Spectral Analysis Tools Research Articles

Modelling of derivatives pricing using methods of spectral analysis

In this article expands the method of finding the approximate price for a wide class of derivative financial instruments. Using the spectral theory of self-adjoint operators in Hilbert space and the wave theory of singular and regular perturbations, the analytical formula of the approximate asset price is established. Methods for calculating the approximate price of options using the tools of spectral analysis, singular and regular wave theory in the case of fast and slow factors are developed. Combining methods from the spectral theory of singular and regular perturbations, it is possible to estimate the price of derivative financial instruments as a schedule by eigenfunctions. The approximate value of securities and their rate of return are calculated. Applying the theory of Sturm-Liouville, Fredholm’s alternative and analysis of singular and regular perturbations at different time scales have enabled us to obtain explicit formulas for the approximate value of securities and their yield on the basis of the development of their eigenfunctions and eigenvalues of self-adjoint operators using boundary value problems for singular and regular perturbations. The theorem of closeness estimates for bond prices approximation is proved. An algorithm for calculating the approximate price of derivatives and the accuracy of estimates has been developed, which allows to analyze and draw precautionary conclusions and suggestions to minimize the risks of pricing derivatives that arise in the stock market. A model for finding the value of derivatives corresponding to the dynamics of the stock market and the size of financial flows has been developed. This model allows you to find the prices of derivatives and their volatility, as well as minimize speculative changes in pricing, analyze the progress of stock market processes and take concrete steps to improve the situation to optimize financial strategies. The used methodology of European options pricing based on the study of volatility behavior and analysis of the yield of financial instruments allows to increase the accuracy of the forecast and make sound management strategic decisions by stock market participants.

S‐transform: from main concepts to some power quality applications

Among various spectral analysis tools arisen in the last years, some were more prominent, such as Fourier transform, windowed Fourier transform and wavelet transform (WT). Nevertheless, all of them present implementation restrictions for an ideal extraction for low as well as high frequencies, of variant signals in time, as, for example, signals containing time-varying harmonics. In this sense, this study presents a review of concepts on the S-transform (ST), also known as Stockwell transform, applied in the analysis of some signals in the context of power quality (PQ). ST gathers, in a single function, positive qualities of both short time Fourier transform (STFT) and WT. This study presents a mathematical basis and some considerations regarding ST, referring to published papers, including a comparison between ST and STFT, as well as WT. It is worth emphasising that a final solution for the extraction of the low- and high-frequency information from time-varying signals is not yet available. ST is a satisfactory approach, but it still needs more detailed studies. This study presents a necessary set of steps for a better understanding of ST, reproduction of examples found in correspondent literature, as well as the ones regarding PQ.

From modulational instability to focusing dam breaks in water waves

We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a range of initial parameters, the nonlinear wave packet is not disintegrated by the Benjamin-Feir instability but exhibits a specific, strongly nonlinear modulation, which propagates from the edges of the wavepacket towards the center with finite speed. Using numerical tools of nonlinear spectral analysis of experimental data we identify the observed envelope wave structures with focusing dispersive dam break flows, a peculiar type of dispersive shock waves recently described in the framework of the semi-classical limit of the 1D focusing nonlinear Schrodinger equation (1D-NLSE). Our experimental results are shown to be in a good quantitative agreement with the predictions of the semi-classical 1D-NLSE theory. This is the first observation of the persisting dispersive shock wave dynamics in a modulationally unstable water wave system.

Multifractal and multiscale entropy scaling of in-situ soil moisture time series: Study of SMOSMANIA network data, southwestern France

