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.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Optimal offering strategies for wind power producers considering uncertainty and risk

This paper provides a two-stage stochastic programming approach for the development of optimal offering strategies for wind power producers. Uncertainty is related to electricity market prices and wind power production. A hybrid intelligent approach, combining wavelet transform, particle swarm optimization and adaptive-network-based fuzzy inference system, is used in this paper to generate plausible scenarios. Also, risk aversion is explicitly modeled using the conditional value-at-risk methodology. Results from a realistic case study, based on a wind farm in Portugal, are provided and analyzed. Finally, conclusions are duly drawn.

Comparative analysis of time-frequency methods estimating the time-varying microstructure of sleep EEG spindles

Proceedings of the Information Technology Applications in Biomedicine, Ioannina - Epirus, Greece, October 26-28, 2006

Técnicas de deteção de dano estrutural com base na monitorização

Ao longo dos últimos anos, acompanhada da evolução tecnológica, da dificuldade da inspeção visual e da consciencialização dos efeitos de uma má inspeção, verificou-se uma maior sensibilidade para a importância da monitorização estrutural, principalmente nas grandes infra-estruturas de engenharia civil. Os sistemas de monitorização estrutural permitem o acompanhamento contínuo do comportamento de uma determinada estrutura de tal forma que com os dados obtidos, é possível avaliar alterações no comportamento da mesma. Com isso, tem-se desenvolvido e implementado estratégias de identificação de danos estruturais com o intuito de aumentar a fiabilidade estrutural e evitar precocemente que alterações na condição da estrutura possam evoluir para situações mais severas. Neste contexto, a primeira parte desta dissertação consiste numa introdução à monitorização estrutural e à deteção de dano estrutural. Relativamente à monitorização, são expostos os seus objetivos e os princípios da sua aplicação. Conjuntamente são apresentados e descritos os principais sensores e são explicadas as funcionalidades de um sistema de aquisição de dados. O segundo tema aborda a importância da deteção de dano introduzindo os métodos estudados neste trabalho. Destaca-se o método das linhas de influência, o método da curvatura dos modos de vibração e o método da transformada de wavelet. Na segunda parte desta dissertação são apresentados dois casos de estudo. O primeiro estudo apresenta uma componente numérica e uma componente experimental. Estuda-se um modelo de viga que se encontra submetida a vários cenários de dano e valida-se a capacidade do método das linhas de influência em detetar e localizar essas anomalias. O segundo estudo consiste na modelação numérica de uma ponte real, na posterior simulação de cenários de dano e na análise comparativa da eficácia de cada um dos três métodos de deteção de dano na identificação e localização dos danos simulados. Por último, são apresentadas as principais conclusões deste trabalho e são sugeridos alguns tópicos a explorar na elaboração de trabalhos futuros.

Alterações da Actividade Autonómica Durante o Teste de Inclinação em Doentes com Fibrilhação Auricular Paroxística: Análise com Wavelets

