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Estimation and Testing in a Perturbed Multivariate Long Memory Framework

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  • Less, Vivien
  • Sibbertsen, Philipp

Abstract

We propose a semiparametric multivariate estimator and a multivariate score-type testing procedure under a perturbed multivariate fractional process. The estimator is based on the periodogram and uses a local Whittle criterion function which is generalised by an additional constant to capture the perturbation given in the long memory process. Explicitly addressing the noise term when approximating the spectral density near the origin results in a bias reduction, but at the cost of an increase in the asymptotic variance of the estimator. Further, we introduce a multivariate testing procedure to detect spurious long memory under a perturbed fractional framework. The test statistic is based on the weighted sum of the partial derivatives of the multivariate local Whittle with noise estimator. We show consistency of the test against the alternatives of smooth trend and random level shift processes. In addition, we prove consistency and asymptotic normality of the local Whittle estimator and we derive the limiting distribution of the test. An empirical example on the squared returns and the realised volatilities from the BEL 20, S&P BSE SENSEX, and the Spanish IBEX is conducted, and shows the usefulness of the procedures.

Suggested Citation

  • Less, Vivien & Sibbertsen, Philipp, 2022. "Estimation and Testing in a Perturbed Multivariate Long Memory Framework," Hannover Economic Papers (HEP) dp-704, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
  • Handle: RePEc:han:dpaper:dp-704
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    References listed on IDEAS

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    1. Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.
    2. Lu, Yang K. & Perron, Pierre, 2010. "Modeling and forecasting stock return volatility using a random level shift model," Journal of Empirical Finance, Elsevier, vol. 17(1), pages 138-156, January.
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    4. Rasmus T. Varneskov & Pierre Perron, 2018. "Combining long memory and level shifts in modelling and forecasting the volatility of asset returns," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 371-393, March.
    5. Davidson James & Rambaccussing Dooruj, 2015. "A Test of the Long Memory Hypothesis Based on Self-Similarity," Journal of Time Series Econometrics, De Gruyter, vol. 7(2), pages 115-141, July.
    6. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(4), pages 686-710, August.
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    9. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1196-1237, December.
    10. Xu, Jiawen & Perron, Pierre, 2014. "Forecasting return volatility: Level shifts with varying jump probability and mean reversion," International Journal of Forecasting, Elsevier, vol. 30(3), pages 449-463.
    11. Christian Leschinski & Michelle Voges & Philipp Sibbertsen, 2021. "A comparison of semiparametric tests for fractional cointegration," Statistical Papers, Springer, vol. 62(4), pages 1997-2030, August.
    12. Frederiksen, Per & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2012. "Local polynomial Whittle estimation of perturbed fractional processes," Journal of Econometrics, Elsevier, vol. 167(2), pages 426-447.
    13. Donald W. K. Andrews & Yixiao Sun, 2004. "Adaptive Local Polynomial Whittle Estimation of Long-range Dependence," Econometrica, Econometric Society, vol. 72(2), pages 569-614, March.
    14. Donald W. K. Andrews & Patrik Guggenberger, 2003. "A Bias--Reduced Log--Periodogram Regression Estimator for the Long--Memory Parameter," Econometrica, Econometric Society, vol. 71(2), pages 675-712, March.
    15. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    16. Niels Haldrup & Robinson Kruse, 2014. "Discriminating between fractional integration and spurious long memory," CREATES Research Papers 2014-19, Department of Economics and Business Economics, Aarhus University.
    17. Juan J. Dolado & Jesús Gonzalo & Laura Mayoral, 2005. "What is What? A Simple Time-Domain Test of Long-memory vs. Structural Breaks," Working Papers 258, Barcelona School of Economics.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Signal-plus-noise; Multivariate local Whittle; Perturbation; Spurious long memory; Semi-parametric estimation; Stochastic volatility;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: 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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