Soil moisture processes exhibit a strong variability in space and time due to the variability of the meteorological forcing and the spatial heterogeneity of soil properties. This study aims at providing a statistical description of soil moisture variability by analyzing data from nine in situ stations located over an West-East gradient in southwestern France (SMOSMANIA stations, distributed over an area of about 300 × 200 km). For each station, four time series of soil moisture observed at four different depths ranging from 5 cm to 30 cm are analyzed. First, possible scaling properties are investigated within the Fourier domain with the help of spectral analysis tools. Red noise-like (1/f2) scaling properties could be noticed over a fairly wide scale range (1000 h–1 h) with relatively homogeneous scaling parameters for 5 cm depth soil moistures regardless of the station. These properties are confirmed at other depths with slightly steeper spectra and more heterogeneity across stations. In a second step, multifractal analysis has been carried out on the same data. Multifractal scaling is observed over a narrower scaling range (128 h–1 h). Moment scaling functions can be parameterized within the framework of Universal Multifractals: typical parameters are C1≈0.25 and α ≈ 1.6–1.8 for surface data while both parameters are subject to strong changes (C1 increases and α decreases) as the depth increases. In a third step, Multiscale Entropy (MSE) analysis has been applied in order to analyze the dataset from an information theory point of view and to infer whether multifractal properties could have a signature on MSE estimates. The MSE function has been found to follow a power law of the aggregation time with a scaling exponent close to 0.3–0.4 for surface data. These exponents were generally close to the Hurst exponent H estimated by first-order structure functions. While it is already known that MSE should follow scaling properties in the case of monofractal signals, the results suggest that the latter property holds for natural multifractal processes. Finally, complementary numerical tests based on synthetic multifractal time series are done in order to assess the relationship between the MSE scaling exponent H′ and multifractal parameters C1, α and H. A dependency on the three multifractal parameters has been observed, yet in practice the approximation H′ ≈ H seems somewhat acceptable for processes with relatively large Hurst exponents and/or low multifractal intermittency (C1). On a more broad perspective, the existence of relationships between multifractal scaling and MSE properties could help to refine the physical interpretation of observed scaling properties in many geophysical processes.

Non‐Hermitian perturbations of Hermitian matrix‐sequences and applications to the spectral analysis of the numerical approximation of partial differential equations

SummaryThis article concerns the spectral analysis of matrix‐sequences which can be written as a non‐Hermitian perturbation of a given Hermitian matrix‐sequence. The main result reads as follows. Suppose that for every n there is a Hermitian matrix Xn of size n and that {Xn}n∼λf, that is, the matrix‐sequence {Xn}n enjoys an asymptotic spectral distribution, in the Weyl sense, described by a Lebesgue measurable function f; if with ‖·‖2 being the Schatten 2 norm, then {Xn+Yn}n∼λf. In a previous article by Leonid Golinskii and the second author, a similar result was proved, but under the technical restrictive assumption that the involved matrix‐sequences {Xn}n and {Yn}n are uniformly bounded in spectral norm. Nevertheless, the result had a remarkable impact in the analysis of both spectral distribution and clustering of matrix‐sequences arising from various applications, including the numerical approximation of partial differential equations (PDEs) and the preconditioning of PDE discretization matrices. The new result considerably extends the spectral analysis tools provided by the former one, and in fact we are now allowed to analyze linear PDEs with (unbounded) variable coefficients, preconditioned matrix‐sequences, and so forth. A few selected applications are considered, extensive numerical experiments are discussed, and a further conjecture is illustrated at the end of the article.

COLMAR Lipids Web Server and Ultrahigh-Resolution Methods for Two-Dimensional Nuclear Magnetic Resonance- and Mass Spectrometry-Based Lipidomics

Accurate identification of lipids in biological samples is a key step in lipidomics studies. Multidimensional nuclear magnetic resonance (NMR) spectroscopy is a powerful analytical tool for this purpose as it provides comprehensive structural information on lipid composition at atomic resolution. However, the interpretation of NMR spectra of complex lipid mixtures is currently hampered by limited spectral resolution and the absence of a customized lipid NMR database along with user-friendly spectral analysis tools. We introduce a new two-dimensional (2D) NMR metabolite database "COLMAR Lipids" that was specifically curated for hydrophobic metabolites presently containing 501 compounds with accurate experimental 2D 13C-1H heteronuclear single quantum coherence (HSQC) chemical shift data measured in CDCl3. A new module in the public COLMAR suite of NMR web servers was developed for the (semi)automated analysis of complex lipidomics mixtures (http://spin.ccic.osu.edu/index.php/colmarm/index2). To obtain 2D HSQC spectra with the necessary high spectral resolution along both 13C and 1H dimensions, nonuniform sampling in combination with pure shift spectroscopy was applied allowing the extraction of an abundance of unique cross-peaks belonging to hydrophobic compounds in complex lipidomics mixtures. As shown here, this information is critical for the unambiguous identification of underlying lipid molecules by means of the new COLMAR Lipids web server, also in combination with mass spectrometry, as is demonstrated for Caco-2 cell and lung tissue cell extracts.

