Wavelet Methods in Statistics with R

Nason, Guy P.

doi:10.1007/978-0-387-75961-6

Cited by 233 publications

(6 citation statements)

References 187 publications

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“…In that sense, Nason (2008) appoints that the Haar wavelet is a good choice because it exhibits many characteristic features of wavelets. Two relevant characteristics are the oscillation (the Haar wavelet goes up and down), mathematically this can be expressed by the condition that ∫ ( ) , a property shared by all wavelets; and the compact support (not all wavelets have compact support, but they must decay to zero rapidly).…”

Section: Methodsmentioning

confidence: 99%

Estimation of Non-Linear Dependence between Exchange Rate and Stock Market through Different Time Scales: Latin Case

Righi

Ceretta

Coronel

2014

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The aim of this paper was to investigate a relationship between stock returns and exchange rate in Brazilian stock market over different time scales. Therefore we used daily quotations of Ibovespa and ratio between the U.S. Dollar and Brazilian Real, from April, 2003 to August, 2011. The initial analysis evidenced that Brazilian stock market is more volatile than Real/Dollar exchange rate. With the time scales coefficients we estimated families of copulas for the relationship between daily log-returns of Dollar/Real exchange rate and Ibovespa. The results of estimated copulas evidenced that dependence between the variables is negative in all time scales, thus confirming the balanced portfolio theory. The coarse scales exhibit great negative dependence, which is reduced in the middle scales and reaches the lower level at the finest scales. This confirms that investors, holding portfolios composed by Brazilian stocks for long time, are more sensitive to Dollar/Real exchange rate. Regarding the shape of joint probability of the variables, there was a predominance of Student's t copula. This result emphasized that there is more dependence in the tails between exchange rate and Brazilian stock markets than the normally expected. It highlights the necessity of risk management in portfolios composed by stocks of Brazilian market in situations of great variation in Dollar/Real exchange rate. No less important is the caution of the exchange rate policy of the Brazilian government to huge variations and turbulence periods in the stock market.

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Section: Methodsmentioning

confidence: 99%

Estimation of Non-Linear Dependence between Exchange Rate and Stock Market through Different Time Scales: Latin Case

Righi

Ceretta

Coronel

2014

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“…Each of these sequences is length n/2. Consequently, in whole, the amount of wavelet coefficients in both decimals on the better scale is 2 × n/2 = n [11].…”

Section: Wavelet Analysismentioning

confidence: 99%

The Bioinformatics Tools for Discovery of Genetic Diversity by Means of Elastic Net and Hurst Exponent

Ferreira¹,

Sáfadi²,

Setotaw³

et al. 2019

Bioinformatics Tools for Detection and Clinical Interpretation of Genomic Variations

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The genome era allowed us to evaluate different aspects on genetic variation, with a precise manner followed by a valuable tip to guide the improvement of knowledge and direct to upgrade to human life. In order to scrutinize these treasured resources, some bioinformatics tools permit us a deep exploration of these data. Among them, we show the importance of the discrete non-decimated wavelet transform (NDWT). The wavelets have a better ability to capture hidden components of biological data and an efficient link between biological systems and the mathematical objects used to describe them. The decomposition of signals/ sequences at different levels of resolution allows obtaining distinct characteristics in each level. The analysis using technique of wavelets has been growing increasingly in the study of genomes. One of the great advantages associated to this method corresponds to the computational gain, that is, the analyses are processed almost in real time. The applicability is in several areas of science, such as physics, mathematics, engineering, and genetics, among others. In this context, we believe that using R software and applied NDWT coupled with elastic net domains and Hurst exponent will be of valuable guideline to researchers of genetics in the investigation of the genetic variability.

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“…Shannon's entropy and fractal analysis have recently been used in urban analysis, especially in studies that integrate remote sensing and GIS (Dewan, Corner 2014). Shannon's entropy is suggested as a measure of spread (Nason 2008). It is one of the most commonly used and one of the most reliable assEssMEnT of urBan spraWl usInG sHannon's EnTropY and fracTal analYsIs: a casE sTudY of aTaKuM, IlKadIM and canIK (saMsun, TurKEY)…”

Section: Introductionmentioning

confidence: 99%

Assessment of Urban Sprawl Using Shannon’s Entropy and Fractal Analysis: A Case Study of Atakum, Ilkadim and Canik (Samsun, Turkey)

Öztürk

2017

Journal of Environmental Engineering and Landscape Management

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Urban sprawl is one of the most important problems in urban development due to its negative environmental and societal impacts. Therefore, the spatial pattern of urban growth should be accurately analyzed and well understood for effective urban planning. This paper focuses on urban sprawl analysis in the Atakum, Ilkadim and Canik districts of Samsun, Turkey. In this study, urban sprawl was examined over a period of 24 years using Shannon's entropy and fractal analysis based on remote sensing and Geographic Information System (GIS). The built-up areas in 1989, 2000 and 2013 were extracted from Landsat TM/ETM+/OLI images using the maximum likelihood classification method, and urban form changes in the 1989–2013 period were investigated. The Shannon's entropy method was used to determine the degree of urban sprawl, and a fractal analysis method based on box counting was used to characterize the urban sprawl. The results show that Atakum, Ilkadim and Canik experienced important changes and have considerable sprawl and complex characteristics now. The study also revealed that there is no monotonic relationship between Shannon's entropy and fractal dimension.

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Wavelet Methods in Statistics with R

Cited by 233 publications

References 187 publications

Estimation of Non-Linear Dependence between Exchange Rate and Stock Market through Different Time Scales: Latin Case

Estimation of Non-Linear Dependence between Exchange Rate and Stock Market through Different Time Scales: Latin Case

The Bioinformatics Tools for Discovery of Genetic Diversity by Means of Elastic Net and Hurst Exponent

Assessment of Urban Sprawl Using Shannon’s Entropy and Fractal Analysis: A Case Study of Atakum, Ilkadim and Canik (Samsun, Turkey)

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