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IAI Actuarial Core Principles · Risk Modelling and Survival Analysis · Core concepts of time series models

An actuary fits an ARIMA(1,1,0) model to monthly claim counts. Which statement about the model is correct?

In an ARIMA(1,1,0) model, the series is differenced once and the differenced series follows a stationary AR(1) process. The original series is therefore non-stationary, and the model has no moving average terms and no seasonal differencing.

  1. AThe series itself must be stationary for the model to be valid
  2. BThe first differenced series is modelled as a stationary AR(1) processCorrect
  3. CThe second differenced series is modelled as white noise
  4. DThe model contains one moving average term
  5. The model requires seasonal differencing at lag 12

Explanation

In ARIMA(p,d,q), d is the number of differences needed for stationarity. With (1,1,0), the series is differenced once and the differenced series is a stationary AR(1) with no moving average terms. The original series is non-stationary, and no seasonal differencing is implied.

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