Modified sequential change point procedures based on estimating functions

A Likelihood Ratio Approach to Sequential Change Point Detection for a General Class of Parameters

“…An important direction for future research is the development of a corresponding methodology for open end procedures as considered by Chu et al (1996), Horváth et al (2004) or Kirch and Weber (2018), for example. Moreover, it remains to find suitable threshold functions for the monitoring procedure based onD.…”

A new approach for open‐end sequential change point monitoring

“…For a future research project it is of interest to replace Assumption 2.3 by an FCLT for any fixed time horizon and Háyék-Réyni-inequalities, as done for instance in Kirch and Weber (2018) and Kirch and Stoehr (2019). Since these conditions are slightly weaker, it would be a benefit to establish the results at hand under those conditions.…”

“…In the closed-end case it is usually sufficient to assume the existence of functional central limit theorems (FCLTs) as the underlying time frame is compact (see for instance Aue et al, 2012;Wied and Galeano, 2013;Pape et al, 2016;Dette and Gösmann, 2019). To the best of the authors' knowledge, an FCLT is insufficient in the open-end case and one commonly assumes stronger, uniform stochastic approximations or combines an FCLT with Háyék-Réyni type inequalities (see also Section 2, Horváth et al, 2004;Aue et al, 2009aAue et al, , 2009bFremdt 2014Fremdt , 2015Kirch and Weber, 2018).…”

“…The procedure based onQ was originally proposed by Horváth et al (2004) for detecting changes in the parameters of linear models and since then reconsidered for example by Aue et al (2012), Wied and Galeano (2013), and Pape et al (2016) for the detection of changes in the CAPM-model, correlation and variances respectively. A statistic of the typeP was recently proposed by Fremdt (2015) and has been already reconsidered by Kirch and Weber (2018). In the simulation study we will restrict ourselves to the commonly used class of weight functions w defined in (2.14), where we set the involved, technical constant = 10 −10 when computing the statistics.…”

“…A MOSUM‐approach was employed by Leisch et al (2000), Horváth et al (2008), or Chen and Tian (2010) to monitor the mean and linear models respectively. Recently, Hoga (2017) used an ℓ 1 ‐norm to detect changes in the mean and variance of a multivariate time series, Kirch and Weber (2018) defined a unifying framework for detecting changes in different parameters with the help of several statistics and Otto and Breitung (2020) considered a Backward CUSUM, which monitors changes based on recursive residuals in a linear model. A helpful but not exhaustive overview of different sequential procedures can be found in Section 1, in particular Table 1, of Anatolyev and Kosenok (2018).…”