Why is it important to evaluate the quality of a risk forecast model?

Why is it difficult to use operational criteria to evaluate risk forecast models?

Define the terms estimation window and testing window.

Describe the terms VaR violation and violation ratio.

Consider the coverage test. How does it work, what is the main advantage of the test and the main disadvantage?

Consider the independence test. How does it work? Identify two disadvantages to the test.

Identify one reason why backtesting ES is more challenging than backtesting VaR.

Both the coverage test and the independence test have asymptotically \(\chi^2\) distributed test statistics. How many are the degrees of freedom of the test statistic? How accurate do you think the asymptotic approximation is in typical applications, and how would that affect the robustness of the test?

Briefly discuss the application of backtesting to evaluating the quality of volatility forecast models.

Why is backtesting ES more challenging than backtesting VaR?