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

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

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File URL: http://hdl.handle.net/10.1007/s11294-005-6624-3
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Article provided by International Atlantic Economic Society in its journal International Advances in Economic Research.

Volume (Year): 11 (2005)
Issue (Month): 3 (August)
Pages: 257-266

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Handle: RePEc:kap:iaecre:v:11:y:2005:i:3:p:257-266
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  1. Francis X. Diebold & Glenn D. Rudebusch, 1988. "Long memory and persistence in aggregate output," Finance and Economics Discussion Series 7, Board of Governors of the Federal Reserve System (U.S.).
  2. Engle, R. F. & Granger, C. W. J. & Hylleberg, S. & Lee, H. S., 1993. "The Japanese consumption function," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 275-298.
  3. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
  4. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  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 455-61, October.
  6. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  7. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  8. Gil-Alana, Luis A., 1999. "Testing fractional integration with monthly data," Economic Modelling, Elsevier, vol. 16(4), pages 613-629, December.
  9. 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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