Author George Athanasopoulos and Don Weatherburn
Published November 2018
Report Type Crime and Justice Bulletin No. 219
Subject Prisons and prisoners; Statistical methods and modelling
Keywords Prison population, forecasting accuracy, ARIMA, exponential smoothing, absolute percentage error

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The aim of this report is to generate point and interval forecasts for the monthly average male and female prison population in NSW.


Separate ARIMA and Exponential Smoothing (ETS) models were fitted to data on the daily average number of male and female prisoners held in NSW correctional centres between July 1997 and April 2018. Model residuals were examined to check model adequacy. Comparative model evaluation began with a minimum training window of 36 months. The training window was then expanded one observation at a time until the end of the sample. Models were re-identified and re-estimated with each step and forecasts were generated and evaluated against actual observations using absolute percentage errors (APEs) and forecast interval coverage was calculated.


Over the short-term, both classes of models returned fairly accurate forecasts for both male and female prisoners. For the male series the accuracy of the models varied from 0.51% to 2.86% for the mean APE across the 1 to 12-steps ahead forecast horizons. The forecasts for the females were slightly less accurate, varying from 1.67% to 6.31%. Over the longer term the forecasts from the two models began to diverge.


For both the male and female series it seems that ARIMA forecasts are slightly more accurate and are probably preferable to those generated by ETS models.

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