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

A risk manager computes PIT values for a 10-day-ahead VaR model using overlapping daily forecasts, then applies a standard Kolmogorov-Smirnov test of uniformity assuming independence. What is the main problem with this approach?

Overlapping multi-day forecasts share common daily returns, creating serial dependence in the PIT values even if the model is correct. This breaks the independence assumption behind the Kolmogorov-Smirnov test and distorts its rejection rates; non-overlapping observations or adjusted tests are needed.

  1. AOverlapping horizons induce serial dependence in PIT values, so the test's independence assumption is violated and size is distortedCorrect
  2. BThe PIT cannot be computed for horizons longer than one day
  3. COverlapping forecasts force PIT values to be exactly uniform, so the test never rejects
  4. DThe Kolmogorov-Smirnov test only works for normal distributions

Explanation

With overlapping multi-day horizons, consecutive realized outcomes share common daily returns, so PIT values are autocorrelated even for a correct model. The KS test assumes i.i.d. draws, so its critical values are unreliable and it may reject too often. Non-overlapping samples or adjusted tests avoid this.

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