Bayes inference for technological substitution data with data-based transformation

Abstract

Bayesian inference via Gibbs sampling is studied for forecasting technological substitutions. The Box-Cox transformation is applied to the time series AR(I) data to enhance the linear model fit. We compute Bayes point and interval estimates for each of the parameters from the Gibbs sampler. The unknown parameters are the regression coefficients, the power in the Box-Cox transformation, the serial correlation coefficient, and the variance of the disturbance terms. In addition, we forecast the future technological substitution rate and its interval. Model validation and model choice issues are also addressed. Two numerical examples with real data sets are given.