Coherent forecasting for stationary time series of discrete data

Abstract

Coherent forecasting for discrete-valued stationary time series is considered in this article. In the context of count time series, different methods of coherent forecasting such as median forecasting and mode forecasting are used to obtain \(h\)-step ahead coherent forecasting. However, there are not many existing works in the context of categorical time series. Here, we consider the case of a finite number of categories with different possible models, such as the Pegram’s operator-based ARMA(\(p\),\(q\)) model, the mixture transition distribution model and the logistic regression model, and study their \(h\)-step ahead coherent forecasting. Some theoretical results are derived along with some numerical examples. To facilitate comparison among the three models, we use some forecasting measures. The procedure is illustrated using one real-life categorical data, namely the infant sleep status data.