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

After fitting an ARMA model, an analyst finds that the Ljung-Box test on the residuals has a p-value of 0.01. What is the proper conclusion?

The residuals still show autocorrelation, so the model is inadequate. The Ljung-Box null is that residuals are white noise, and a p-value of 0.01 rejects it. The analyst should respecify the model, for example by adding AR or MA terms.

  1. AThe residuals appear to be white noise, so the model is adequate
  2. BThe residuals show remaining autocorrelation, so the model is misspecified and should be revisedCorrect
  3. CThe series is nonstationary and must be differenced
  4. DThe model is overfitted and parameters should be removed

Explanation

The Ljung-Box null hypothesis is that residual autocorrelations are jointly zero. A p-value of 0.01 rejects the null at usual levels, indicating remaining serial dependence and an inadequate model. It does not directly diagnose nonstationarity.

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