Monitoring multivariate variance changes

Pape, Katharina; Wied, Dominik; Galeano, Pedro

doi:10.1016/j.jempfin.2016.08.007

Cited by 17 publications

(20 citation statements)

References 31 publications

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“…Below, we consider three on-line CP approaches, based on the general assumptions for the underlying process: i) a non-parametric approach based on [48], denoted by NP; ii) a linear time series (ARMA) approach as in [49], denoted by L; and, iii) a nonlinear time series (GARCH) approach like in [50], denoted by NL. The quantities {TS on , b, cv on , g} will be indexed accordingly.…”

Section: On-line Methodsmentioning

confidence: 99%

Real-Time Algorithms for the Detection of Changes in the Variance of Video Content Popularity

2020

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As video content is responsible for more than 70% of the global IP traffic, related resource allocation approaches, e.g., using content caching, become increasingly important. In this context, to avoid under-provisioning, it is important to rapidly detect and respond to changes in content popularity dynamics, including volatility, i.e., changes in the second order moment of the underlying process. In this paper, we focus on the early identification of changes in the variance of video content popularity, which we address as a statistical change point (CP) detection problem. Unlike changes in the mean that can be well captured by non-parametric statistical approaches, to address this more demanding problem, we construct a hypothesis test that uses in the test statistic both parametric and non-parametric approaches. In the context of parametric models, we consider linear, in the form of autoregressive moving average (ARMA), and, nonlinear, in the form of generalized autoregressive conditional heteroskedasticity (GARCH) processes. We propose an integrated algorithm that combines off-line and on-line CP schemes, with the off-line scheme used as a training (learning) phase. The algorithm is first assessed over synthetic data; our analysis demonstrates that non parametric and GARCH model based approaches can better generalize and are better suited for content views time series with unknown statistics. Finally, the non-parametric and the GARCH based variations of our proposed integrated algorithm are applied on real YouTube video content views time series, to illustrate the performance of the proposed approach of volatility change detection. INDEX TERMS Content popularity dynamics detection, change point analysis, variance change detection, volatility detection.

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Section: On-line Methodsmentioning

confidence: 99%

Real-Time Algorithms for the Detection of Changes in the Variance of Video Content Popularity

2020

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“…Even if the statistical problems of closed-and open-end scenarios are naturally related, the reader should note, that the mathematical/technical access to both problem is completely different. 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).…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

“…Berkes et al (2004) designed a detector for changes in the coefficient in the parameters of a GARCH-process. Horváth et al (2004), Aue et al (2006Aue et al ( , 2009bAue et al ( , 2014, and Fremdt (2015) developed methodology for detecting changes in the coefficients of a linear model, while Wied and Galeano (2013) and Pape et al (2016) considered sequential monitoring schemes for changes in special functionals such as the correlation or variance. 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.…”

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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“…The ability to detect parameter changes is distinctly higher for changes located at the begin of the monitoring period than for later ones which is a typical property of sequential monitoring schemes, see e.g. Wied and Galeano (2013) or Pape et al (2016).…”

Section: Changes In the Variance Parametersmentioning

confidence: 99%

“…While other articles often consider either variances or correlations, see, for instance, Wied and Galeano (2013) and Pape et al (2016), among others, this paper aims at monitoring structural changes in both volatilities and correlations jointly. For that, we consider the well-known Dynamic Conditional Correlation (DCC) model by Engle (2002) and provide a method to monitor its parameters which steer the conditional volatilities and correlations.…”

Section: Introductionmentioning

confidence: 99%

Sequential detection of parameter changes in dynamic conditional correlation models

Pape

Galeano

Wied

2020

Appl Stoch Models Bus & Ind

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A multivariate monitoring procedure is presented to detect changes in the parameter vector of the dynamic conditional correlation model proposed by Robert Engle in 2002. The benefit of the proposed procedure is that it can be used to detect changes in both the conditional and unconditional variance as well as in the correlation structure of the model. The detector is based on quasi log likelihood scores. More precisely, standardized derivations of quasi log likelihood contributions of points in the monitoring period are evaluated at parameter estimates calculated from a historical period. The null hypothesis of a constant parameter vector is rejected if these standardized terms differ too much from those that were expected under the assumption of a constant parameter vector. Under appropriate assumptions on moments and the structure of the parameter space, limit results are derived both under null hypothesis and alternatives. In a simulation study, size and power properties of the procedure are examined in various scenarios.

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Monitoring multivariate variance changes

Cited by 17 publications

References 31 publications

Real-Time Algorithms for the Detection of Changes in the Variance of Video Content Popularity

Real-Time Algorithms for the Detection of Changes in the Variance of Video Content Popularity

A new approach for open‐end sequential change point monitoring

Sequential detection of parameter changes in dynamic conditional correlation models

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