Tests for scale changes based on pairwise differences

Carina Gerstenberger, Daniel Vogel, Martin Wendler

Research output: Working paper

Abstract

In many applications it is important to know whether the amount of fluctuation in a series of observations changes over time. In this article, we investigate different tests for detecting change in the scale of mean-stationary time series. The classical approach based on the CUSUM test applied to the squared centered, is very vulnerable to outliers and impractical for heavy-tailed data, which leads us to contemplate test statistics based on alternative, less outlier-sensitive scale estimators.
It turns out that the tests based on Gini's mean difference (the average of all pairwise distances) or generalized Qn estimators (sample quantiles of all pairwise distances) are very suitable candidates. They improve upon the classical test not only under heavy tails or in the presence of outliers, but also under normality. An explanation for this at first counterintuitive result is that the corresponding long-run variance estimates are less affected by a scale change than in the case of the sample-variance-based test.
We use recent results on the process convergence of U-statistics and U-quantiles for dependent sequences to derive the limiting distribution of the test statistics and propose estimators for the long-run variance. We perform a simulations study to investigate the finite sample behavior of the test and their power. Furthermore, we demonstrate the applicability of the new change-point detection methods at two real-life data examples from hydrology and finance.
Original languageEnglish
PublisherArXiv
Pages1-32
Number of pages32
Publication statusSubmitted - 13 Nov 2016

Fingerprint

Pairwise
Outlier
Long-run
Estimator
Test Statistic
CUSUM Test
Sample Quantiles
Change-point Detection
Sample variance
Stationary Time Series
Hydrology
Heavy Tails
U-statistics
Quantile
Limiting Distribution
Finance
Normality
Simulation Study
Fluctuations
Series

Keywords

  • Asymptotic relative efficiency
  • Change-point analysis
  • Gini’s mean difference
  • Long-run variance estimation
  • Median absolute deviation
  • Qn scale estimator
  • U-quantile
  • U-statistic

Cite this

Gerstenberger, C., Vogel, D., & Wendler, M. (2016). Tests for scale changes based on pairwise differences. (pp. 1-32). ArXiv.

Tests for scale changes based on pairwise differences. / Gerstenberger, Carina; Vogel, Daniel; Wendler, Martin.

ArXiv, 2016. p. 1-32.

Research output: Working paper

Gerstenberger, C, Vogel, D & Wendler, M 2016 'Tests for scale changes based on pairwise differences' ArXiv, pp. 1-32.
Gerstenberger C, Vogel D, Wendler M. Tests for scale changes based on pairwise differences. ArXiv. 2016 Nov 13, p. 1-32.
Gerstenberger, Carina ; Vogel, Daniel ; Wendler, Martin. / Tests for scale changes based on pairwise differences. ArXiv, 2016. pp. 1-32
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