Search results for: Fourier series analysis

Authors: Kejal Khatri, Vishnu Narayan Mishra

Abstract:

We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Balachandra Kumaraswamy, P. G. Poonacha

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Automatic Music Information Retrieval has been one of the challenging topics of research for a few decades now with several interesting approaches reported in the literature. In this paper we have developed a pitch extraction method based on a finite Fourier series approximation to the given window of samples. We then estimate pitch as the fundamental period of the finite Fourier series approximation to the given window of samples. This method uses analysis of the strength of harmonics present in the signal to reduce octave as well as harmonic errors. The performance of our method is compared with three best known methods for pitch extraction, namely, Yin, Windowed Special Normalization of the Auto-Correlation Function and Harmonic Product Spectrum methods of pitch extraction. Our study with artificially created signals as well as music files show that Fourier Approximation method gives much better estimate of pitch with less octave and harmonic errors.

Keywords: pitch, fourier series, yin, normalization of the auto- correlation function, harmonic product, mean square error

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Authors: Emanuel Guariglia

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In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry.

Keywords: Chebyshev wavelets, Fourier transform, connection coefficients, Taylor series, local fractional derivative, Cantor set

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Authors: Jatinderdeep Kaur

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In this paper, the results of Kano from one-dimensional cosine and sine series are extended to two-dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as the class of semi convexity and class R are extended from one dimension to two dimensions. Under these extended classes, I have checked the function f(x,y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function. Further, some results are obtained which are the generalization of Moricz's results.

Keywords: conjugate dirichlet kernel, conjugate fejer kernel, fourier series, semi-convexity

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Authors: Smita Sonker

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Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski.

Keywords: signals, trigonometric fourier approximation, class W(L^r, \xi(t), conjugate fourier series

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Authors: Rufus Temidayo Akinnubi, M. O. Adeniyi

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Existing diurnal air temperature models simulate night time air temperature over Nigeria with high biases. An improved parameterization is presented for modeling the diurnal pattern of air temperature (Ta) which is applicable in the calculation of turbulent heat fluxes in Global climate models, based on Nigeria Micrometeorological Experimental site (NIMEX) surface layer observations. Five diurnal Ta models for estimating hourly Ta from daily maximum, daily minimum, and daily mean air temperature were validated using root-mean-square error (RMSE), Mean Error Bias (MBE) and scatter graphs. The original Fourier series model showed better performance for unstable air temperature parameterizations while the stable Ta was strongly overestimated with a large error. The model was improved with the inclusion of the atmospheric cooling rate that accounts for the temperature inversion that occurs during the nocturnal boundary layer condition. The MBE and RMSE estimated by the modified Fourier series model reduced by 4.45 oC and 3.12 oC during the transitional period from dry to wet stable atmospheric conditions. The modified Fourier series model gave good estimation of the diurnal weather patterns of Ta when compared with other existing models for a tropical environment.

Keywords: air temperature, mean bias error, Fourier series analysis, surface energy balance,

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Authors: Hare Krishna Nigam

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In this paper, for the first time, (E,q)(C,2) product summability method is introduced and two quite new results on degree of approximation of the function f belonging to Lip (alpha,r)class and W(L(r), xi(t)) class by (E,q)(C,2) product means of Fourier series, has been obtained.

Keywords: Degree of approximation, (E, q)(C, 2) means, Fourier series, Lebesgue integral, Lip (alpha, r)class, W(L(r), xi(t))class of functions

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Authors: A. S. Issa, S. K. Q. AL-Omari

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In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Boehmian, Fourier integral, Fourier type integral, generalized quotient

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Authors: Smita Sonker, Uaday Singh

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Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

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Authors: Hisyam Hidayatullah

Abstract:

This world events consciously or not realize everything has a pattern, until the events of the universe according to the Big Bang theory of the solar system which makes so regular in the rotation. The author would like to create a results curve area between the quadratic function y=kx2 and line y=ka2 using GeoGebra application version 4.2. This paper can provide a series that is no less interesting with Fourier series, so that will add new material about the series can be calculated with sigma notation. In addition, the ranks of the unique natural numbers of extensive changes in established areas. Finally, this paper provides analytical and geometric proof of the vast area in between the lines and curves that give the area is formed by y=ka2 dan kurva y=kx2, x-axis, line x=√a and x=-√a make a series of numbers for k=1 and a ∈ original numbers. ∑_(i=0)^n=(4n√n)/3=0+4/3+(8√2)/3+4√3+⋯+(4n√n)/3. The author calls the series “H154M”.