2D-Infrared Spectroscopy of Proteins in Water: Using the Solvent Thermal Response as an Internal Standard.

Ultrafast two-dimensional infrared (2D-IR) spectra can now be obtained in a matter of seconds, opening up the possibility of high-throughput screening applications of relevance to the biomedical and pharmaceutical sectors. Determining quantitative information from 2D-IR spectra recorded on different samples and different instruments is however made difficult by variations in beam alignment, laser intensity, and sample conditions. Recently, we demonstrated that 2D-IR spectroscopy of the protein amide I band can be performed in aqueous (H2O) rather than deuterated (D2O) solvents, and we now report a method that uses the magnitude of the associated thermal response of H2O as an internal normalization standard for 2D-IR spectra. Using the water response, which is temporally separated from the protein signal, to normalize the spectra allows significant reduction of the impact of measurement-to-measurement fluctuations on the data. We demonstrate that this normalization method enables creation of calibration curves for measurement of absolute protein concentrations and facilitates reproducible difference spectroscopy methodologies. These advances make significant progress toward the robust data handling strategies that will be essential for the realization of automated spectral analysis tools for large scale 2D-IR screening studies of protein-containing solutions and biofluids.

Rapid Identification of Atmospheric Gaseous Pollutants Using Fourier-Transform Infrared Spectroscopy Combined with Independent Component Analysis

Fourier-transform infrared (FTIR) spectroscopy is a rapid and nondestructive technology for monitoring atmospheric quality. The identification of each component from the FTIR spectra is a prerequisite for the accurate quantitative analysis of gaseous pollutants. Due to the overlap of different gas absorption peaks and the interference of water vapor in the actual measurement, the existing identification methods of gas spectra have drawbacks of low identification rate and the inability to carry out real-time online analysis in atmospheric quality monitoring. In this work, independent component analysis (ICA) is applied to the spectral separation of heavily overlapped spectra of gaseous pollutants. The proposed method is validated by the analysis of mixture spectra obtained in laboratory and actual atmospheric spectra collected from stationary source. The average time consumption of separation process is less than 0.2 seconds, and the identification rate of experimental gases is up to 100%, as shown by the results of peak searching and the analysis of the correction coefficient between the separated spectra and the standard spectra database. The identification results of actual atmospheric spectra demonstrated that the proposed method can effectively identify the gaseous pollutants whose concentration changes in the measured spectra, and it is a promising qualitative spectral analysis tool that can shorten the identification time, as well as increase the identification rate. Therefore, this method can be a useful alternative to traditional qualitative identification methods for real-time online atmospheric pollutant detection.

Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations

Rank-revealing matrix decompositions provide an essential tool in spectral analysis of matrices, including the Singular Value Decomposition (SVD) and related low-rank approximation techniques. QR w...

Wavelet analysis for early identification of HRV changes in offspring with genetic predisposition to hypertension in Oman.

Offspring with a genetic predisposition to hypertension may have higher blood pressure (BP) at rest compared with those without a genetic predisposition to hypertension. They are also expected to have a higher sympathetic component in the heart rate variability (HRV) which could be computed with signal processing algorithms. The purpose of this study is to design a wavelet-based system to estimate the heart rate variability that can be used to detect early cardiovascular changes in offspring with a genetic predisposition to hypertension. Early detection will help in the treatment of those young people. In this work, the relation between the hypertension and the changes in HRV is investigated. The frequency domain and time domain analysis of heart rate variability (HRV) are studied to understand their relationship to the autonomic nervous system in offspring with and without a genetic predisposition to hypertension in Oman at resting state. The wavelet-based soft-decision algorithm is used as the spectral analysis tool to obtain different features from the HRV signal and to select the best performing features for detection of hypertension. The main task is to classify between three categories of subjects: 36 subjects with both normotensive parents (ONT), 22 subjects with single hypertensive parent (OHT1), and 11 subjects with both hypertensive parents (OHT2). The summation of the power of bands B4 and B5 of the 32 bands HRV wavelet-based spectrum, which is equivalent to the frequency range (0.046875 Hz-0.078125 Hz), is used as a classification factor among OHT2, OHT1, and ONT groups. The efficiency of classification between ONT and OHT2 is 85.10%, and between OHT1 and OHT2 is 81.81%. The result of classifying between (ONT and OHT1 as one group) and OHT2 is 85.50%. The work proves that the wavelet-based spectral analysis technique is a successful tool for classifying the three groups of subjects (ONT, OHT1, and OHT2) with different susceptibility for development of hypertension.

