Estimating the Number of Change Points in Exponential Families Distributions
A simple method is proposed to detect the number of change points in a sequence of independent exponential family random variables. An estimator to maximize some criterion, say SC(k), which is to maximize the log- likelihood function with some penalty term, is used in detection. Under some mild assumptions, the consistency of the estimator for the true number of change points and the boundedness between the estimated change locations and the true change location are obtained. Some simulated results are given, and the Nile problem is investigated by this method.
In this paper we present a macro-economic demographic growth modelhaving a special focus on social security. It is designed to study the variability of responses of the system in presence of risks and uncertainties. Here we analyze the robustness of the model towards uncertainties in parameterspecifications, introduced by ARCH-M models with the incorporation ofintervention processes. The parameters varied are labor force participationrates (one of the key sources of uncertainty in the social security policydebate), and the parameters of the production function (the key source ofuncertainty in any long-run economic analysis). The sensitivity analysisfocuses on two variables: assets of the private pension system and thebalance of the public `Pay As You Go' pension system. Special attentionis given to convergence properties of the macro-economic model.