Whittle-type estimation under long memory and nonstationarity

Ying Lun Cheung and Uwe Hassler

AStA Advances in Statistical Analysis, 2020, vol. 104, issue 3, No 2, 363-383

Abstract: Abstract We consider six variants of (local) Whittle estimators of the fractional order of integration d. They follow a limiting normal distribution under stationarity as well as under (a certain degree of) nonstationarity. Experimentally, we observe a lack of continuity of the objective functions of the two fully extended versions at $$d=1/2$$ d = 1 / 2 that has not been reported before. It results in a pileup of the estimates at $$d=1/2$$ d = 1 / 2 when the true value is in a neighborhood to this half point. Consequently, studentized test statistics may be heavily oversized. The other four versions suffer from size distortions, too, although of a different pattern and to a different extent.

Keywords: Fractionally integrated time series; Discontinuity; Test distortion (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10182-019-00358-0

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