The autonomic nervous system (ANS) is known to be an important modulator in the pathogenesis of paroxysmal atrial fibrillation (PAF). Changes in ANS control of heart rate variability (HRV) occur during orthostatism to maintain cardiovascular homeostasis. Wavelet transform has emerged as a useful tool that provides time-frequency decomposition of the signal under investigation, enabling intermittent components of transient phenomena to be analyzed. AIM: To study HRV during head-up tilt (HUT) with wavelet transform analysis in PAF patients and healthy individuals (normals). METHODS: Twenty-one patients with PAF (8 men; age 58 +/- 14 yrs) were examined and compared with 21 normals (7 men, age 48 +/- 12 yrs). After a supine resting period, all subjects underwent passive HUT (60 degrees) while in sinus rhythm. Continuous monitoring of ECG and blood pressure was carried out (Task Force Monitor, CNSystems). Acute changes in RR-intervals were assessed by wavelet analysis and low-frequency power (LF: 0.04-0.15 Hz), high-frequency power (HF: 0.15-0.60 Hz) and LF/HF (sympathovagal) were calculated for 1) the last 2 min of the supine period; 2) the 15 sec of tilting movement (TM); and 3) the 1st (TT1) and 2nd (TT2) min of HUT. Data are expressed as means +/- SEM. RESULTS: Baseline and HUT RR-intervals were similar for the two groups. Supine basal blood pressure was also similar for the two groups, with a sustained increase in PAF patients, and a decrease followed by an increase and then recovery in normals. Basal LF, HF and LF/ HF values in PAF patients were 632 +/- 162 ms2, 534 +/- 231 ms2 and 1.95 +/- 0.39 respectively, and 1058 +/- 223 ms2, 789 +/- 244 ms2 and 2.4 +/- 0.36 respectively in normals (p = NS). During TM, LF, HF and LF/HF values for PAF patients were 747 +/- 277 ms2, 387 +/- 94 ms2 and 2.9 +/- 0.6 respectively, and 1316 +/- 315 ms2, 698 +/- 148 ms2 and 2.8 +/- 0.6 respectively in normals (p < 0.05 for LF and HF). During TF1, LF, HF and LF/ HF values for PAF patients were 1243 +/- 432 ms2, 302 +/- 88 ms2 and 7.7 +/- 2.4 respectively, and 1992 +/- 398 ms2, 333 +/- 76 ms2 and 7.8 +/- 0.98 respectively for normals (p < 0.05 for LF). During TF2, LF, HF and LF/HF values for PAF patients were 871 +/- 256 ms2, 242 +/- 51 ms2 and 4.7 +/- 0.9 respectively, and 1263 +/- 335 ms2, 317 +/- 108 ms2 and 8.6 +/- 0.68 respectively for normals (p < 0.05 for LF/HF). The dynamic profile of HRV showed that LF and HF values in PAF patients did not change significantly during TM or TT2, and LF/HF did not change during TM but increased in TT1 and TT2. CONCLUSION: Patients with PAF present alterations in HRV during orthostatism, with decreased LF and HF power during TM, without significant variations during the first minutes of HUT. These findings suggest that wavelet transform analysis may provide new insights when assessing autonomic heart regulation and highlight the presence of ANS disturbances in PAF.

Application of wavelets to the study of political history

\The idea that social processes develop in a cyclical manner is somewhat like a `Lorelei'. Researchers are lured to it because of its theoretical promise, only to become entangled in (if not wrecked by) messy problems of empirical inference. The reasoning leading to hypotheses of some kind of cycle is often elegant enough, yet the data from repeated observations rarely display the supposed cyclical pattern. (...) In addition, various `schools' seem to exist which frequently arrive at di erent conclusions on the basis of the same data." (van der Eijk and Weber 1987:271). Much of the empirical controversies around these issues arise because of three distinct problems: the coexistence of cycles of di erent periodicities, the possibility of transient cycles and the existence of cycles without xed periodicity. In some cases, there are no reasons to expect any of these phenomena to be relevant. Seasonality caused by Christmas is one such example (Wen 2002). In such cases, researchers mostly rely on spectral analysis and Auto-Regressive Moving-Average (ARMA) models to estimate the periodicity of cycles.1 However, and this is particularly true in social sciences, sometimes there are good theoretical reasons to expect irregular cycles. In such cases, \the identi cation of periodic movement in something like the vote is a daunting task all by itself. When a pendulum swings with an irregular beat (frequency), and the extent of the swing (amplitude) is not constant, mathematical functions like sine-waves are of no use."(Lebo and Norpoth 2007:73) In the past, this di culty has led to two di erent approaches. On the one hand, some researchers dismissed these methods altogether, relying on informal alternatives that do not meet rigorous standards of statistical inference. Goldstein (1985 and 1988), studying the severity of Great power wars is one such example. On the other hand, there are authors who transfer the assumptions of spectral analysis (and ARMA models) into fundamental assumptions about the nature of social phenomena. This type of argument was produced by Beck (1991) who, in a reply to Goldstein (1988), claimed that only \ xed period models are meaningful models of cyclic phenomena".We argue that wavelet analysis|a mathematical framework developed in the mid-1980s (Grossman and Morlet 1984; Goupillaud et al. 1984) | is a very viable alternative to study cycles in political time-series. It has the advantage of staying close to the frequency domain approach of spectral analysis while addressing its main limitations. Its principal contribution comes from estimating the spectral characteristics of a time-series as a function of time, thus revealing how its di erent periodic components may change over time. The rest of article proceeds as follows. In the section \Time-frequency Analysis", we study in some detail the continuous wavelet transform and compare its time-frequency properties with the more standard tool for that purpose, the windowed Fourier transform. In the section \The British Political Pendulum", we apply wavelet analysis to essentially the same data analyzed by Lebo and Norpoth (2007) and Merrill, Grofman and Brunell (2011) and try to provide a more nuanced answer to the same question discussed by these authors: do British electoral politics exhibit cycles? Finally, in the last section, we present a concise list of future directions.

