Bayesian dynamic analysis of the relation between steel consumption and GNP in various countries

A Bayesian nonstationary regression model with a smoothness prior is introduced for inferring the dynamic relationship between steel consumption and GNP. A smoothness prior in the form of a Gaussian stochastic difference equation is imposed on the regression coefficient. The estimates of hyperparameters and the best order of the difference equation are determined by maximizing the marginal likelihood of the hyperparameters and using the minimum ABIC (Akaike Bayesian Information Criterion) procedure. The estimate of the time varying regression coefficient is obtained by maximizing the posterior density of the coefficient. The model is applied to the analysis of the dynamic dependence of steel consumption on GNP for various countries; China, Soviet Union, Japan, U.S.A., Germany, Britain, and France. By using the Bayesian nonstationary regression model with a smoothness prior, the dynamic relationship between two time series can be successfully estimated and even with a comparatively small sample a reasonable estimate can be obtained. [In Japanese.]