A Bayes analysis of autoregressive model having functional-coefficients and its application on exchange rate data

The paper provides a Bayes analysis, based on free-knot spline technique, of the popular autoregressive model having functional-coefficients. The model was initially proposed by Chen and Tsay (1993). The technique of polynomial splines of different orders is used to approximate the functional-coefficients. A sample based approach using the Gibbs sampler algorithm with intermediate Metropolis steps is adopted to draw the posterior estimates for the parameters involved. Additionally, the technique of reversible jump Markov chain Monte Carlo is incorporated to update the location and number of knots in the polynomial spline. The paper then proceeds with the motive of obtaining both retrospective and prospective predictions based on the selected model. The complete procedure is illustrated by both simulated and a real dataset representing the exchange rate of Indian rupees relative to the US dollars.