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Schmidt SK, Wornowizki M, Fried R, Dehling H. An asymptotic test for constancy of the variance under short-range dependence. Ann Stat 2021. [DOI: 10.1214/21-aos2092] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | | | - Roland Fried
- Department of Statistics, TU Dortmund University
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Abstract
AbstractIn many situations, it is crucial to estimate the variance properly.
Ordinary variance estimators perform poorly in the presence of shifts in the mean. We investigate an approach based on non-overlapping blocks, which yields good results in change-point scenarios.
We show the strong consistency and the asymptotic normality of such blocks-estimators of the variance under independence. Weak consistency is shown for short-range dependent strictly stationary data. We provide recommendations on the appropriate choice of the block size and compare this blocks-approach with difference-based estimators. If level shifts occur frequently and are rather large, the best results can be obtained by adaptive trimming of the blocks.
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