A note on the monitoring of changes in linear models with dependent errors

Schmitz, Alexander; Steinebach, Josef

doi:10.1007/978-3-642-14104-1_9

Cited by 3 publications

(3 citation statements)

References 14 publications

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“…we will include many of the commonly applied time series models for the error terms as well as for the regressors in our setting. Other contributions assuming dependencies are given by, e.g., Schmitz and Steinebach (2010) who considered strongly mixing error terms in a linear model or Hušková, Prášková and Steinebach (2007) who studied autoregressive time series in a closed-end setting.…”

Section: Introductionmentioning

confidence: 99%

Page's sequential procedure for change-point detection in time series regression

Fremdt

2014

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In a variety of different settings cumulative sum (CUSUM) procedures have been applied for the sequential detection of structural breaks in the parameters of stochastic models. Yet their performance depends strongly on the time of change and is best under early-change scenarios. For later changes their finite sample behavior is rather questionable. We therefore propose modified CUSUM procedures for the detection of abrupt changes in the regression parameter of multiple time series regression models, that show a higher stability with respect to the time of change than ordinary CUSUM procedures. The asymptotic distributions of the test statistics and the consistency of the procedures are provided. In a simulation study it is shown that the proposed procedures behave well in finite samples. Finally the procedures are applied to a set of capital asset pricing data related to the Fama-French extension of the capital asset pricing model.

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Section: Introductionmentioning

confidence: 99%

Page's sequential procedure for change-point detection in time series regression

Fremdt

2014

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“…In the sequential change point literature monitoring schemes based on the differences 3 are usually called (ordinary) CUSUM procedures and have been considered by Horváth et al (2004), Aue et al . (2006, 2009b, 2014), Schmitz and Steinebach (2010), or Hoga (2017). Other authors suggest using a function of the differences

\begin{matrix} alignleft \\ align-1 {{\hat{θ}}_{1}^{m} - {\hat{θ}}_{m + j + 1}^{m + k}}_{j = 0, \dots, k - 1} & align-2 \end{matrix}

(in dependence of k ) and the corresponding procedures are usually called Page‐CUSUM tests (see Fremdt, 2015; Aue, et al .…”

Section: Introductionmentioning

confidence: 99%

A new approach for open‐end sequential change point monitoring

Gösmann

Kley

Dette

2020

Journal Time Series Analysis

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We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the sample at each time point after the training sample. Estimators from the sample before and after all separation points are then continuously compared calculating a maximum of norms of their differences. For open-end scenarios our approach yields an asymptotic level procedure, which is consistent under the alternative of a change in the parameter. By means of a simulation study it is demonstrated that the new method outperforms the commonly used procedures with respect to power and the feasibility of our approach is illustrated by analyzing two data examples.

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“…, X j . In the sequential change point literature monitoring schemes based on the differences (1.3) are usually called (ordinary) CUSUM procedures and have been considered by Horváth et al (2004), Aue et al (2006Aue et al ( , 2009Aue et al ( , 2014, Schmitz and Steinebach (2010) or Hoga (2017). Other authors suggest using a function of the differences θm 1 − θm+k m+j+1 j=0,...,k−1 (1.4) (in dependence of k) and the corresponding procedures are usually called Page-CUSUM tests [see Fremdt (2014b), Aue et al (2015), or Kirch and Weber (2018) (1.5)…”

Section: Introductionmentioning

confidence: 99%

A new approach for open-end sequential change point monitoring

Gösmann¹,

Kley²,

Dette³

2019

Preprint

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We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the sample at each time point after the training sample. Estimators from the sample before and after all separation points are then continuously compared calculating a maximum of norms of their differences. For openend scenarios our approach yields an asymptotic level α procedure, which is consistent under the alternative of a change in the parameter.

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A note on the monitoring of changes in linear models with dependent errors

Cited by 3 publications

References 14 publications

Page's sequential procedure for change-point detection in time series regression

Page's sequential procedure for change-point detection in time series regression

A new approach for open‐end sequential change point monitoring

A new approach for open-end sequential change point monitoring

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