93 resultados para Fractional-order calculus


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Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.

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A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator iseasy to compute and is consistent and asymptotically normally distributed for fractionallyintegrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

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We present a rule-based Huet’s style anti-unification algorithm for simply-typed lambda-terms in ɳ long β normal form, which computes a least general higher-order pattern generalization. For a pair of arbitrary terms of the same type, such a generalization always exists and is unique modulo α equivalence and variable renaming. The algorithm computes it in cubic time within linear space. It has been implemented and the code is freely available

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Hydrodynamical equations act as a link between the local observed magnitudes of galactic motion and the general ones accounting for the behaviour of the Galaxy as a whole. Constraints are set usually in order to use them even in the lower order hierarchy. The authors present in this paper the complete expressions up to their fourth order. These equations will be used in the next future in their general form taking into account both the expected increase of kinematic data that the astrometric mission Hipparcos will provide, and some recent results indicating the possibility to obtain estimates for the momenta gradients.

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Floods are the natural hazards that produce the highest number of casualties and material damage in the Western Mediterranean. An improvement in flood risk assessment and study of a possible increase in flooding occurrence are therefore needed. To carry out these tasks it is important to have at our disposal extensive knowledge on historical floods and to find an efficient way to manage this geographical data. In this paper we present a complete flood database spanning the 20th century for the whole of Catalonia (NE Spain), which includes documentary information (affected areas and damage) and instrumental information (meteorological and hydrological records). This geodatabase, named Inungama, has been implemented on a GIS (Geographical Information System) in order to display all the information within a given geographical scenario, as well as to carry out an analysis thereof using queries, overlays and calculus. Following a description of the type and amount of information stored in the database and the structure of the information system, the first applications of Inungama are presented. The geographical distribution of floods shows the localities which are more likely to be flooded, confirming that the most affected municipalities are the most densely populated ones in coastal areas. Regarding the existence of an increase in flooding occurrence, a temporal analysis has been carried out, showing a steady increase over the last 30 years.

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We propose an iterative procedure to minimize the sum of squares function which avoids the nonlinear nature of estimating the first order moving average parameter and provides a closed form of the estimator. The asymptotic properties of the method are discussed and the consistency of the linear least squares estimator is proved for the invertible case. We perform various Monte Carlo experiments in order to compare the sample properties of the linear least squares estimator with its nonlinear counterpart for the conditional and unconditional cases. Some examples are also discussed

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A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

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We consider systems that can be described in terms of two kinds of degree of freedom. The corresponding ordering modes may, under certain conditions, be coupled to each other. We may thus assume that the primary ordering mode gives rise to a diffusionless first-order phase transition. The change of its thermodynamic properties as a function of the secondary-ordering-mode state is then analyzed. Two specific examples are discussed. First, we study a three-state Potts model in a binary system. Using mean-field techniques, we obtain the phase diagram and different properties of the system as a function of the distribution of atoms on the different lattice sites. In the second case, the properties of a displacive structural phase transition of martensitic type in a binary alloy are studied as a function of atomic order. Because of the directional character of the martensitic-transition mechanism, we find only a very weak dependence of the entropy on atomic order. Experimental results are found to be in quite good agreement with theoretical predictions.

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We present a study of the influence of atomic order on the relative stability of the bcc and the 18R martensitic structures in a Cu2.96Al0.92Be0.12 crystal. Calorimetric measurements have shown that disorder increases the stability of the 18R phase, contrary to what happens in Cu-Zn-Al alloys for which it is the bcc phase that is stabilized by disordering the system. This different behavior has been explained in terms of a model recently reported. We have also proved that the entropy change at the martensitic transition is independent of the state of atomic order of the crystal, as predicted theoretically. Our results suggest that differences in the vibrational spectrum of the crystal due to different states of atomic order must be equal in the bcc and in the close-packed phases.

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We study the behavior of the random-bond Ising model at zero temperature by numerical simulations for a variable amount of disorder. The model is an example of systems exhibiting a fluctuationless first-order phase transition similar to some field-induced phase transitions in ferromagnetic systems and the martensitic phase transition appearing in a number of metallic alloys. We focus on the study of the hysteresis cycles appearing when the external field is swept from positive to negative values. By using a finite-size scaling hypothesis, we analyze the disorder-induced phase transition between the phase exhibiting a discontinuity in the hysteresis cycle and the phase with the continuous hysteresis cycle. Critical exponents characterizing the transition are obtained. We also analyze the size and duration distributions of the magnetization jumps (avalanches).

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We have measured the changes in the ultrasonic wave velocity, induced by the application of uniaxial stresses in a Cu-Al-Ni single crystal. From these measurements, the complete set of third-order elastic constants has been obtained. The comparison of results for Cu-Al-Ni with available data for other Cu-based alloys has shown that all these alloys exhibit similar anharmonic behavior. By using the measured elastic constants in a Landau expansion for elastic phase transitions, we have been able to give an estimation of the value of a fourth-order elastic constants combination. The experiments have also shown that the application of a stress in the [001] direction, reduces the material resistance to a (110)[110] shear and thus favors the martensitic transition.