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On the Memory of Products of Long Range Dependent Time Series

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  • Leschinski, Christian

Abstract

This paper derives the memory of the product series $x_ty_t$, where $x_t$ and $y_t$ are stationary long memory time series of orders $d_x$ and $d_y$, respectively. Special attention is paid to the case of squared series and products of series driven by a common stochastic factor. It is found that the memory of products of series with non-zero means is determined by the maximal memory of the factor series, whereas the memory is reduced if the series are mean zero.

Suggested Citation

  • Leschinski, Christian, 2016. "On the Memory of Products of Long Range Dependent Time Series," Hannover Economic Papers (HEP) dp-569, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    • Handle: RePEc:han:dpaper:dp-569
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    References listed on IDEAS

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    1. Dittmann, Ingolf & Granger, Clive W. J., 2002. "Properties of nonlinear transformations of fractionally integrated processes," Journal of Econometrics, Elsevier, vol. 110(2), pages 113-133, October.
    2. 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.
    3. C. W. J. Granger & Jeff Hallman, 1991. "Nonlinear Transformations Of Integrated Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(3), pages 207-224, May.
    4. Robert F. Engle & Magdalena E. Sokalska, 0. "Forecasting intraday volatility in the US equity market. Multiplicative component GARCH," Journal of Financial Econometrics, Oxford University Press, vol. 10(1), pages 54-83.
    5. Eric Ghysels, 1998. "On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?," Journal of Finance, American Finance Association, vol. 53(2), pages 549-573, April.
    6. Abadir, Karim M. & Talmain, Gabriel, 2005. "Autocovariance functions of series and of their transforms," Journal of Econometrics, Elsevier, vol. 124(2), pages 227-252, February.
    7. Bollerslev, Tim & Zhang, Benjamin Y. B., 2003. "Measuring and modeling systematic risk in factor pricing models using high-frequency data," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 533-558, December.
    8. Chung, Ching-Fan, 2002. "Sample Means, Sample Autocovariances, And Linear Regression Of Stationary Multivariate Long Memory Processes," Econometric Theory, Cambridge University Press, vol. 18(1), pages 51-78, February.
    9. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-1072, November.
    10. Wecker, William E., 1978. "A note on the time series which is the product of two stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 8(2), pages 153-157, December.
    11. Phillips, Peter C.B. & Kim, Chang Sik, 2007. "Long-Run Covariance Matrices For Fractionally Integrated Processes," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1233-1247, December.
    12. Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Multiplicative Error Models," Econometrics Working Papers Archive 2011_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Apr 2011.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Long Memory; Products of Time Series; Squared Time Series; Fractional Cointegration;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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