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ARIMA Diagnostic Tests

When the model fit is adequate, the model residuals should behave like white noise.

Check residual autocorrelations
  • For overall significance, and for significance at individual lags
  • Box-Pierce test, or Ljung-Box test
  • Look at the acf and pacf of model residuals

Model residuals should be iid N(0, s2)

The AR and MA terms are defined by the roots of the model polynomials.  The roots of the polynomials should pass the Unit Root test.

An AR model should be stationary.

An MA model is always stationary, but should be invertible.