The yearly trend analysis of the data for the food balance sheet through the empirical bayes smoothing method combined with the polynomial regression model

The yearly trend of data sets for the food Balance Sheet (1967-1997) are analyzed through a newly developed smoothing method. Several attractive findings are obtained, which makes out under standings of trends of the supply and the demand of selected and deeper. A reason why we attempt to extend the existing smoothing method is in the notable characteristics of the data sets in the present study. The behavior of the present data is characterized by their large systematic variations in contrast with their small irregular variations. As a result, the existing smoothing method is likely to provide us with an unexpectedly non-smoothed curve. In the new method, the polynomial regression curves are fitted first, followed by the associated empirical Bayes smoothing method. Here we note that the empirical Bayes smoothing method in terms of the prior distribution based on the k-th order difference matrix is associated with the polynomial regression curve of degree k-1. The model selection between the estimated polyn omial regression curve and the associated smoothing curve is based on the marginal likelihood ratio statistic. When the polynomial regression model is rejected, the associated smoothed curve is employed as the trend curve. The method was applied to the yearly trend analysis; specifically the supply and demand of rice, soybean and beef in Japan. The domestic production of rice was confirmed to show the linear decrease. A quadratic curve was chosen as the trend curve of the consumption amounts per capita of rice. This curve suggests that the consumption amounts per capita of rice traced the steady depression of decrease, and that the estimated year when it will reach the bottom level was 1999. The yearly trend of domestic production of soybean was fitted by the smoothed curve based on the 3rd order difference matrix