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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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    1. Marinucci, D & Robinson, Peter M., 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
    2. Morten Ørregaard Nielsen & Per Frederiksen, 2011. "Fully modified narrow‐band least squares estimation of weak fractional cointegration," Econometrics Journal, Royal Economic Society, vol. 14, pages 77-120, February.
    3. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    4. Nielsen, Morten Orregaard, 2007. "Local Whittle Analysis of Stationary Fractional Cointegration and the ImpliedRealized Volatility Relation," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 427-446, October.
    5. Lobato, Ignacio N., 1999. "A semiparametric two-step estimator in a multivariate long memory model," Journal of Econometrics, Elsevier, vol. 90(1), pages 129-153, May.
    6. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
    7. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    8. Shimotsu, Katsumi, 2007. "Gaussian semiparametric estimation of multivariate fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 137(2), pages 277-310, April.
    9. Chen, Willa W. & Hurvich, Clifford M., 2003. "Semiparametric Estimation of Multivariate Fractional Cointegration," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 629-642, January.
    10. Frank S. Nielsen, 2011. "Local Whittle estimation of multi‐variate fractionally integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(3), pages 317-335, May.
    11. Ørregaard Nielsen, Morten, 2004. "Local empirical spectral measure of multivariate processes with long range dependence," Stochastic Processes and their Applications, Elsevier, vol. 109(1), pages 145-166, January.
    12. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
    13. Carlos Velasco, 2003. "Gaussian Semi‐parametric Estimation of Fractional Cointegration," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(3), pages 345-378, May.
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    Cited by:

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    2. Kruse, Robinson & Leschinski, Christian & Will, Michael, 2016. "Comparing Predictive Accuracy under Long Memory - With an Application to Volatility Forecasting," Hannover Economic Papers (HEP) dp-571, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    3. Sibbertsen, Philipp & Leschinski, Christian & Busch, Marie, 2018. "A multivariate test against spurious long memory," Journal of Econometrics, Elsevier, vol. 203(1), pages 33-49.
    4. 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.
    5. 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.
    6. 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.
    7. Voges, Michelle & Sibbertsen, Philipp, 2021. "Cyclical fractional cointegration," Econometrics and Statistics, Elsevier, vol. 19(C), pages 114-129.
    8. 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.
    9. 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.
    10. Shelton Peiris & Richard Hunt, 2023. "Revisiting the Autocorrelation of Long Memory Time Series Models," Mathematics, MDPI, vol. 11(4), pages 1-8, February.
    11. 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.

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