CEV MODEL WITH STOCHASTIC VOLATILITY

This paper develops a systematic method for calculating approximate prices for a wide range of securities implying the tools of spectral analysis, singular and regular perturbation theory. Price options depend on stochastic volatility, which may be multiscale, in the sense that it may be driven by one fast-varying and one slow-varying factor. The found the approximate price of two-barrier options with multifactor volatility as a schedule for own functions. The theorem of estimation of accuracy of approximation of option prices is established. Explicit formulas have been found for finding the value of derivatives based on the development of eigenfunctions and eigenvalues of self-adjoint operators using boundary-value problems for singular and regular perturbations. This article develops a general method of obtaining a guide price for a broad class of securities. A general theory of derivative valuation of options generated by diffusion processes is developed. The algorithm of calculating the approximate price is given. The accuracy of the estimates is established. The theory developed is applied to a diffusion operator, which is decomposed by eigenfunctions and eigenvalues. The purpose of the article is to develop an algorithm for finding the approximate price of two-barrier options and to find explicit formulas for finding the value of derivatives based on the development of self-functions and eigenvalues of self-adjoint operators using boundary-value problems for singular and regular perturbations. Price finding is reduced to the problem solving of eigenvalues and eigenfunctions of a certain equation. The main advantage of our pricing methodology is that, by combining methods in spectral theory, regular perturbation theory, and singular perturbation theory, we reduce everything to equations to find eigenfunctions and eigenvalues.

Fourier-transform spectrometer chip covering visible band on silica planar waveguide

To minimise a spectrometer maximally, using a micro-electro-mechanical system or planar waveguide chip, has aroused interest in both academia and industry. This is because a portable and inexpensive spectral analysis tool has tremendous potential in various applications including scientific exploration, industrial inspection, and environmental protection. Here, we design, fabricate, and characterise a Fourier-transform spectrometer (FTS) chip consisting of 101 Mach–Zehnder interferometers (MZIs) with gradually varying optical path differences on a silica planar waveguide platform, aiming to cover the entire visible band. To ensure a wide-band operation while simultaneously compressing the size of the chip, wide-bending arm waveguides that can support high-order modes in a short wavelength range are employed in the design of the MZI array. The experimental result of our FTS chip shows its ability to analyse the visible spectrum with a minimum resolution of better than 10 nm and to reproduce the original spectrum with an accuracy of less than 0.5 nm. The successful implementation of the FTS chip based on a matured and low-cost silica planar lightwave circuit process makes it quite promising to realise mass production and widespread application.

Time-slicing spiral galaxies with SDSS-IV MaNGA

ABSTRACT Spectra of galaxies contain a wealth of information about the stellar populations from which they are made. With integral field unit (IFU) surveys, such data can be used to map out stellar population properties across the face of a galaxy, allowing one to go beyond simple radial profiles and study details of non-axisymmetric structure. To-date, however, such studies have been limited by the quality of available data and the power of spectral analysis tools. We now take the next step and study the barred spiral galaxy MCG + 07-28-064 from observations obtained as part of the SDSS-IV MaNGA project. We find that we can decompose this galaxy into ‘time slices,’ which reveal the varying contributions that stars of differing ages make to its bar and spiral structure, offering new insight into the evolution of these features. We find evidence for the ongoing growth of the bar, including the most recent star formation on its leading edge, and for the underlying density wave responsible for spiral structure. This pilot study indicates that there is a wealth of untapped information on the spatial distribution of star formation histories available in the current generation of IFU galaxy surveys.

