Bayesian Forecasting for Time Series of Count Data

Abstract

Time series of count data is not a widely studied research topic. This paper develops Bayesian forecasting method of counts whose conditional distributions given past observations and explanatory variables follow a Poisson distribution. To determine a forecasted value of an observation-driven integer valued autoregressive model, a series of well thought alghoritm needs to be developed, resulting in the use of Bayesian framework. This effective alghoritm sets is then used for the aforementioned calculation for the modelling of time series count data. To get the demanded results, a particle MCMC algorithm for the autoregressive Poisson regression model is introduced in the equation. Two real-life data sets, monthly demand for medicines type X and type Y (2016–2018) are successfully be analysed. We also illustrate that the Bayesian forecasting is more accurate than the corresponding frequentist’s approach.