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A Gini Autocovariance Function for Time Series Modelling

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  • Marcel Carcea
  • Robert Serfling

Abstract

type="main" xml:id="jtsa12130-abs-0001"> In stationary time series modelling, the autocovariance function (ACV) through its associated autocorrelation function provides an appealing description of the dependence structure but presupposes finite second moments. Here, we provide an alternative, the Gini ACV, which captures some key features of the usual ACV while requiring only first moments. For fitting autoregressive, moving-average and autoregressive–moving-average models under just first-order assumptions, we derive equations based on the Gini ACV instead of the usual ACV. As another application, we treat a nonlinear autoregressive (Pareto) model allowing heavy tails and obtain via the Gini ACV an explicit correlational analysis in terms of model parameters, whereas the usual ACV even when defined is not available in explicit form. Finally, we formulate a sample Gini ACV that is straightforward to evaluate.

Suggested Citation

  • Marcel Carcea & Robert Serfling, 2015. "A Gini Autocovariance Function for Time Series Modelling," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 817-838, November.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:6:p:817-838
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    File URL: http://hdl.handle.net/10.1111/jtsa.12130
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    References listed on IDEAS

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    Cited by:

    1. Xin Dang & Hailin Sang & Lauren Weatherall, 2019. "Gini covariance matrix and its affine equivariant version," Statistical Papers, Springer, vol. 60(3), pages 641-666, June.
    2. Arthur Charpentier & Ndéné Ka & Stéphane Mussard & Oumar Hamady Ndiaye, 2019. "Gini Regressions and Heteroskedasticity," Econometrics, MDPI, vol. 7(1), pages 1-16, January.
    3. Charpentier, Arthur & Mussard, Stéphane & Ouraga, Téa, 2021. "Principal component analysis: A generalized Gini approach," European Journal of Operational Research, Elsevier, vol. 294(1), pages 236-249.
    4. Charles Condevaux & Stéphane Mussard & Téa Ouraga & Guillaume Zambrano, 2020. "Generalized Gini linear and quadratic discriminant analyses," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 219-236, August.
    5. N. V. Gribkova & J. Su & R. Zitikis, 2022. "Empirical tail conditional allocation and its consistency under minimal assumptions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(4), pages 713-735, August.
    6. Anastasia Dimiski, 2020. "Factors that affect Students’ performance in Science: An application using Gini-BMA methodology in PISA 2015 dataset," Working Papers 2004, University of Guelph, Department of Economics and Finance.
    7. Amit Shelef & Edna Schechtman, 2019. "A Gini-based time series analysis and test for reversibility," Statistical Papers, Springer, vol. 60(3), pages 687-716, June.
    8. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.
    9. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.

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