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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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