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

After fitting an ARMA model to a return series, an analyst wants to check that the model has captured the serial dependence. Which diagnostic result would indicate an adequate fit?

An adequate fit is shown by residuals that look like white noise: insignificant autocorrelations and a Ljung-Box test that fails to reject its null of no autocorrelation. Significant residual autocorrelation means the model has left serial dependence unexplained and should be respecified.

  1. AResidual autocorrelations that are individually and jointly insignificant, as in a Ljung-Box test that fails to rejectCorrect
  2. BSignificant spikes in the residual ACF at several low lags
  3. CA Ljung-Box test on the residuals that rejects the null at the 1% level
  4. DResiduals that are highly correlated with the fitted values

Explanation

An adequate model leaves residuals resembling white noise. The Ljung-Box null is no autocorrelation, so failing to reject supports adequacy. Significant residual spikes or rejection indicate remaining dependence and a misspecified model.

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