title: Dispersion of the test statistic of round-trip criteria Foster—Stuart
metadata.name: dc.contributor.author
metadata.value: Chepurko, Valery A.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2016-08-01T11:47:18Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2016-08-01T11:47:18Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-06
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/2462
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The criterion Foster—Stuart in the analysis of time series to determine trends is often used. The criterion
  is based on the calculation of the lower and upper time series records x1, . . . ,xn. Unlike other tests of
  randomness, tests based on records are not invariant under a reversal of the direction of the time variable.
  To construct invariant round-trip tests is necessary to count the records in both forward and backward
  time variable. Thus far the construction of such test was impossible. When the null hypothesis is true the
  variances of test statistics were not known. Foster—Stewart round-trip criteria D and S dispersion statistics
  has been found in this article. This criteria was designed for x1, . . . ,xn time series mean and dispersion
  positive and negative trend receiving. Assuming H0 randomness null-hypothesis criteria variances statistics
  S and D was found. Asymptotic approximations was obtained for dispersions. This is possible to construct
  an invariant test for two-sided alternatives. Foster—Stewart round-trip criteria application example is
  reviewed. Refs 8. Tables 3.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: time series
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: randomness
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: trend
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: lower record
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: upper record
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: order statistics
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: beta function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Euler’s constant
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the amendment continuity
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Dispersion of the test statistic of round-trip criteria Foster—Stuart
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: Чепурко.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/2462/1/%d0%a7%d0%b5%d0%bf%d1%83%d1%80%d0%ba%d0%be.pdf
resources.format: Adobe PDF
resources.size: 263,78 kB