Optimal Surveillance Based on Exponentially Weighted Moving Averages

Frisén, Marianne; Sonesson, Christian

doi:10.1080/07474940600934821

Cited by 34 publications

(32 citation statements)

References 61 publications

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“…Due to the opposite behaviour of the error spending of LR(0.2) it has the smallest PFA. Like an equal MRL 0 does apparently not imply equal PFA and vice versa, Frisén and Wessman (1999) and Frisén and Sonesson (2003) demonstrated the same difference between ARL 0 and PFA. Consequently, comparisons between methods depend on which measure that is controlled.…”

Section: Figure 1 the Density Of The Time Of Alarm P(t A =T|d) Shementioning

confidence: 93%

“…This criterion might be suitable in an industrial manufacturing process where one considers various start-up problems. An advantage is that the criterion does not require an assumption regarding the distribution of τ but Frisén (2003) and Frisén and Sonesson (2003) has questioned it as a formal criterion.…”

Section: Measures Of Evaluation and Optimality Criteriamentioning

confidence: 99%

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Evaluations of Likelihood‐Based Surveillance of Volatility

Bock

2007

Financial Surveillance

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The volatility of asset returns are important in finance. Different likelihood based methods of statistical surveillance for detecting a change in the variance are evaluated. The differences are how the partial likelihood ratios are weighted. The full likelihood ratio, Shiryaev-Roberts, Shewhart and the CUSUM methods are derived in case of an independent and identically distributed Gaussian process. The behavior of the methods is studied both when there is no change and when the change occurs at different time points. The false alarms are controlled by the median run length. Differences and limiting equalities of the methods are shown. The performances when the process parameters for which the methods are optimized for differ from the true values of the parameters are evaluated. The methods are illustrated on a period of Standard and Poor's 500 stock market index.

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Section: Figure 1 the Density Of The Time Of Alarm P(t A =T|d) Shementioning

confidence: 93%

Section: Measures Of Evaluation and Optimality Criteriamentioning

confidence: 99%

Evaluations of Likelihood‐Based Surveillance of Volatility

Bock

2007

Financial Surveillance

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“…Another function of the partial likelihood ratios is the maximum likelihood ratio component L(s,t) with respect to t. This alarm statistic is mini-max optimal, as proved by Moustakides, (1986). The EWMA method was demonstrated by Frisén, (2003) and Frisén & Sonesson, (2006) to be an approximation of the full likelihood ratio method.…”

Section: Optimalitymentioning

confidence: 99%

“…As regards the variance of the EWMA statistic there are two versions: the exact and the asymptotic variance. We will use the asymptotic variance, both for simplicity and on the basis of the arguments given in Frisén & Sonesson, (2006) concerning properties. At time s the statistic of the EWMA method for the univariate surveillance of Y is…”

Section: Methodsmentioning

confidence: 99%

Sufficient Reduction in Multivariate Surveillance

Frisén

Andersson

Schiöler

2011

Communications in Statistics - Theory and Methods

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“…CUSUM is the maximal of the likelihood ratios at the decision time s. Another surveillance method is EWMA, where all observations are weighted together. EWMA can not be exactly derived from the likelihood ratio, but for certain values of the smoothing constant, EWMA is approximately the same as LR (see Frisén and Sonesson (2002)). For the situation when it is important to detect if there has been a change at some time point since the start of the surveillance, we specify C ={τ≤s}={{τ=1}, {τ=2}, ..., {τ=s}}.…”

Section: Optimal Statistical Surveillancementioning

confidence: 99%

Effect of Dependency in Systems for Multivariate Surveillance

Andersson

2009

Communications in Statistics - Simulation and Computation

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In many situations we need a system for detecting changes early. Examples are early detection of disease outbreaks, of patients at risk and of financial instability. In influenza outbreaks, for example, we want to detect an increase in the number of cases. Important indicators might be the number of cases of influenza-like illness and pharmacy sales (e.g. aspirin). By continually monitoring these indicators, we can early detect a change in the process of interest. The methodology of statistical surveillance is used. Often, the conclusions about the process(es) of interest is improved if the surveillance is based on several indicators. Here three systems for multivariate surveillance are compared. One system, called LRpar, is based on parallel likelihood ratio methods, since the likelihood ratio has been shown to have several optimality properties. In LRpar, the marginal density of each indicator is monitored and an alarm is called as soon as one of the likelihood ratios exceeds its alarm limit. The LRpar is compared to an optimal alarm system, called LRjoint, which is derived from the full likelihood ratio for the joint density. The performances of LRpar and LRjoint are compared to a system where the Hotellings T2 is monitored. The evaluation is made using the delay of a motivated alarm, as a function of the times of the changes. The effect of dependency is investigated: both dependency between the monitored processes and correlation between the time points when the changes occur. When the first change occurs immediately, the three methods work rather similarly, for independent processes and zero correlation between the change times. But when all processes change later, the T2 has much longer delay than LRjoint and LRpar. This holds both when the processes are independent and when they have a positive covariance. When we assume a positive correlation between the change times, the LRjoint yields a shorter delay than LRpar when the changes actually do occur simultaneously, whereas the opposite is true when the changes do actually occur at different time point.

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Optimal Surveillance Based on Exponentially Weighted Moving Averages

Cited by 34 publications

References 61 publications

Evaluations of Likelihood‐Based Surveillance of Volatility

Evaluations of Likelihood‐Based Surveillance of Volatility

Sufficient Reduction in Multivariate Surveillance

Effect of Dependency in Systems for Multivariate Surveillance

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