Enhancing the performance of spread spectrum techniques in different applications

Spread spectrum, Automotive Radar, Indoor Positioning Systems, Ultrasonic and Microwave Imaging, super resolution technique and wavelet transform

Efficiency Comparison of DFT/IDFT Algorithms by Evaluating Diverse Hardware Implementations

In this paper we investigate various algorithms for performing Fast Fourier Transformation (FFT)/Inverse Fast Fourier Transformation (IFFT), and proper techniques for maximizing the FFT/IFFT execution speed, such as pipelining or parallel processing, and use of memory structures with pre-computed values (look up tables -LUT) or other dedicated hardware components (usually multipliers). Furthermore, we discuss the optimal hardware architectures that best apply to various FFT/IFFT algorithms, along with their abilities to exploit parallel processing with minimal data dependences of the FFT/IFFT calculations. An interesting approach that is also considered in this paper is the application of the integrated processing-in-memory Intelligent RAM (IRAM) chip to high speed FFT/IFFT computing. The results of the assessment study emphasize that the execution speed of the FFT/IFFT algorithms is tightly connected to the capabilities of the FFT/IFFT hardware to support the provided parallelism of the given algorithm. Therefore, we suggest that the basic Discrete Fourier Transform (DFT)/Inverse Discrete Fourier Transform (IDFT) can also provide high performances, by utilizing a specialized FFT/IFFT hardware architecture that can exploit the provided parallelism of the DFT/IDF operations. The proposed improvements include simplified multiplications over symbols given in polar coordinate system, using sinе and cosine look up tables, and an approach for performing parallel addition of N input symbols.

Efficiency Comparison of DFT/IDFT Algorithms by Evaluating Diverse Hardware : Implementations,Parallelization Prospectsand Possible Improvements

In this paper we investigate various algorithms for performing Fast Fourier Transformation (FFT)/Inverse Fast Fourier Transformation (IFFT), and proper techniquesfor maximizing the FFT/IFFT execution speed, such as pipelining or parallel processing, and use of memory structures with pre-computed values (look up tables -LUT) or other dedicated hardware components (usually multipliers). Furthermore, we discuss the optimal hardware architectures that best apply to various FFT/IFFT algorithms, along with their abilities to exploit parallel processing with minimal data dependences of the FFT/IFFT calculations. An interesting approach that is also considered in this paper is the application of the integrated processing-in-memory Intelligent RAM (IRAM) chip to high speed FFT/IFFT computing. The results of the assessment study emphasize that the execution speed of the FFT/IFFT algorithms is tightly connected to the capabilities of the FFT/IFFT hardware to support the provided parallelism of the given algorithm. Therefore, we suggest that the basic Discrete Fourier Transform (DFT)/Inverse Discrete Fourier Transform (IDFT) can also provide high performances, by utilizing a specialized FFT/IFFT hardware architecture that can exploit the provided parallelism of the DFT/IDF operations. The proposed improvements include simplified multiplications over symbols given in polar coordinate system, using sinе and cosine look up tables,and an approach for performing parallel addition of N input symbols.

BOI 2.0: disseny d'una implementació de JPEG 2000

JPEG 2000 és un estàndard de compressió d'imatges que utilitza tècniques estat de l’art basades en la transformada wavelet. Els principals avantatges són la millor compressió, la possibilitat d’operar amb dades comprimides i que es pot comprimir amb i sense pèrdua amb el mateix mètode. BOI és la implementació de JPEG 2000 del Grup de Compressió Interactiva d’Imatges del departament d’Enginyeria de la Informació i les Comunicacions, pensada per entendre, criticar i millorar les tecnologies de JPEG 2000. La nova versió intenta arribar a tots els extrems de l’estàndard on la versió anterior no va arribar.

