Percorrer por autor "Duarte, Fernando B."
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- Analysis of financial data series using fractional Fourier transform and multidimensional scalingPublication . Machado, J. A. Tenreiro; Duarte, Fernando B.; Duarte, Gonçalo MonteiroThe goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indexes during the period 2000–2009. We analyze, under a regional criterium, ten main indexes at a daily time horizon. The methods and algorithms that have been explored for the description of dynamical phenomena become an effective background in the analysis of economical data. We start by applying the classical concepts of signal analysis, fractional Fourier transform, and methods of fractional calculus. In a second phase we adopt the multidimensional scaling approach. Stock market indexes are examples of complex interacting systems for which a huge amount of data exists. Therefore, these indexes, viewed from a different perspectives, lead to new classification patterns.
- Analysis of Financial Indexes with Computational TechniquesPublication . Tenreiro Machado, J. A.; Duarte, Gonçalo M.; Duarte, Fernando B.This paper applies Multidimensional scalling techniques and Fourier Transform for visualizing possible time-varying correlations between twenty five stock market values. The method is useful for observing stable or emerging clusters of stock markets with similar behavior. The graphs may also guide the construction of mutivariate econometric models.
- Analysis of financial indices by means of the windowed Fourier transformPublication . Machado, J. A. Tenreiro; Duarte, Fernando B.; Duarte, Gonçalo MonteiroThe goal of this study is to analyze the dynamical properties of financial data series from nineteen worldwide stock market indices (SMI) during the period 1995–2009. SMI reveal a complex behavior that can be explored since it is available a considerable volume of data. In this paper is applied the window Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional order systems.
- Analysis of stock market indices through multidimensional scalingPublication . Machado, J. A. Tenreiro; Duarte, Fernando B.; Duarte, Gonçalo MonteiroWe propose a graphical method to visualize possible time-varying correlations between fifteen stock market values. The method is useful for observing stable or emerging clusters of stock markets with similar behaviour. The graphs, originated from applying multidimensional scaling techniques (MDS), may also guide the construction of multivariate econometric models.
- Analysis of stock market indices with multidimensional scaling and waveletsPublication . Machado, J. A. Tenreiro; Duarte, Fernando B.; Duarte, Gonçalo MonteiroStock market indices SMIs are important measures of financial and economical performance. Considerable research efforts during the last years demonstrated that these signals have a chaotic nature and require sophisticated mathematical tools for analyzing their characteristics. Classical methods, such as the Fourier transform, reveal considerable limitations in discriminating different periods of time. This paper studies the dynamics of SMI by combining the wavelet transform and the multidimensional scaling MDS . Six continuous wavelets are tested for analyzing the information content of the stock signals. In a first phase, the real Shannon wavelet is adopted for performing the evaluation of the SMI dynamics, while their comparison is visualized by means of the MDS. In a second phase, the other wavelets are also tested, and the corresponding MDS plots are analyzed.
- Application of continuous wavelet transform to the analysis of the modulus of the fractional Fourier transform bands for resolving two component mixturePublication . Dinç, Erdal; Duarte, Fernando B.; Machado, J. A. Tenreiro; Baleanu, DumitruIn this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter a of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.
- Application of Fractional Calculus in the Dynamical Analysis and Control of Mechanical ManipulatorsPublication . Ferreira, N. M. Fonseca; Duarte, Fernando B.; Lima, Miguel F. M.; Marcos, Maria G.; Tenreiro Machado, J. A.Mathematics Subject Classification: 26A33, 93C83, 93C85, 68T40Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. This article illustrates several applications of fractional calculus in robot manipulator path planning and control.
- Describing function of two masses with backlashPublication . Duarte, Fernando B.; Machado, J. A. TenreiroThis paper analyzes the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional dynamics is compared with that of standard models.
- Dynamics of the Dow Jones and the NASDAQ stock indexesPublication . Duarte, Fernando B.; Machado, J. A. Tenreiro; Duarte, Gonçalo MonteiroThe goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indices. We analyze the Dow Jones Industrial Average ( ∧ DJI) and the NASDAQ Composite ( ∧ IXIC) indexes at a daily time horizon. The methods and algorithms that have been explored for description of physical phenomena become an effective background, and even inspiration, for very productive methods used in the analysis of economical data. We start by applying the classical concepts of signal analysis, Fourier transform, and methods of fractional calculus. In a second phase we adopt a pseudo phase plane approach.
- Fractional describing function of systems with Coulomb frictionPublication . Duarte, Fernando B.; Machado, J. A. TenreiroThis paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed into two components, namely, the viscous and the Coulomb friction. The system dynamics is analyzed in the DF perspective revealing a fractional-order behavior. The reliability of the DF method is evaluated through the signal harmonic contents.