Answer-first summary for fast verification
Answer: The unconditional coverage property restricts the number of observed exceptions at a determined significance level, which corresponds to a standard uniformly distributed PIT series., The independence property requires that each observed exception is informative of future exceptions, which corresponds to an iid standard uniformly distributed PIT series.
## Explanation For PIT-based backtesting: **Unconditional Coverage Property**: This property tests whether the number of exceptions (losses exceeding VaR) is consistent with the VaR confidence level. For example, for a 99% VaR, we expect about 1% exceptions. This corresponds to a **standard uniformly distributed PIT series** (Option B is correct). **Independence Property**: This property tests whether exceptions are independent over time (no clustering). This corresponds to an **iid standard uniformly distributed PIT series** (Option C is correct). **Key Points**: - PIT values should follow a uniform distribution U(0,1) if the model is correct - Unconditional coverage tests the marginal distribution (uniformity) - Independence tests the serial independence (iid property) - Options A and D are incorrect because PIT values follow uniform distribution, not normal distribution The correct statements are B and C.
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Any backtesting of a VaR model could be reduced to the problem of determining whether the sequence of exceptions satisfies two properties, namely the unconditional coverage property and the independence property. Which of the following statements correctly links these two properties to the backtesting based on probability integral transform (PIT)?
A
The unconditional coverage property requires the consistency between the number of observed exceptions and the VaR confidence level, which corresponds to a standard normally distributed PIT series.
B
The unconditional coverage property restricts the number of observed exceptions at a determined significance level, which corresponds to a standard uniformly distributed PIT series.
C
The independence property requires that each observed exception is informative of future exceptions, which corresponds to an iid standard uniformly distributed PIT series.
D
The independence property requires that the observed exceptions should be independent from one another, which corresponds to an iid standard normally distributed PIT series.