An Analysis of Time-Series Models for Age-Specific Mortality Rates in India

Abstract

Mortality is a continuous force of attrition, tending to reduce the population, a prime negative force in the balance of vital processes (Bhasin and Nag, 2004). Sample Registration System (SRS) serves as the only source of annual data on vital events on a full scale from 1969-70 in India. Few studies have examined the trends and patterns of mortality across time and regions in India (Preston and Bhat, 1984). The Under 5 Mortality Rates (U5MR) can be seen to decrease by more than half from 1970 to 2017 but in contrast little is known about the mortality patterns of the older children (5-9) and young adolescents (10-14), and not many studies have been done on their changing trends (Masquelier et al., 2018). Using the annual data for the 5-14 age, the trend of decline in the mortality patterns is studied from 1970 to 2013. The linear trend in the time series plot suggests analysis using time series models AR(p), MA(q), ARMA(p,q), Box- Jenkins ARIMA(p,d,q) and Random Walk with drift models to get the best fit to the trend of the data. The order of the time series models have been calculated by studying the ACF, PACF plots and the coefficients have been derived using the Yule-Walker equation matrix. An in-sample forecast of the years 2014-17 are taken. The Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE) as a measure of accuracy is used to determine the best fit model. ARIMA(3,1,1) produced lower values making it the best-fit model. Out-of-sample forecasting was done for 2018-2025. The forecast value shows that at the current trend, India would have 0.03 deaths per 1000 population in the 5-14 age group in 2025 showing that the government’s policies and health care interventions towards realization of the MDG4 goal is working positively.