 Testing relevant hypotheses in functional time series via self‐normalizationHolger Dette, Kevin Kokot and Stanislav Volgushev Journal of the Royal Statistical Society Series B, 2020, vol. 82, issue 3, 629-660 Abstract: We develop methodology for testing relevant hypotheses about functional time series in a tuning‐free way. Instead of testing for exact equality, e.g. for the equality of two mean functions from two independent time series, we propose to test the null hypothesis of no relevant deviation. In the two‐sample problem this means that an L2‐distance between the two mean functions is smaller than a prespecified threshold. For such hypotheses self‐normalization, which was introduced in 2010 by Shao, and Shao and Zhang and is commonly used to avoid the estimation of nuisance parameters, is not directly applicable. We develop new self‐normalized procedures for testing relevant hypotheses in the one‐sample, two‐sample and change point problem and investigate their asymptotic properties. Finite sample properties of the tests proposed are illustrated by means of a simulation study and data examples. Our main focus is on functional time series, but extensions to other settings are also briefly discussed. Date: 2020 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:82:y:2020:i:3:p:629-660 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC. |
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