Elsevier, vol. 147(C).
    8. Alain Hecq & Luca Margaritella & Stephan Smeekes, 2023. "Granger Causality Testing in High-Dimensional VARs: A Post-Double-Selection Procedure," Journal of Financial Econometrics, Oxford University Press, vol. 21(3), pages 915-958.

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - 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
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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