Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Detecting changes in covariance via random matrix theory
AU - Ryan, Sean
AU - Killick, Rebecca
PY - 2023/4/10
Y1 - 2023/4/10
N2 - A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying structure of the covariance matrix. We discuss how results from Random Matrix Theory, can be used to study the behaviour of our test statistic in a moderate dimensional setting (i.e. the number of variables is comparable to the length of the data). In particular, we demonstrate that the test statistic converges point wise to a normal distribution under the null hypothesis. We evaluate the performance of the proposed approach on a range of simulated datasets and find that it outperforms a range of alternative recently proposed methods. Finally, we use our approach to study changes in the amount of water on the surface of a plot of soil which feeds into model development for degradation of surface piping.
AB - A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying structure of the covariance matrix. We discuss how results from Random Matrix Theory, can be used to study the behaviour of our test statistic in a moderate dimensional setting (i.e. the number of variables is comparable to the length of the data). In particular, we demonstrate that the test statistic converges point wise to a normal distribution under the null hypothesis. We evaluate the performance of the proposed approach on a range of simulated datasets and find that it outperforms a range of alternative recently proposed methods. Finally, we use our approach to study changes in the amount of water on the surface of a plot of soil which feeds into model development for degradation of surface piping.
KW - changepoint
KW - ratio matrices
KW - eigenvalue
U2 - 10.1080/00401706.2023.2183261
DO - 10.1080/00401706.2023.2183261
M3 - Journal article
SP - 1
EP - 12
JO - Technometrics
JF - Technometrics
SN - 0040-1706
ER -