5 resultados para MODEL-EQUATIONS


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In this thesis we implement estimating procedures in order to estimate threshold parameters for the continuous time threshold models driven by stochastic di®erential equations. The ¯rst procedure is based on the EM (expectation-maximization) algorithm applied to the threshold model built from the Brownian motion with drift process. The second procedure mimics one of the fundamental ideas in the estimation of the thresholds in time series context, that is, conditional least squares estimation. We implement this procedure not only for the threshold model built from the Brownian motion with drift process but also for more generic models as the ones built from the geometric Brownian motion or the Ornstein-Uhlenbeck process. Both procedures are implemented for simu- lated data and the least squares estimation procedure is also implemented for real data of daily prices from a set of international funds. The ¯rst fund is the PF-European Sus- tainable Equities-R fund from the Pictet Funds company and the second is the Parvest Europe Dynamic Growth fund from the BNP Paribas company. The data for both funds are daily prices from the year 2004. The last fund to be considered is the Converging Europe Bond fund from the Schroder company and the data are daily prices from the year 2005.

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33rd IAHR Congress: Water Engineering for a Sustainable Environment

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Proceedings of the Institution of Civil Engineers - Water Management 163 Issue WM6

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There is a family of models with Physical, Human capital and R&D for which convergence properties have been discussed (Arnold, 2000a; Gómez, 2005). However, spillovers in R&D have been ignored in this context. We introduce spillovers in this model and derive its steady-state and stability properties. This new feature implies that the model is characterized by a system of four differential equations. A unique Balanced Growth Path along with a two dimensional stable manifold are obtained under simple and reasonable conditions. Transition is oscillatory toward the steady-state for plausible values of parameters.

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The convergence features of an Endogenous Growth model with Physical capital, Human Capital and R&D have been studied. We add an erosion effect (supported by empirical evidence) to this model, and fully characterize its convergence properties. The dynamics is described by a fourth-order system of differential equations. We show that the model converges along a one-dimensional stable manifold and that its equilibrium is saddle-path stable. We also argue that one of the implications of considering this “erosion effect” is the increase in the adherence of the model to data.