Skip to content

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

Using the Berkowitz approach, an analyst fits z_t = μ + ρ z_(t-1) + σ ε_t to transformed PIT values and gets a log-likelihood of -310.0 for the unrestricted model. The log-likelihood under the null (μ = 0, ρ = 0, σ = 1) is -316.5. The 5% critical value of the chi-square distribution with 3 degrees of freedom is 7.81. What is the LR statistic and conclusion?

The LR statistic is 13.0, calculated as 2 times the log-likelihood difference of 6.5. This exceeds the 5% chi-square critical value of 7.81 with three degrees of freedom, so the null of a correctly specified model is rejected.

  1. ALR = 6.5; fail to reject the model at 5%
  2. BLR = 13.0; reject the model at 5%Correct
  3. CLR = 13.0; fail to reject the model at 5%
  4. DLR = 6.5; reject the model at 5%

Explanation

LR = -2(LL_null - LL_unrestricted) = -2(-316.5 + 310.0) = 13.0. Three restrictions imply 3 degrees of freedom, with a critical value of 7.81. Since 13.0 > 7.81 the null is rejected. The value 6.5 comes from forgetting the factor of 2, and would not reject.

Did you get it right without looking?

One question tells you little. A timed set on Beyond Exceedance-Based Backtesting of Value-at-Risk Models shows your real accuracy, how long you take and where you lose marks.

Practise Beyond Exceedance-Based Backtesting of Value-at-Risk ModelsFree diagnostic mock

More Beyond Exceedance-Based Backtesting of Value-at-Risk Models questions