Keywords: sequence, series, sigma notation, application GeoGebra

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Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia

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The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: conjugate Dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums

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Authors: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: Erzen Muharemi, Emmanuel De Jaeger, Jos Knockaert

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The work presented here investigates the modeling of power electronics converters in terms of their harmonic production. Specifically, it addresses high-frequency emissions in the range of 2-150 kHz, referred to as supraharmonics. This paper models a conventional converter, namely the boost converter used as an active power factor corrector (APFC). Furthermore, the modeling is extended to the case of the interleaved boost converter, which offers advantages such as halving the emissions. Finally, a comparison between the theoretical, numerical, and experimental results will be provided.

Keywords: APFC, boost converter, converter modeling, double fourier series, supraharmonics

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Authors: Manana Chumburidze

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We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Salim Belouettar, Kodjo Attipou

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The thermal wrinkling behavior of thin membranes is investigated. The Fourier double scale series are used to deduce the macroscopic membrane wrinkling equations. The obtained equations account for the global and local wrinkling modes. Numerical examples are conducted to assess the validity of the approach developed. Compared to the finite element full model, the present model needs only few degrees of freedom to recover accurately the bifurcation curves and wrinkling paths. Different parameters such as membrane’s aspect ratio, wave number, pre-stressed membranes are discussed from a numerical point of view and the properties of the wrinkles (critical load, wavelength, size and location) are presented.

Keywords: wrinkling, thermal stresses, Fourier series, thin membranes

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Authors: A. Cherifi, B. S. Bouazza, A. O. Dahman, B. Yagoubi

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Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed.

Keywords: OFDM, fractional fourier transform, internet and information technology

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Authors: Siriporn Meenanan

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The objective of this study is to investigate the attitude of Thai students towards the Thai series "Hormones the Series Season 2". This study was conducted in the quantitative research, and the questionnaires were used to collect data from 400 people of the sample group. Descriptive statistics were used in data analysis. The findings reveal that most participants have positive comments regarding the series. They strongly agreed that the series reflects on the way of life and problems of teenagers in Thailand. Hence, the participants believe that if adults have a chance to watch the series, they will have the better understanding of the teenagers. In addition, the participants also agreed that the contents of the play are appropriate and satisfiable as the contents of “Hormones the Series Season 2” will raise awareness among the teens and use it as a guide to prevent problems that might happen during their teenage life.

Keywords: content analysis, attitude, Thai series, hormones the Series

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Authors: Sandra Baßler, Peter Dünow, Mathias Marquardt

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A Fourier series based learning control (FSBLC) algorithm for tracking trajectories of mechanical systems with unknown nonlinearities is presented. Two processes are introduced to which the FSBLC with PD controller is applied. One is a simplified service robot capable of climbing stairs due to special wheels and the other is a propeller driven pendulum with nearly the same requirements on control. Additionally to the investigation of learning the feed forward for the desired trajectories some considerations on the implementation of such an algorithm on low cost microcontroller hardware are made. Simulations of the service robot as well as practical experiments on the pendulum show the capability of the used FSBLC algorithm to perform the task of improving control behavior for repetitive task of such mechanical systems.

Keywords: climbing stairs, FSBLC, ILC, service robot

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Authors: A. Cherifi, B. Bouazza, A. O. Dahmane, B. Yagoubi

Abstract:

Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed.

Keywords: OFDM, (FrFT) fractional fourier transform, optical OFDM, equalization algorithm

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Authors: Xianwei Zheng, Yuan Yan Tang

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Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals.

Keywords: graph signals, windowed graph Fourier transform, windowed graph Fourier frames, vertex frequency analysis

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization

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Authors: Olivier Delage, Thierry Portafaix, Hassan Bencherif, Guillaume Guimbretiere

