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FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models

A validator runs a Berkowitz test and rejects the null. Estimated parameters show mu close to 0 and sigma^2 close to 1, but rho is estimated at 0.35 and is statistically significant. What is the most appropriate interpretation?

A significant rho means the transformed PIT series is serially correlated, violating the independence expected of a correct model. This typically signals that the VaR model fails to capture volatility clustering or persistence, even though its average level and variance look right.

  1. AThe model's forecasts are biased in the mean but have the correct volatility
  2. BThe model overstates volatility but captures dependence correctly
  3. CThe transformed series shows serial dependence, indicating the model does not capture clustering or persistence in riskCorrect
  4. DThe PIT values are uniform, so the rejection is a false positive

Explanation

Rho measures first-order autocorrelation of the normal-transformed PIT series. A significant positive rho means forecast errors are not independent, as when the model fails to adapt to volatility clustering. Mean and variance appear correct since mu is near 0 and sigma^2 near 1.

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