The Auto Regressive Functional Bounded, a theory of the state stable of the life expectancy at birth

The aim of this paper is to develop a new theory to project the life expectancy at birth, called the Auto Regressive Functional Bounded, which is a result of the union of two theories, the Multiple Auto Regressive, that allows you to estimate the value of stability in the future and the Generatrix of Bounded Functions which constructs an increasing function that is bounded by the estimated value of stability.

The Multiple Auto Regressive is a model based on three fundamental assumptions. If these assumptions are true can be proved the life expectancy at birth ( ) when time tends to infinity converges to specific value, so, under these assumptions that specific value is an estimation of the value of the stability. In Norway, Netherlands, New Zealand, Australia and Iceland there are periods of stability in their historical series, by what the model was applied by estimating the values of stability and were compared with the observed values. The predictions and observations are almost equal.


Finally, in Japan, Switzerland and Italy both theories were applied, estimating the values of stability and constructing an increasing function that is bounded for each of these countries. With the functions was projected life expectancy at birth in these countries until the year 2050.