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Most observation data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several time and space scales. As a consequence, measurements time series in geophysics have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at all time-scales and require a time-frequency representation to analyze their variability. Empirical Mode Decomposition (EMD) is a relatively new technic as part of a more general signal processing method called the Hilbert-Huang transform. This analysis method turns out to be particularly suitable for non-linear and non-stationary signals and consists in decomposing a signal in an auto adaptive way into a sum of oscillating components named IMFs (Intrinsic Mode Functions), and thereby acts as a bank of bandpass filters. The advantages of the EMD technic are to be entirely data driven and to provide the principal variability modes of the dynamics represented by the original time series. However, the main limiting factor is the frequency resolution that may give rise to the mode mixing phenomenon where the spectral contents of some IMFs overlap each other. To overcome this problem, J. Gilles proposed an alternative entitled “Empirical Wavelet Transform” (EWT) which consists in building from the segmentation of the original signal Fourier spectrum, a bank of filters. The method used is based on the idea utilized in the construction of both Littlewood-Paley and Meyer’s wavelets. The heart of the method lies in the segmentation of the Fourier spectrum based on the local maxima detection in order to obtain a set of non-overlapping segments. Because linked to the Fourier spectrum, the frequency resolution provided by EWT is higher than that provided by EMD and therefore allows to overcome the mode-mixing problem. On the other hand, if the EWT technique is able to detect the frequencies involved in the original time series fluctuations, EWT does not allow to associate the detected frequencies to a specific mode of variability as in the EMD technic. Because EMD is closer to the observation of physical phenomena than EWT, we propose here a new technic called EAWD (Empirical Adaptive Wavelet Decomposition) based on the coupling of the EMD and EWT technics by using the IMFs density spectral content to optimize the segmentation of the Fourier spectrum required by EWT. In this study, EMD and EWT technics are described, then EAWD technic is presented. Comparison of results obtained respectively by EMD, EWT and EAWD technics on time series of ozone total columns recorded at Reunion island over [1978-2019] period is discussed. This study was carried out as part of the SOLSTYCE project dedicated to the characterization and modeling of the underlying dynamics of time series issued from complex systems in atmospheric sciences

Keywords: adaptive filtering, empirical mode decomposition, empirical wavelet transform, filter banks, mode-mixing, non-linear and non-stationary time series, wavelet

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Authors: Ramakrishna Rao Mamidi

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It is essential for Surface Mounted Permanent Magnet (SMPM) generators to determine the performance prediction and analyze the magnet’s air gap flux density wave shape. The flux density wave shape is neither a pure sine wave or square wave nor a combination. This is due to the variation of air gap reluctance between the stator and permanent magnets. The stator slot openings and the number of slots make the wave shape highly complicated. To reduce the complexity of analysis, approximations are made to the wave shape using Fourier analysis. In contrast to the traditional integration method, the Fourier coefficients, an and bn, are obtained by direct search method optimization. The wave shape with optimized coefficients gives a wave shape close to the desired wave shape. Harmonics amplitudes are worked out and compared with initial values. It can be concluded that the direct search method can be used for estimating Fourier coefficients for irregular wave shapes.

Keywords: direct search, flux plot, fourier analysis, permanent magnets

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Authors: Wiem Gadri

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This study delves into the intriguing properties of Pisot and Salem numbers within the framework of formal Laurent series over finite fields, a domain where these numbers’ spectral charac-teristics, Λm(β) and lm(β), have yet to be fully explored. Utilizing a methodological approach that combines algebraic number theory with the analysis of power series, we extend the foundational work of Erdos, Joo, and Komornik to this new setting. Our research uncovers bounds for lm(β), revealing how these depend on the degree of the minimal polynomial of β and thus offering a novel characterization of Pisot and Salem formal power series. The findings significantly contribute to our understanding of these numbers, highlighting their distribution and properties in the context of formal power series. This investigation not only bridges number theory with formal power series analysis but also sets the stage for further interdisciplinary research in these areas.

Keywords: Pisot numbers, Salem numbers, formal power series, over a finite field

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Authors: Chetsada Noknoi

Abstract:

The acceptance of Y series refers to the willingness and enjoyment of watching Y series without feeling different from general series. This occurs when people watch Y series and derive happiness and entertainment from it. The viewing experience has the most significant impact on Y series acceptance. This research aims to 1) investigate the levels of acceptance of sexual diversity, image of Y series Actors, media exposure, and Y series acceptance among the residents in three southern border provinces of Thailand, and 2) examine how acceptance of sexual diversity, actor perceptions in Y series, and media exposure influence Y series acceptance in these provinces. The sample consisted of 322 participants from the three southern border provinces of Thailand. The research instrument used was a questionnaire, and data were analyzed using frequency, percentage, mean, standard deviation, and multiple regression analysis. The findings revealed that overall, acceptance of sexual diversity, Image of Y series Actors, and Y series acceptance among the residents in three southern border provinces of Thailand were at a high level, while media exposure was moderate overall. However, the two factors that had the most significant impact on Y series acceptance in these provinces, ranked from highest to lowest influence, were media exposure and acceptance of sexual diversity. Both of these factors had a positive effect on Y series acceptance among the residents in three southern border provinces of Thailand. Collectively, these factors accounted for 40.7% of the variance in Y series acceptance among the residents in three southern border provinces of Thailand.

