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FRM Part I · FRM Exam Part I · Stationary Time Series

A model's residuals are uncorrelated with constant variance, but large absolute residuals tend to cluster together in time. Which statement is most accurate?

The residuals can still be weak white noise because they are uncorrelated with constant unconditional variance, but they are not independent white noise, since clustering of large absolute values shows dependence in higher moments.

  1. AThe residuals cannot be weak white noise because they are heteroskedastic
  2. BThe residuals can still be weak white noise, but they are not independent white noiseCorrect
  3. CThe residuals are independent white noise because they are uncorrelated
  4. DThe residuals are non-stationary because large values cluster

Explanation

Weak white noise requires only zero mean, constant variance and zero autocorrelation, which hold here. Clustering of absolute values signals dependence in higher moments, so the series is not independent white noise. Uncorrelated does not imply independent, and the series remains covariance stationary.

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