On change-points tests based on two-samples U-Statistics for weakly dependent observations

2021 ◽  
Author(s):  
Joseph Ngatchou-Wandji ◽  
Echarif Elharfaoui ◽  
Michel Harel
Keyword(s):  
Change Points ◽  
Dependent Observations ◽  
U Statistics ◽  
Two Samples ◽  
Weakly Dependent

scholarly journals A robust method for shift detection in time series

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 647-660
Author(s):  
H Dehling ◽  
R Fried ◽  
M Wendler
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Test Statistic ◽  
Moment Conditions ◽  
Limit Theory ◽  
Dependent Observations ◽  
U Statistics ◽  
Shift Detection ◽  
Heavy Tailed ◽  
The Stability

Summary We present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges–Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.

BICKEL–ROSENBLATT TEST FOR WEAKLY DEPENDENT DATA

2012 ◽  
Vol 17 (3) ◽  
pp. 383-395 ◽  
Author(s):  
Janis Valeinis ◽  
Audris Locmelis
Keyword(s):  
Goodness Of Fit ◽  
Simulation Analysis ◽  
Dependent Data ◽  
Practical Implementation ◽  
Test Statistic ◽  
Goodness Of Fit Test ◽  
Dependent Observations ◽  
Simple Hypothesis ◽  
Weakly Dependent Data ◽  
Weakly Dependent

The aim of this paper is to analyze the Bickel–Rosenblatt test for simple hypothesis in case of weakly dependent data. Although the test has nice theoretical properties, it is not clear how to implement it in practice. Choosing different band-width sequences first we analyze percentage rejections of the test statistic under H0 by some empirical simulation analysis. This can serve as an approximate rule for choosing the bandwidth in case of simple hypothesis for practical implementation of the test. In the recent paper [12] a version of Neyman goodness-of-fit test was established for weakly dependent data in the case of simple hypotheses. In this paper we also aim to compare and discuss the applicability of these tests for both independent and dependent observations.

scholarly journals Monotonic trend and change points in southern Brazil precipitation

2013 ◽  
Vol 33 (2) ◽  
pp. 258-268 ◽  
Author(s):  
Rita de C. F. Damé ◽  
Claudia F. A. Teixeira ◽  
Luiz C. S. Bacelar ◽  
Antoniony S. Winkler ◽  
Jacira P. dos Santos
Keyword(s):  
Scientific Evidence ◽  
Kendall Test ◽  
Nonparametric Tests ◽  
Change Points ◽  
Annual Precipitation ◽  
Monotonic Trend ◽  
Two Samples ◽  
Complete Series ◽  
Weather Stations ◽  
Impacts Of Climate Change

Scientific evidence on climate changes at global level has gained increasing interest in the scientific community in general. The impacts of climate change as well as anthropogenic actions may cause errors in hydro-agricultural projects existent in the watershed under study. This study aimed to identify the presence or absence of trend in total annual precipitation series of the watershed of the Mirim Lagoon, state of Rio Grande do Sul-RS / Brazil / Uruguay (Brazilian side) as well as to detect the period in which they occurred. For that, it was analyzed the precipitation data belonging to 14 weather stations. To detect the existence of monotonic trend and change points, it was used the nonparametric tests of Mann-Kendall and Mann-Whitney, the "t" test of Student for two samples of unpaired data (parametric), as well as the technique of progressive mean. The Weather Station 3152014 (Pelotas) presented changes in the trend in the series of annual precipitation in the period from 1953 to 2007. The methodologies that use subdivided series were more efficient in detecting change in trend when compared with the Mann-Kendall test, which uses the complete series (from 1921 to 2007).

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