Author Neil Donnelly and Wai-Yin Wan
Published September 2016
Report Type Crime and Justice Bulletin No. 199
Subject Prisons and prisoners; Statistical methods and modelling
Keywords prison population, forecasting accuracy, ARIMA, Holt-Winters additive; exponential smoothing, trend, seasonality, time series cross-validation

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To compare the accuracy of Autoregressive Integrated Moving Average (ARIMA) model and Holt-Winters additive exponential smoothing method for forecasting the size of the total NSW adult prison population.


NSW adult prison population data was obtained up until July 2016. A rolling origin approach was used with 20 estimation periods (of increasing length) and 20 validation periods (12-months length). ARIMA model and Holt-Winters additive method were applied to each rolling estimation period. Shorter term (e.g. 1 to 3 months) through longer term (e.g. 6 to 12 months) forecasts were made for the relevant 12-months validation period. These forecasts were compared with the actual monthly number of prisoners using mean absolute error (MAE), root mean square error (RMSE) and mean absolute percentage error (MAPE) to assess accuracy. The average of each accuracy measure was calculated for the one-step through 12-steps lead times across the 20 estimation and validation periods.


For shorter forecast lead times (e.g. one-step through three-steps) the ARIMA model and Holt-Winters additive method gave similar accuracy measures for MAE, RMSE and MAPE. In each case, the accuracy of the forecasts decreased as the lead time increased. ARIMA was more accurate than Holt-Winters additive at longer lead times (e.g. six-steps through 12-steps) with smaller forecasting errors.


The ARIMA model provided more accurate forecasts compared with the Holt-Winters additive method for longer periods such as six-months to 12-months.

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