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

## Author

Listed:
• Shimotsu, Katsumi

## Abstract

Recently, Shimotsu and Phillips (2005, Annals of Statistics 33, 1890â€“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 $N(0,{\textstyle{1 \over 4}})$ 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 $N(0,{\textstyle{1 \over 4}})$ asymptotic distribution for $d \in (- {\textstyle{1 \over 2}},2)$ (or $d \in (- {\textstyle{1 \over 2}},{\textstyle{7 \over 4}})$ 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(2), pages 501-540, April.
• Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:501-540_10
as

File URL: https://www.cambridge.org/core/product/identifier/S0266466609100075/type/journal_article
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## References listed on IDEAS

as
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Full references (including those not matched with items on IDEAS)

### 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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