Analysis of stock market indices with multidimensional scaling and wavelets

Stock 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

Analysis of financial data series using fractional Fourier transform and multidimensional scaling

The 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 stock market indices through multidimensional scaling

We 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 financial indices by means of the windowed Fourier transform

The 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

Power law analysis of financial index dynamics

Power law PL and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution

Fractional describing function of systems with Coulomb friction

This 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

Describing function of two masses with backlash

This 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

Pathway Weathering in Granitoid Rocks from Central Region of Angola: Geochemical and Mineralogical Data

The Central Region of Angola is characterized by the abundance of granitoid rocks, whose weathering “in situ” originated the so-called residual soils. The textural, geochemical and mineralogical properties of these soils depend not only on the chemical composition of parent rock, but mainly on the local climatic and geomorphological characteristics. In the study area, sampling sites were selected, which extend from the region of Kwanza- Norte (Kassenda, Dondo) through Kwanza-Sul (Cangulo, Quibala and Waco Kungo) until the plateau of Huambo, where samples of fresh rock, weathered rock and its residual soil were collected along each weathering profile. Chemical analytical data were determined using X-ray fluorescence (XRF) analysis of the major and minor elements, whereas mineralogical data were determined using X-ray diffraction (XRD), on the samples of rock and on the respective residual soil. The results obtained and their comparative analysis between the sampling sites, as well as along each weathering profile is presented. This paper allows contributing to the knowledge of the geochemical weathering in tropical areas, as is the case of Angola

Fractional dynamics in the describing function analysis of nonlinear friction

This paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective revealing a fractional-order behaviour. The reliability of the DF method is evaluated through the signal harmonic content and the limit cycle prediction.N/

Describing function of systems with nonlinear friction

This paper studies the describing function (DF) of systems composed of a mass subjected to nonlinear friction. The friction force is decomposed in three components namely, the viscous, the Coulomb and the static forces. The system dynamics is analyzed in the DF perspective and the reliability of the DF method is evaluated through the signal harmonic content.N/