AN APPLICATION OF FUNCTIONAL DATA ANALYSIS TO LOCAL DAMAGE DETECTION

Abstract Vibration signals sampled with a high frequency constitute a basic source of information about machine behaviour. Few minutes of signal observations easily translate into several millions of data points to be processed with the purpose of the damage detection. Big dimensionality of data sets creates serious difficulties with detection of frequencies specific for a particular local damage. In view of that, traditional spectral analysis tools like spectrograms should be improved to efficiently identify the frequency bands where the impulsivity is most marked (the so-called informative frequency bands or IFB). We propose the functional approach known in modern time series analysis to overcome these difficulties. We will process data sets as collections of random functions to apply techniques of the functional data analysis. As a result, we will be able to represent massive data sets through few real-valued functions and corresponding parameters, which are the eigenfunctions and eigen-values of the covariance operator describing the signal. We will also propose a new technique based on the bootstrap resampling to choose the optimal dimension in representing big data sets that we process. Using real data generated by a gearbox and a wheel bearings we will show how these techniques work in practice.

Modification of urban built-up area extraction method based on the thematic index-derived bands

This research aims to develop new automatic and quicker spectral signature analysis tools to separate urban built-up area and determines urban area changes. Nowadays, researcher uses thematic index-derived bands for automatic urban data extraction. The extraction of urban built-up land can be automatically done with New Built-Up Index (NBUI) although it has a limitation on separating built-up land and water body. This study attempts to obtain the maximum accuracy of the extraction by merging several indices including Enhanced Built-Up and Bareness Index (EBBI), Soil Adjusted Vegetation Index (SAVI), Modified Normalized Difference Water Index (MNDWI), New Water Index (NWI) and Normalized Different Pond Index (NDPI) and compared its accuracy with NBUI. The results showed that merging EBBI, SAVI, MNDWI and NDPI produces the highest accuracy of 98.21% by addition and subtraction. The combined application of EBBI, SAVI and NWI also gives a good effect for extracting urban built-up areas and has 94.64% mapping accuracy.

The ‘plantspec’ r package: A tool for spectral analysis of plant stoichiometry

Abstract Data on plant elemental stoichiometry are essential for ecologists investigating ecosystem function, nutrient cycling, plant–herbivore interactions and leaf economics. A cost‐effective approach to leaf elemental analysis is near‐infrared spectroscopy (NIRS), whereby components such as carbon (C), nitrogen (N), phosphorus (P) and potassium (K) can be predicted using NIR spectra from plant material. However, a major factor limiting the widespread use of NIRS by plant ecologists is the availability of free software and calibration data for developing plant chemistry datasets from spectra. Here, we present a pair of companion r packages (‘plantspec’ and ‘plantspecDB’) that satisfy this need by providing an entire workflow, from spectra to predicted elemental data. The main r package, called ‘plantspec’, allows users to manipulate spectral data and develop custom partial least square (PLS) models for predicting the elemental composition of their own datasets. The second package, ‘plantspecDB’, provides NIR spectra, and matched elemental data obtained with standard analytical techniques, for herbaceous samples collected from 18 grassland sites around the world, primarily sourced from the Nutrient Network experiment. The ‘plantspecDB’ data package also provides calibrations for C, N, P and K for bulk samples and separated by plant functional type: grasses, forbs and legumes. Finally, we provide an example of the ‘plantspec’ workflow, and external validation of these models, and an example application to the stoichiometry of East African grasses as it relates to their evolutionary relationships. The r package ‘plantspec’, and our associated workflow, provides a template to produce robust calibration models and increase the application of NIR in ecology. Although, we focus on plant stoichiometry, the workflow presented here can be applied broadly for a broad range of applications, including soils, remote sensing data, solutions and tissues. Finally, our global dataset provides unprecedented access to NIR calibration data as they pertain to tissue concentrations of key plant limiting elements.

