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Unit and Fractional Roots at the Long Run and the Seasonal Frequencies in Macroeconomic Time Series

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  • Luis Gil-Alana

Abstract

In this article, we show that macroeconomic time series may contain unit and fractional roots at both, at zero and at zero and at the seasonal frequencies. The importance of the root at the long run or zero frequency requires in many cases to consider this root at both, separately in an independent polynomial, and also included in the seasonal one. Several Monte Carlo experiments are conducted to examine cases when the root at the zero frequency is not appropriately considered. An empirical application based on the tests of Robinson, Peter M. “Efficient Tests of Nonstationary Hypotheses,” Journal of the American Statistical Association, 89, 1994, pp. 1420–37 is also carried out at the end of the article. Copyright International Atlantic Economic Society 2005

Suggested Citation

  • Luis Gil-Alana, 2005. "Unit and Fractional Roots at the Long Run and the Seasonal Frequencies in Macroeconomic Time Series," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 11(3), pages 257-266, August.
    • Handle: RePEc:kap:iaecre:v:11:y:2005:i:3:p:257-266:10.1007/s11294-005-6624-3
    DOI: 10.1007/s11294-005-6624-3
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    References listed on IDEAS

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    1. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September.
    2. Wing‐kuen Tam & Gregory Reinsel, 1998. "Seasonal Moving‐average Unit Root Tests in the Presence of a Linear Trend," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(5), pages 609-625, September.
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    4. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    5. Dickey, David A & Pantula, Sastry G, 1987. "Determining the Ordering of Differencing in Autoregressive Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 455-461, October.
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    7. Gil-Alana, Luis A., 1999. "Testing fractional integration with monthly data," Economic Modelling, Elsevier, vol. 16(4), pages 613-629, December.
    8. William R. Parke, 1999. "What Is Fractional Integration?," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 632-638, November.
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    Keywords

    C15; C22;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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