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Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets

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  • Cavaliere, Giuseppe
  • Nielsen, Morten Ørregaard
  • Taylor, A.M. Robert
Abstract
Empirical evidence from time series methods which assume the usual I(0)/I(1) paradigm suggests that the efficient market hypothesis, stating that spot and futures prices of a commodity should co-integrate with a unit slope on futures prices, does not hold. However, these statistical methods are known to be unreliable if the data are fractionally integrated. Moreover, spot and futures price data tend to display clear patterns of time-varying volatility which also has the potential to invalidate the use of these methods. Using new tests constructed within a more general heteroskedastic fractionally integrated model we are able to find a body of evidence in support of the efficient market hypothesis for a number of commodities. Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series. These tests are designed to be robust to both conditional and unconditional heteroskedasticity of a quite general and unknown form in the shocks. We show that the asymptotic tests do not admit pivotal asymptotic null distributions in the presence of heteroskedasticity, but that the corresponding tests based on the wild bootstrap principle do. A Monte Carlo simulation study demonstrates that very significant improvements in finite sample behaviour can be obtained by the bootstrap vis-à-vis the corresponding asymptotic tests in both heteroskedastic and homoskedastic environments.

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  • Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
  • Handle: RePEc:eee:econom:v:187:y:2015:i:2:p:557-579
    DOI: 10.1016/j.jeconom.2015.02.039
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    Cited by:

    1. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2017. "Quasi-maximum likelihood estimation and bootstrap inference in fractional time series models with heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 198(1), pages 165-188.
    2. Gil-Alana, Luis A. & Mudida, Robert & Yaya, OlaOluwa S & Osuolale, Kazeem & Ogbonna, Ephraim A, 2019. "Influence of US Presidential Terms on S&P500 Index Using a Time Series Analysis Approach," MPRA Paper 93941, University Library of Munich, Germany.
    3. Javier Hualde & Morten {O}rregaard Nielsen, 2022. "Fractional integration and cointegration," Papers 2211.10235, arXiv.org.
    4. Dony Abdul Chalid & Rangga Handika, 2022. "Comovement and contagion in commodity markets," Cogent Economics & Finance, Taylor & Francis Journals, vol. 10(1), pages 2064079-206, December.
    5. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    6. Chang, Chia-Lin & McAleer, Michael, 2015. "Econometric analysis of financial derivatives: An overview," Journal of Econometrics, Elsevier, vol. 187(2), pages 403-407.
    7. Javier Hualde & Morten Ørregaard Nielsen, 2022. "Truncated sum-of-squares estimation of fractional time series models with generalized power law trend," CREATES Research Papers 2022-07, Department of Economics and Business Economics, Aarhus University.
    8. Chang, C-L. & McAleer, M.J., 2014. "Econometric Analysis of Financial Derivatives," Econometric Institute Research Papers EI 2015-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. Demetrescu, Matei & Sibbertsen, Philipp, 2016. "Inference on the long-memory properties of time series with non-stationary volatility," Economics Letters, Elsevier, vol. 144(C), pages 80-84.
    10. Luis A. Gil‐Alana & Robert Mudida & OlaOluwa S. Yaya & Kazeem A. Osuolale & Ahamuefula E. Ogbonna, 2021. "Mapping US presidential terms with S&P500 index: Time series analysis approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 1938-1954, April.
    11. Arteche, Josu, 2024. "Bootstrapping long memory time series: Application in low frequency estimators," Econometrics and Statistics, Elsevier, vol. 29(C), pages 1-15.

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    More about this item

    Keywords

    Bootstrap; Efficient market hypothesis; Fractional integration; Score tests; Spot and futures commodity prices; Time-varying volatility;
    All these keywords.

    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
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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