## Local Whittle estimation in nonstationary and unit root cases.(English)Zbl 1091.62084

Summary: Asymptotic properties of the local Whittle estimator in the nonstationary case $$(d>1/2)$$ are explored. For $$1/2 < d \leq 1$$, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of $$d$$. For $$d=1$$, the limit distribution is mixed normal. For $$d>1$$ and when the process has a polynomial trend of order $$a>1/2$$, the estimator is shown to be inconsistent and to converge in probability to unity.

### MSC:

 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62E20 Asymptotic distribution theory in statistics 62G20 Asymptotic properties of nonparametric inference
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### References:

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