Keywords: acceptance, acceptance of sexual diversity, image of Y series actors, media exposure, Y series

Procedia PDF Downloads 78

Authors: O. Delage, H. Bencherif, T. Portafaix, A. Bourdier

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The main purpose of time series analysis is to learn about the dynamics behind some time ordered measurement data. Two approaches are used in the literature to get a better knowledge of the dynamics contained in observation data sequences. The first of these approaches concerns time series decomposition, which is an important analysis step allowing patterns and behaviors to be extracted as components providing insight into the mechanisms producing the time series. As in many cases, time series are short, noisy, and non-stationary. To provide components which are physically meaningful, methods such as Empirical Mode Decomposition (EMD), Empirical Wavelet Transform (EWT) or, more recently, Empirical Adaptive Wavelet Decomposition (EAWD) have been proposed. The second approach is to reconstruct the dynamics underlying the time series as a trajectory in state space by mapping a time series into a set of Rᵐ lag vectors by using the method of delays (MOD). Takens has proved that the trajectory obtained with the MOD technic is equivalent to the trajectory representing the dynamics behind the original time series. This work introduces the singular spectrum decomposition (SSD), which is a new adaptive method for decomposing non-linear and non-stationary time series in narrow-banded components. This method takes its origin from singular spectrum analysis (SSA), a nonparametric spectral estimation method used for the analysis and prediction of time series. As the first step of SSD is to constitute a trajectory matrix by embedding a one-dimensional time series into a set of lagged vectors, SSD can also be seen as a reconstruction method like MOD. We will first give a brief overview of the existing decomposition methods (EMD-EWT-EAWD). The SSD method will then be described in detail and applied to experimental time series of observations resulting from total columns of ozone measurements. The results obtained will be compared with those provided by the previously mentioned decomposition methods. We will also compare the reconstruction qualities of the observed dynamics obtained from the SSD and MOD methods.

Keywords: time series analysis, adaptive time series decomposition, wavelet, phase space reconstruction, singular spectrum analysis

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Authors: Muhammad Tariq, Hammad Tahir, Fawwad Mahmood Butt

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Purpose: This study attempts to examine the best forecasting methodologies in the time series. The time series forecasting models such as VAR, ARCH and the ARMA are considered for the analysis. Methodology: The Bench Marks or the parameters such as Adjusted R square, F-stats, Durban Watson, and Direction of the roots have been critically and empirically analyzed. The empirical analysis consists of time series data of Consumer Price Index and Closing Stock Price. Findings: The results show that the VAR model performed better in comparison to other models. Both the reliability and significance of VAR model is highly appreciable. In contrary to it, the ARCH model showed very poor results for forecasting. However, the results of ARMA model appeared double standards i.e. the AR roots showed that model is stationary and that of MA roots showed that the model is invertible. Therefore, the forecasting would remain doubtful if it made on the bases of ARMA model. It has been concluded that VAR model provides best forecasting results. Practical Implications: This paper provides empirical evidences for the application of time series forecasting model. This paper therefore provides the base for the application of best time series forecasting model.

Keywords: forecasting, time series, auto regression, ARCH, ARMA

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Tak-Chung Fu, Ying-Kit Hung, Fu-Lai Chung

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In the field of time series data mining, the concept of the Perceptually Important Point (PIP) identification process is first introduced in 2001. This process originally works for financial time series pattern matching and it is then found suitable for time series dimensionality reduction and representation. Its strength is on preserving the overall shape of the time series by identifying the salient points in it. With the rise of Big Data, time series data contributes a major proportion, especially on the data which generates by sensors in the Internet of Things (IoT) environment. According to the nature of PIP identification and the successful cases, it is worth to further explore the opportunity to apply PIP in time series ‘Big Data’. However, the performance of PIP identification is always considered as the limitation when dealing with ‘Big’ time series data. In this paper, two distributed versions of PIP identification based on the Specialized Binary (SB) Tree are proposed. The proposed approaches solve the bottleneck when running the PIP identification process in a standalone computer. Improvement in term of speed is obtained by the distributed versions.

Keywords: distributed computing, performance analysis, Perceptually Important Point identification, time series data mining

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Authors: Valeria Bondarenko

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We proposed algorithms for: estimation of parameters fBm (volatility and Hurst exponent) and for the approximation of random time series by functional of fBm. We proved the consistency of the estimators, which constitute the above algorithms, and proved the optimal forecast of approximated time series. The adequacy of estimation algorithms, approximation, and forecasting is proved by numerical experiment. During the process of creating software, the system has been created, which is displayed by the hierarchical structure. The comparative analysis of proposed algorithms with the other methods gives evidence of the advantage of approximation method. The results can be used to develop methods for the analysis and modeling of time series describing the economic, physical, biological and other processes.

Keywords: mathematical model, random process, Wiener process, fractional Brownian motion

Procedia PDF Downloads 358