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Quantile regression for long memory testing: A case of realized volatility

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  • Paulo M.M. Rodrigues
  • Uwe Hassler

Abstract

In this paper we derive a quantile regression approach to formally test for long memory in time series. We propose both individual and joint quantile tests which are useful to determine the order of integration along the different percentiles of the conditional distribution and, therefore, allow to address more robustly the overall hypothesis of fractional integration. The null distributions of these tests obey standard laws (e.g., standard normal) and are free of nuisance parameters. The finite sample validity of the approach is established through Monte Carlo simulations, showing, for instance, large power gains over several alternative procedures under non-Gaussian errors. An empirical application of the testing procedure on different measures of daily realized volatility is presented. Our analysis reveals several interesting features, but the main finding is that the suitability of a long-memory model with a constant order of integration around 0.4 cannot be rejected along the different percentiles of the distribution, which provides strong support to the existence of long memory in realized volatility from a completely new perspective.

Suggested Citation

  • Paulo M.M. Rodrigues & Uwe Hassler, 2012. "Quantile regression for long memory testing: A case of realized volatility," Working Papers w201207, Banco de Portugal, Economics and Research Department.
    • Handle: RePEc:ptu:wpaper:w201207
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    Cited by:

    1. Belbute, José M. & Pereira, Alfredo M., 2022. "ARFIMA Reference Forecasts for Worldwide CO2 Emissions and the National Dimension of the Policy Efforts to Meet IPCC Targets," Journal of Economic Development, The Economic Research Institute, Chung-Ang University, vol. 47(1), pages 1-27, March.
    2. Paulo M.M. Rodrigues & Matei Demetrescu, 2018. "Testing the fractionally integrated hypothesis using M estimation: With an application to stock market volatility," Working Papers w201817, Banco de Portugal, Economics and Research Department.
    3. Hassler, Uwe & Rodrigues, Paulo M.M. & Rubia, Antonio, 2014. "Persistence in the banking industry: Fractional integration and breaks in memory," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 95-112.
    4. José Manuel Belbute & Alfredo Marvão Pereira, 2016. "Does final energy demand in Portugal exhibit long memory? A fractional integration analysis," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 15(2), pages 59-77, August.
    5. 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.
    6. González-Rivera, Gloria & Veiga, Helena, 2016. "A Bootstrap Approach for Generalized Autocontour Testing," DES - Working Papers. Statistics and Econometrics. WS 23457, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Yalama, Abdullah & Celik, Sibel, 2013. "Real or spurious long memory characteristics of volatility: Empirical evidence from an emerging market," Economic Modelling, Elsevier, vol. 30(C), pages 67-72.
    8. Belbute, José M. & Pereira, Alfredo M., 2020. "Reference forecasts for CO2 emissions from fossil-fuel combustion and cement production in Portugal," Energy Policy, Elsevier, vol. 144(C).
    9. Hiroyuki Kawakatsu, 2021. "Information in daily data volatility measurements," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 1642-1656, April.
    10. Jorge M. L. Andraz & Raúl F. C. Guerreiro & Paulo M. M. Rodrigues, 2018. "Persistence of travel and leisure sector equity indices," Empirical Economics, Springer, vol. 54(4), pages 1801-1825, June.
    11. Luca Barbaglia & Christophe Croux & Ines Wilms, 2017. "Volatility spillovers and heavy tails: a large t-Vector AutoRegressive approach," Working Papers of Department of Decision Sciences and Information Management, Leuven 590528, KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven.
    12. Barbaglia, Luca & Croux, Christophe & Wilms, Ines, 2020. "Volatility spillovers in commodity markets: A large t-vector autoregressive approach," Energy Economics, Elsevier, vol. 85(C).

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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