# A convergence-speed-dependent data quantity definition and its effect on risk estimation

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## Abstract

Data quantity plays a crucial role in the estimation of risk measures since ‘more data’ lead to a better estimator convergence and consequently to a better risk assessment. The objective of this paper is to use this relationship between data quantity and estimator convergence to formally derive a measure of data quantity for estimators based on weighted observations. For the case of a variance estimation and using exponentially weighted observations, this procedure leads to analytical formulas for the implied measure of data quantity. As such, this paper specifies the theoretical underpinnings of measures of data quantity which have been present in the literature (effective number of scenarios) and, as an application, demonstrates the effect of the specific measure of data quantity on risk assessment.

## Keywords

Data Quantity EWMA Weighted estimation## Notes

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