Solved – How does R’s auto.arima() function determine the order of differencing when estimating a regression with seasonal ARIMA errors

The authors' paper about the method (Hyndman and Khandakar 2008) states that an extended an extended Canova-Hansen test is used, although the helpfile updates this to say than an OCSB test is used.

I have two questions, therefore:

  1. What is an OCSB test?
  2. Is the method of determining seasonal differencing the same for regression with ARIMA errors as it is for ARIMA modelling with no covariates?
  1. OCSB test: Osborn DR, Chui APL, Smith J, and Birchenhall CR (1988) "Seasonality and the order of integration for consumption", Oxford Bulletin of Economics and Statistics 50(4):361-377.

    The change in the algorithm is explained at

  2. When regressors are used, auto.arima() fits the linear model using lm() and applies the unit root tests to the residuals.

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