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The most used time series model is the time series model which assumes the variables being tested are continuous in a discrete time period and produces continuous values. Whereas in many applications, such as number of monthly accidents, number of doctor visits per year a person makes, etc., needed a discrete time series model to handle discrete variables and produce discrete values as well. Time series model that handles count or non-negative integer data is the Integer-valued Autoregressive model with the pth-order or INAR(p). INAR(p) is the counterpart of AR(p) model for integer data. To get integer results, this model uses binomial thinning operator which implements probabilistic operations with discrete distribution that are suitable to model count data such as Poisson and Binomial, also use median forecasting method. Model parameters will be estimated using the Yule-Walker method. In this research, INAR(p) time series model will be applied to number of prisoners in Nganjuk from April 2013 until July 2016 to help tackle overcapacity problems in prisons that led to many negative impacts. Through model specification, the best model for forecast the case is INAR(2). In this data, based on the measure of AIC, BIC, and AICc, the INAR(2) model achieved better performance than its AR(2) counterpart.

Forecasting the Number of Prisoners in Nganjuk With Integer-Valued Pth-Order Autoregressive (INAR(P))