Author Wai-Yin Wan, Steve Moffatt, Zachary Xie, Simon Corben and Don Weatherburn
Published October 2013
Report Type Crime and Justice Bulletin No. 174
Subject Bail / Remand; Prisons and prisoners; Sentencing; Statistical methods and modelling
Keywords prison population forecast, ARIMAX model, remand population, sentenced prisoner population, seasonal effects, simulation model

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To develop a method for forecasting the NSW remand and sentenced prisoner populations.


Autoregressive Integrated Moving Average (ARIMA) models with other time series as input variables were employed to estimate and forecast changes in the remand and sentenced prisoner populations. Models were tested by estimating model parameters over the period January 1998 – December 2010 and then comparing model forecasts with actual prison population trends over the period January 2011 – March 2013. Comparison of actual with forecast remand and sentenced prisoner numbers revealed that both models provide fairly reliable predictions of prison population trends over a three year time horizon.


Barring any significant change to policing and penal policy, the prison population is expected to rise in the first half of 2013 and then to drop steadily over the next three years. Although modelling suggests an uptrend in the remand prisoner population, this should be more than offset by a decrease in the sentenced prisoner population over the next thirty-three months.


Although the models developed here provide accurate forecasts in retrospective testing, they should not be used as the sole basis for projecting future prison numbers. Future projections of prisoner numbers should also be based on advice from correctional administrators, police prosecutors, legal policy analysts, and others on the likely effects of any proposed change to policing, bail or sentence policy. Construction of a simulation model may help in quantifying the effects of these changes.

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