A machine learning approach for automated ULF wave recognition

Machine learning techniques have been successfully introduced in the fields of Space Physics and Space Weather, yielding highly promising results in modeling and predicting many disparate aspects of the geospace environment. Magnetospheric ultra-low frequency (ULF) waves can have a strong impact on the dynamics of charged particles in the radiation belts, which can affect satellite operation. Here, we employ a method based on Fuzzy Artificial Neural Networks in order to detect ULF waves in the time series of the magnetic field measurements on board the low-Earth orbit CHAMP satellite. The outputs of the method are validated against a previously established, wavelet-based, spectral analysis tool, that was designed to perform the same task, and show encouragingly high scores in the detection and correct classification of these signals.

Upscaling of Geological Models of Oil Reservoirs with Unstructured Grids Using Lifting-Based Graph Wavelet Transforms

Wavelet transforms (WTs) constitute a class of powerful tools for spectral and local analysis of data, such as time series, geophysical data, and well logs, as well as modeling of various problems in oil reservoirs, and in particular upscaling their geological models. The application to upscaling has, however, been limited to the reservoir models that are represented by regular computational grids with blocks or cells with regular shapes, such as squares and cubes. The most natural structure of the computational grid is, however, one with irregular and unequal cells, distributed spatially with stochastic orientations. Such a grid is also the ideal computational model for, for example, fractured reservoirs as it allows inclusion of fractures with spatially distributed orientations. In this paper, we propose a generalization of the WT approach to upscaling by developing a new model of a reservoir based on irregular graphs that make it possible to use the WTs for upscaling the geological model highly efficiently. To do so, we first define a computational grid representing a reservoir as a graph and its adjacency matrix and, then, introduce graph WTs using the concept of lifting, utilized in classical signal processing and its extension to graphs. The application of the lifting-based graph WT to upscaling is then developed. The result is an algorithm that may be applied to upscaling of any unstructured geological model represented by a computational grid in which the multiresolution graph WT is applied directly to the spatial distribution of the permeabilities (or other suitable properties). Examples in which the geological model is represented by the Voronoi tessellations are described, and simulation of waterflooding with such graph networks is carried out in order to demonstrate the accuracy and efficiency of the new method.

Analysis of Solar Microwave Burst Spectrum, I. Nonuniform Magnetic Field

Solar microwave bursts carry information about the magnetic field in the emitting region as well as about electrons accelerated during solar flares. While this sensitivity to the coronal magnetic field must be a unique advantage of solar microwave burst observations, it also adds a complexity to spectral analysis targeted to electron diagnostics. This paper introduces a new spectral analysis procedure in which the cross-section and thickness of a microwave source are expressed as power-law functions of the magnetic field so that the degree of magnetic inhomogeneity can systematically be derived. We applied this spectral analysis tool to two contrasting events observed by the Owens Valley Solar Array: the SOL2003-04-04T20:55 flare with a steep microwave spectrum and the SOL2003-10-19T16:50 flare with a broader spectrum. Our analysis shows that the strong flare with the broader microwave spectrum occurred in a region of highly inhomogeneous magnetic field and vice versa. We further demonstrate that such source properties are consistent with the magnetic field observations from the Michelson Doppler Imager instrument onboard the Solar and Heliospheric Observatory (SOHO) spacecraft and the extreme ultraviolet imaging observations from the SOHO extreme ultraviolet imaging telescope. This spectral inversion tool is particularly useful for analyzing microwave flux spectra of strong flares from magnetically complex systems.

Chebyshev Spectra Resistance to Trend of Random Noise

Spectral analysis of random noise in the space of discrete Chebyshev polynomials is an alternative to spectral Fourier analysis. The importance of Chebyshev spectral approach is associated with the fact that the discrete Chebyshev transformation of the [Formula: see text]-th order eliminates automatically the polynomial trend of the ([Formula: see text]−1) order. Using the method of artificial trend, it was found that, under the real experimental conditions, the intensity of Chebyshev spectral lines with numbers higher than 1 is resistant to a strong trend of random process. This effect is observed when we use both the arithmetic averaging and the median. The Chebyshev spectral approach is a powerful tool for spectral analysis of random time series with a strong trend.