Integer-valued Pth-order autoregressive model

The most commonly used time series model is the discrete time series which assumes the variables being tested are continuous and produce continuous values. Whereas in many applications, a discrete time series model is needed to handle discrete variables and produce discrete values as well. The time series model that handles count or non-negative integer data is the Integer-valued Autoregressive model with the pth-order or INAR(p). This model is built with binomial thinning operator which implements probabilistic operations with discrete distribution that are suitable to model count data such as Poisson and Binomial. Model parameters will be estimated using the Yule-Walker method. In this research, we will discuss and describe the characteristics of the INAR(p) model using the binomial thinning operator. The INAR(p) specification follows the Autoregressive model with the pth order, AR(p). Forecasting in INAR(p) uses median forecasting by calculating the conditional probability of each possible non-negative integer value, then selecting a forecast value with a cumulative conditional probability greater than 0.5. The INAR(p) time series model will be applied to the 115 simulated data with non-negative integer values.