Representació no-lineal de les imatges per a codificació perceptiva

JPEG2000 és un estàndard de compressió d’imatges que utilitza la transformada wavelet i, posteriorment, una quantificació uniforme dels coeficients amb dead-zone. Els coeficients wavelet presenten certes dependències tant estadístiques com visuals. Les dependències estadístiques es tenen en compte a l'esquema JPEG2000, no obstant, no passa el mateix amb les dependències visuals. En aquest treball, es pretén trobar una representació més adaptada al sistema visual que la que proporciona JPEG2000 directament. Per trobar-la utilitzarem la normalització divisiva dels coeficients, tècnica que ja ha demostrat resultats tant en decorrelació estadística de coeficients com perceptiva. Idealment, el que es voldria fer és reconvertir els coeficients a un espai de valors en els quals un valor més elevat dels coeficients impliqui un valor més elevat d'aportació visual, i utilitzar aquest espai de valors per a codificar. A la pràctica, però, volem que el nostre sistema de codificació estigui integrat a un estàndard. És per això que utilitzarem JPEG2000, estàndard de la ITU que permet una elecció de les distorsions en la codificació, i utilitzarem la distorsió en el domini de coeficients normalitzats com a mesura de distorsió per a escollir quines dades s'envien abans.

Music identification

L'evolució ens els últims decennis de les possibilitats relacionades amb les tecnologies de la informació han provocat l'aparició de diferents camps, entre ells l'anomenat “recuperació de música basant-se en el contingut”, que tracta de calcular la similitud entre diferents sons. En aquest projecte hem fet una recerca sobre els diferents mètodes que existeixen avui en dia, i posteriorment n'hem comparat tres, un basat en característiques del so, un basat en la transformada discreta del cosinus, i un que combina els dos anteriors. Els resultats han mostrat, que el basat en la transformada de Fourier és el més fiable.

Sound Texture Modelling

In the PhD thesis “Sound Texture Modeling” we deal with statistical modelling or textural sounds like water, wind, rain, etc. For synthesis and classification. Our initial model is based on a wavelet tree signal decomposition and the modeling of the resulting sequence by means of a parametric probabilistic model, that can be situated within the family of models trainable via expectation maximization (hidden Markov tree model ). Our model is able to capture key characteristics of the source textures (water, rain, fire, applause, crowd chatter ), and faithfully reproduces some of the sound classes. In terms of a more general taxonomy of natural events proposed by Graver, we worked on models for natural event classification and segmentation. While the event labels comprise physical interactions between materials that do not have textural propierties in their enterity, those segmentation models can help in identifying textural portions of an audio recording useful for analysis and resynthesis. Following our work on concatenative synthesis of musical instruments, we have developed a pattern-based synthesis system, that allows to sonically explore a database of units by means of their representation in a perceptual feature space. Concatenative syntyhesis with “molecules” built from sparse atomic representations also allows capture low-level correlations in perceptual audio features, while facilitating the manipulation of textural sounds based on their physical and perceptual properties. We have approached the problem of sound texture modelling for synthesis from different directions, namely a low-level signal-theoretic point of view through a wavelet transform, and a more high-level point of view driven by perceptual audio features in the concatenative synthesis setting. The developed framework provides unified approach to the high-quality resynthesis of natural texture sounds. Our research is embedded within the Metaverse 1 European project (2008-2011), where our models are contributting as low level building blocks within a semi-automated soundscape generation system.

Analysis of multi-scale systemic risk in Brazil's financial market

This work analyzes whether the relationship between risk and returns predicted by the Capital Asset Pricing Model (CAPM) is valid in the Brazilian stock market. The analysis is based on discrete wavelet decomposition on different time scales. This technique allows to analyze the relationship between different time horizons, since the short-term ones (2 to 4 days) up to the long-term ones (64 to 128 days). The results indicate that there is a negative or null relationship between systemic risk and returns for Brazil from 2004 to 2007. As the average excess return of a market portfolio in relation to a risk-free asset during that period was positive, it would be expected this relationship to be positive. That is, higher systematic risk should result in higher excess returns, which did not occur. Therefore, during that period, appropriate compensation for systemic risk was not observed in the Brazilian market. The scales that proved to be most significant to the risk-return relation were the first three, which corresponded to short-term time horizons. When treating differently, year-by-year, and consequently separating positive and negative premiums, some relevance is found, during some years, in the risk/return relation predicted by the CAPM. However, this pattern did not persist throughout the years. Therefore, there is not any evidence strong enough confirming that the asset pricing follows the model.