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Definitions And Representations Of Multivariate Long-Range Dependent Time Series

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  • Stefanos Kechagias
  • Vladas Pipiras

Abstract

type="main" xml:id="jtsa12086-abs-0001"> The notion of multivariate long-range dependence is reexamined here from the perspectives of time and spectral domains. The role of the so-called phase parameters is clarified and stressed throughout. In particular, examples of causal (one-sided) representations of multivariate long-range dependent time series with general-phase parameters are constructed. A multivariate extension of the autoregressive fractionally integrated moving-average series is introduced with explicit formulas for its autocovariance function.

Suggested Citation

  • Stefanos Kechagias & Vladas Pipiras, 2015. "Definitions And Representations Of Multivariate Long-Range Dependent Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 1-25, January.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:1:p:1-25
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    File URL: http://hdl.handle.net/10.1111/jtsa.12086
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    References listed on IDEAS

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    Cited by:

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    3. Robinson Kruse & Christian Leschinski & Michael Will, 2016. "Comparing Predictive Accuracy under Long Memory - With an Application to Volatility Forecasting," CREATES Research Papers 2016-17, Department of Economics and Business Economics, Aarhus University.
    4. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    5. Düker, Marie-Christine, 2020. "Limit theorems in the context of multivariate long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 130(9), pages 5394-5425.
    6. Sibbertsen, Philipp & Wenger, Kai & Wingert, Simon, 2020. "Testing for Multiple Structural Breaks in Multivariate Long Memory Time Series," Hannover Economic Papers (HEP) dp-676, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    7. Shelton Peiris & Richard Hunt, 2023. "Revisiting the Autocorrelation of Long Memory Time Series Models," Mathematics, MDPI, vol. 11(4), pages 1-8, February.
    8. Stefanos Kechagias & Vladas Pipiras, 2020. "Modeling bivariate long‐range dependence with general phase," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(2), pages 268-292, March.
    9. Gannaz, Irène, 2023. "Asymptotic normality of wavelet covariances and multivariate wavelet Whittle estimators," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 485-534.
    10. Sophie Achard & Irène Gannaz, 2016. "Multivariate Wavelet Whittle Estimation in Long-range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 476-512, July.
    11. Didier, Gustavo & Meerschaert, Mark M. & Pipiras, Vladas, 2018. "Domain and range symmetries of operator fractional Brownian fields," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 39-78.

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