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Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend

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  • Shimotsu, Katsumi

Abstract

Recently, Shimotsu and Phillips (2005, Annals of Statistics 33, 1890–1933) 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 it has the same null asymptotic distribution for all values of d , if the optimization covers an interval of width less than 9/2 and the mean of the process is known. With the intent to provide a semiparametric estimator suitable for economic data, we extend the ELW estimator so that it accommodates an unknown mean and a polynomial time trend. We show that the two-step ELW estimator, which is based on a modified ELW objective function using a tapered local Whittle estimator in the first stage, has an null asymptotic distribution for null (or null when the data have a polynomial trend). Our simulation study illustrates that the two-step ELW estimator inherits the desirable properties of the ELW estimator.

Suggested Citation

  • Shimotsu, Katsumi, 2010. "Exact Local Whittle Estimation Of Fractional Integration With Unknown Mean And Time Trend," Econometric Theory, Cambridge University Press, vol. 26(02), pages 501-540, April.
  • Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:501-540_10
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    JEL classification:

    • 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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