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FRM Part I · FRM Exam Part I · Measuring and Monitoring Volatility

After fitting a GARCH(1,1) model, an analyst wants to check whether it adequately captures volatility clustering. Which diagnostic is most appropriate?

Test the squared standardized residuals for remaining autocorrelation, for example with a Ljung-Box test. If the GARCH model captures volatility clustering, standardized residuals should be approximately independent, so their squares should show no significant serial correlation.

  1. AApply a Ljung-Box test to the squared standardized residuals to see whether autocorrelation remainsCorrect
  2. BCompute the mean of the raw returns and test whether it is zero
  3. CCheck that the sum of alpha and beta exceeds one
  4. DTest whether the raw returns are normally distributed using their sample mean

Explanation

If the model captures clustering, standardized residuals (r/sigma) should be roughly i.i.d., so their squares should show no significant autocorrelation. A Ljung-Box test on squared standardized residuals checks this. Alpha+beta above one would imply non-stationarity, which is undesirable.

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