Abstract
Infant mortality rate (IMR) is a critical indicator of a nation's health and socio-economic development. It represents the number of deaths per thousand live births during the first year of life. It is widely recognized as an essential metric for assessing the overall well-being of a population, especially in the context of maternal and child health. The study attempts to analyze infant mortality rate data using one of the well-known time series models known as the auto-regressive integrated moving average (ARIMA) model. This article mainly focused on classical as well as Bayesian estimation of the parameters of the model considered. To write the likelihood of the ARIMA model, we have used the approach of Kalman filtering. A Random Walk Metropolis algorithm has been used to deal with analytically intractable posterior results from the ARIMA model. After performing the Bayesian analysis of competent ARIMA models, we have selected the most appropriate model using Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and K-fold Cross Validation. Kalman forecast has been performed for infant mortality growth rate data to attain the prospective predictions. Finally, a numerical illustration has been provided for the annual IMR growth rate data of India from 1950-2023. Among the competing models, ARIMA(5,1,0) is identified as the best-fitting model with minimum AIC, BIC, mean squared error (MSE) and some other error metrics. Forecasts based on this model predict a steady decline in IMR from 2024 to 2033. These findings underscore the utility of Bayesian ARIMA modeling in demographic forecasting and public health planning.