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# Effect of dependency in systems for multivariate surveillance

## Author

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() (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

## Abstract

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.

## Suggested Citation

• Andersson, Eva, 2007. "Effect of dependency in systems for multivariate surveillance," Research Reports 2007:1, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
• Handle: RePEc:hhs:gunsru:2007_001
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File URL: http://hdl.handle.net/2077/7555

## References listed on IDEAS

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1. Lars-Erik Öller & Lasse Koskinen, 2004. "A classifying procedure for signalling turning points," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(3), pages 197-214.
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3. Eva Andersson & David Bock & Marianne Frisén, 2004. "Detection of Turning Points in Business Cycles," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2004(1), pages 93-108.
4. H. E. T. Holgersson, 2004. "Testing for Multivariate Autocorrelation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(4), pages 379-395.
5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
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## Citations

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Cited by:

1. Andersson, Eva, 2008. "Hotelling´s T2 Method in Multivariate On-line Surveillance. On the Delay of an Alarm," Research Reports 2008:3, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.

### Keywords

Multivariate; Surveillance; Dependency; Optimal; Covariance; Likelihood ratio;

### JEL classification:

• C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

### NEP fields

This paper has been announced in the following NEP Reports:

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