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Exact Local Whittle Estimation of Fractional Integration with Unknown Mean and Time Trend

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  • Shimotsu, Katsumi
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    Recently, Shimotsu and Phillips (2002a) developed a new semiparametric estimator, the exact local Whittle (ELW) estimator, of the memory parameter d) in fractionally integrated processes. The ELW estimator has been shown to be consistent and have the same N(0, 1/4 ) limit distribution for all values of d. With economic applications in mind, we extend the ELW estimator so that it accommodates an unknown mean and a linear time trend. We show that the resulting feasible ELW estimator is consistent for d > −1/2 and has a N(0, 1/4)limit distribution for dE2 (−1/2, 2) (dE2 (−/12 , 7/4 ) when the data has a linear trend)except for a few negligible intervals. A simulation study shows that the feasible ELW estimator inherits the desirable properties of the ELW estimator even in a small sample.

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    Paper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 8844.

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    Date of creation: 2002
    Handle: RePEc:esx:essedp:8844
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    1. Diebold, Francis X & Rudebusch, Glenn D, 1991. "Is Consumption Too Smooth? Long Memory and the Deaton Paradox," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 1-9, February.
    2. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
    3. Haubrich, Joseph G, 1993. "Consumption and Fractional Differencing: Old and New Anomalies," The Review of Economics and Statistics, MIT Press, vol. 75(4), pages 767-772, November.
    4. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    5. Shimotsu, Katsumi & Phillips, Peter C B, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 8838, University of Essex, Department of Economics.
    6. Alex Maynard & Peter C. B. Phillips, 2001. "Rethinking an old empirical puzzle: econometric evidence on the forward discount anomaly," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(6), pages 671-708.
    7. Crato, Nuno & Rothman, Philip, 1994. "Fractional integration analysis of long-run behavior for US macroeconomic time series," Economics Letters, Elsevier, vol. 45(3), pages 287-291.
    8. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    9. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    10. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
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