Journal of Statistics Applications & Probability

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The paper illustrates a simple methodology to predict total fertility rate of India through an approximate Bayes analysis using a particular case of general autoregressive integrated moving average model. The corresponding results based on classical paradigm are also obtained especially using maximum likelihood estimators. The study first examines the data for its stationarity and the same is achieved by differencing the data twice. Once the stationarity is achieved, some specific cases of general autoregressive integrated moving average model are examined for the given time series data to find the most appropriate candidate. This is being done using Akaike’s information criterion and Bayes information criterion. The selected specific case of the model is analyzed both in Bayesian and classical frameworks, the former using vague prior for the parameters. The posterior computation in Bayesian paradigm is done using Markov chain Monte Carlo simulation. The two paradigms ultimately focus on drawing relevant inferences including the short term predictions, both retrospectively and prospectively. The results are, in general, found to be satisfactory.

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