
Explanation:
Setting the threshold relatively low in the Peaks Over Threshold (POT) approach makes the model less applicable but increases the number of observations in the modeling procedure. The Generalized Pareto Distribution (GPD) is often used in the POT approach as it is considered the natural model for excess losses. All distributions of excess losses converge to the GPD. However, the application of the GPD requires the selection of a reasonable threshold, which determines the number of observations, , exceeding the threshold value. This process involves a trade-off. On one hand, the threshold needs to be sufficiently high for the GPD to apply reasonably closely, as per the Pickands-Balkema-de Haan theorem. On the other hand, setting the threshold too high can result in an insufficient number of excess-threshold observations, leading to unreliable estimates. Therefore, setting the threshold relatively low can increase the number of observations in the modeling procedure, but it can also make the model less applicable as the GPD may not apply as closely.
Choice A is incorrect. Setting the threshold relatively low does not make the model more applicable but decreases the number of observations in the modeling procedure. In fact, a lower threshold increases the number of observations as it includes more data points that exceed this lower limit.
Choice B is incorrect. While a lower threshold may reduce applicability due to inclusion of less extreme values, it does not decrease but rather increases the number of observations in the modeling procedure because more data points will exceed this limit.
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Q.4011 In setting the threshold in the POT approach, which of the following statements is most accurate? Setting the threshold relatively low makes the model:
A
more applicable but decreases the number of observations in the modeling procedure.
B
less applicable and decreases the number of observations in the modeling procedure
C
more applicable but increases the number of observations in the modeling procedure.
D
less applicable but increases the number of observations in the modeling procedure.
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