International business cycles, financial markets and household production

This paper investigates the properties of an international real business cycle model with household production. We show that a model with disturbances to both market and household technologies reproduces the main regularities of the data and improves existing models in matching international consumption, investment and output correlations without irrealistic assumptions on the structure of international financial markets. Sensitivity analysis shows the robustness of the results to alternative specifications of the stochastic processes for the disturbances and to variations of unmeasured parameters within a reasonable range.

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of theAnalysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Modelos de tasas de interes en Chile: una revisión

Con este trabajo revisamos los Modelos de niveles de las tasas de intereses en Chile. Además de los Modelos de Nivel tradicionales por Chan, Karoly, Longstaff y Lijadoras (1992) en EE. UU, y Parisi (1998) en Chile, por el método de Probabilidad Maximun permitimos que la volatilidad condicional también incluya los procesos inesperados de la información (el modelo GARCH ) y también que la volatilidad sea la función del nivel de la tasa de intereses (modelo TVP-NIVELE) como en Brenner, Harjes y la Crona (1996). Para esto usamos producciones de mercado de bonos de reconocimiento, en cambio las producciones mensuales medias de subasta PDBC, y la ampliación del tamaño y la frecuencia de la muestra a 4 producciones semanales con términos(condiciones) diferentes a la madurez: 1 año, 5 años, 10 años y 15 años. Los resultados principales del estudio pueden ser resumidos en esto: la volatilidad de los cambios inesperados de las tarifas depende positivamente del nivel de las tarifas, sobre todo en el modelo de TVP-NIVEL. Obtenemos pruebas de reversión tacañas, tal que los incrementos en las tasas de intereses no eran independientes, contrariamente a lo obtenido por Brenner. en EE. UU. Los modelos de NIVELES no son capaces de ajustar apropiadamente la volatilidad en comparación con un modelo GARCH (1,1), y finalmente, el modelo de TVP-NIVEL no vence los resultados del modelo GARCH (1,1)

Relaxation times of non-Markovian processes

We consider a general class of non-Markovian processes defined by stochastic differential equations with Ornstein-Uhlenbeck noise. We present a general formalism to evaluate relaxation times associated with correlation functions in the steady state. This formalism is a generalization of a previous approach for Markovian processes. The theoretical results are shown to be in satisfactory agreement both with experimental data for a cubic bistable system and also with a computer simulation of the Stratonovich model. We comment on the dynamical role of the non-Markovianicity in different situations.

Dynamical properties of nonmarkovian stochastic differential equations

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an OrnsteinUhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.

Theory for correlation functions of processes driven by external colored noise

We study steady-state correlation functions of nonlinear stochastic processes driven by external colored noise. We present a methodology that provides explicit expressions of correlation functions approximating simultaneously short- and long-time regimes. The non-Markov nature is reduced to an effective Markovian formulation, and the nonlinearities are treated systematically by means of double expansions in high and low frequencies. We also derive some exact expressions for the coefficients of these expansions for arbitrary noise by means of a generalization of projection-operator techniques.

First-passage times for non-Markovian processes

First-passage time statistics for non-Markovian processes have heretofore only been developed for processes driven by dichotomous fluctuations that are themselves Markov. Herein we develop a new method applicable to Markov and non-Markovian dichotomous fluctuations and calculate analytic mean first-passage times for particular examples.

Exactly solvable phase oscillator models with syncrhonization dynamics

Populations of phase oscillators interacting globally through a general coupling function f(x) have been considered. We analyze the conditions required to ensure the existence of a Lyapunov functional giving close expressions for it in terms of a generating function. We have also proposed a family of exactly solvable models with singular couplings showing that it is possible to map the synchronization phenomenon into other physical problems. In particular, the stationary solutions of the least singular coupling considered, f(x) = sgn(x), have been found analytically in terms of elliptic functions. This last case is one of the few nontrivial models for synchronization dynamics which can be analytically solved.

First-passage-time noninteger moments for some diffusion and dichotomous processes

We calculate noninteger moments ¿tq¿ of first passage time to trapping, at both ends of an interval (0,L), for some diffusion and dichotomous processes. We find the critical behavior of ¿tq¿, as a function of q, for free processes. We also show that the addition of a potential can destroy criticality.

Coherent stochastic resonance

We consider Brownian motion on a line terminated by two trapping points. A bias term in the form of a telegraph signal is applied to this system. It is shown that the first two moments of survival time exhibit a minimum at the same resonant frequency.

Integrated random processes exhibiting long tails, finite moments, and power-law spectra

A dynamical model based on a continuous addition of colored shot noises is presented. The resulting process is colored and non-Gaussian. A general expression for the characteristic function of the process is obtained, which, after a scaling assumption, takes on a form that is the basis of the results derived in the rest of the paper. One of these is an expansion for the cumulants, which are all finite, subject to mild conditions on the functions defining the process. This is in contrast with the Lévy distribution¿which can be obtained from our model in certain limits¿which has no finite moments. The evaluation of the spectral density and the form of the probability density function in the tails of the distribution shows that the model exhibits a power-law spectrum and long tails in a natural way. A careful analysis of the characteristic function shows that it may be separated into a part representing a Lévy process together with another part representing the deviation of our model from the Lévy process. This

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Modelos de tasas de interes en Chile: una revisión

Con este trabajo revisamos los Modelos de niveles de las tasas de intereses en Chile. Además de los Modelos de Nivel tradicionales por Chan, Karoly, Longstaff y Lijadoras (1992) en EE. UU, y Parisi (1998) en Chile, por el método de Probabilidad Maximun permitimos que la volatilidad condicional también incluya los procesos inesperados de la información (el modelo GARCH ) y también que la volatilidad sea la función del nivel de la tasa de intereses (modelo TVP-NIVELE) como en Brenner, Harjes y la Crona (1996). Para esto usamos producciones de mercado de bonos de reconocimiento, en cambio las producciones mensuales medias de subasta PDBC, y la ampliación del tamaño y la frecuencia de la muestra a 4 producciones semanales con términos(condiciones) diferentes a la madurez: 1 año, 5 años, 10 años y 15 años. Los resultados principales del estudio pueden ser resumidos en esto: la volatilidad de los cambios inesperados de las tarifas depende positivamente del nivel de las tarifas, sobre todo en el modelo de TVP-NIVEL. Obtenemos pruebas de reversión tacañas, tal que los incrementos en las tasas de intereses no eran independientes, contrariamente a lo obtenido por Brenner. en EE. UU. Los modelos de NIVELES no son capaces de ajustar apropiadamente la volatilidad en comparación con un modelo GARCH (1,1), y finalmente, el modelo de TVP-NIVEL no vence los resultados del modelo GARCH (1,1)