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

In the Box-Jenkins approach to fitting an ARIMA model to a time series, which sequence of stages is correct?

The correct order is to make the series stationary and identify a tentative model, estimate its parameters, check the residuals for white noise, and then forecast. Diagnostics must follow estimation, and forecasting is done only once the model is judged adequate.

  1. AEstimate parameters, identify a tentative model, check diagnostics, then difference the data
  2. BIdentify a tentative model after making the series stationary, estimate parameters, carry out diagnostic checks on the residuals, then forecastCorrect
  3. CForecast, estimate parameters, identify the model, then test the residuals
  4. DCheck the residuals, identify the model, estimate parameters, then make the series stationary
  5. Estimate parameters, forecast, then identify the model and difference the data

Explanation

Box-Jenkins begins by making the series stationary (e.g. differencing) and identifying a tentative ARIMA(p,d,q) from the ACF and PACF. Parameters are then estimated, residuals are checked for white noise, and only an adequate model is used to forecast. Options that put estimation or forecasting before identification reverse the logic.

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