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The purpose of this paper is to show that major reversals of an index (specifically BIST-30 index) can be detected uniquely on the date of reversal by checking the extreme outliers in the rate of change series using daily closing prices.

The extreme outliers are determined by checking if either the rate of change series or the volatility of the rate of change series displays more than two standard deviations on the date of reversal. Furthermore; wavelet analysis is also utilized for this purpose by checking the extreme outlier characteristics of the A1 (approximation level 1) and D3 (detail level 3) wavelet components.

Paper investigates ten major reversals of BIST-30 index during a five year period. It conclusively shows that all these major reversals are characterized by extreme outliers mentioned above. The paper also checks if these major reversals are unique in the sense of being observed only on the date of reversal but not before. The empirical results confirm the uniqueness. The paper also demonstrates empirically the fact that extreme outliers are associated only with major reversals but not minor ones.

The results are important for fund managers for whom the timely identification of the initial phase of a major bullish or bearish trend is crucial. Such timely identification of the major reversals is also important for the hedging applications since a major issue in the practical implementation of the stock index futures as a hedging instrument is the correct timing of derivatives positions.

To the best of the author’ knowledge; this is the first study dealing with the issue of major reversal identification. This is evidently so for the BIST-30 index and the use of extreme outliers for this purpose is also a novelty in the sense that neither the use of rate of change extremity nor the use of wavelet decomposition for this purpose was addressed before in the international literature.

The purpose of this paper is to initiate investigations to develop near infrared (NIR) spectroscopy coupled with spectral dimensionality reduction and multivariate calibration methods to rapidly measure cotton content in blend fabrics.

In total, 124 and 41 samples were used to calibrate models and assess the performance of the models, respectively. The raw spectra are transformed into wavelet coefficients. Multivariate calibration methods of partial least square (PLS), extreme learning machine (ELM) and least square support vector machine (LS-SVM) were employed to develop the models using 100 wavelet coefficients. Through comparing the performance of PLS, ELM and LS-SVM models with new samples, the optimal model of cotton content was obtained with the LS-SVM model.

The correlation coefficient of prediction (r_p) and root mean square errors of prediction were 0.99 and 4.37 percent, respectively. The results suggest that NIR spectroscopy, combining with the LS-SVM method, has significant potential to quantitatively analyze cotton content in blend fabrics.

It may have commercial and regulatory potential to avoid time-consuming work, costly and laborious chemical analysis for cotton content in blend fabrics.

In this chapter we perform a Monte Carlo simulation study of the errors-in-variables model examined in Ramsey, Gallegati, Gallegati, and Semmler (2010) by using a wavelet multiresolution approximation approach. Differently from previous studies applying wavelets to errors-in-variables problem, we use a sequence of multiresolution approximations of the variable measured with error ranging from finer to coarser scales. Our results indicate that multiscale approximations to the variable observed with error based on the coarser scales provide an unbiased asymptotically efficient estimator that also possess good finite sample properties.

The present study utilizes daily mean time series of meteorological parameters (air temperature, relative humidity, barometric pressure and wind speed) and daily totals of rainfall data to understand the changes in these parameters during 17 years period i.e. 1990 to 2006. The analysis of the above data is made using continuous and discrete wavelet transforms because it provides a time‐frequency representation of an analyzed signal in the time domain. Moreover, in the recent years, wavelet methods have become useful and powerful tools for analysis of the variations, periodicities, trends in time series in general and meteorological parameters in particular. In present study, both continues and discrete wavelet transforms were used and found to be capable of showing the increasing or decreasing trends of the meterorological parameters with. The seasonal variability was also very well represented by the wavelet analysis used in this study. High levels of compressions were obtained retaining the originality of the signals.

Interturn winding faults, one of the most important causes of power transformers failures, cannot be detected by existing detection methods until they develop into high‐level faults with more severe damage to the transformer. The purpose of this paper is to describe development of a new discrete wavelet transform (DWT) based approach for detection of winding interturn faults.

The following approach was accomplished for development of the proposed fault detection method in this study. The DWT was first applied to decompose the terminal current signals of a transformer, which in turn were obtained from simulations using a finite elements method model of the transformer, into a series of wavelet components. Based on the characteristic features associated with interturn faults extracted from the decomposed waveforms of the terminal currents, a detection scheme was developed. An experimental setup was used to validate the proposed detection method.

The results of this study demonstrate the efficacy of DWT applied on terminal currents of the transformer to identify interturn faults on the windings well before such faults lead to a catastrophic failure. It is believed that, based on the present findings, there definitely exists scope for improving interturn fault diagnosis with wavelet transform.

Performing more detailed studies to find all relevant characteristics of the wavelet transform in this application, identifying the location of the faulted turns along winding, applying the method for indicating early stages of turn insulation deterioration and evaluating other type of wavelets for this application would be some future directions of this research.

With the proposed method, it is becoming possible to detect early signs of the fault occurrence, so that the necessary corrective actions can be taken to prevent long‐lasting outages and reduce down times of the faulty power transformer. The method will be particularly useful as a complement for the classical protection devices of the power transformers.

Some recent studies have been carried out regarding the application of DWT for discrimination between an internal fault and other disturbances such as magnetizing inrush and external faults. This paper extends those studies for the detection of interturn faults using more quantitative and qualitative characteristics features.

This paper presents a novel framework for solving elliptic partial differential equations (PDEs) over irregularly spaced meshes on bounded domains.

Second‐generation wavelet construction gives rise to a powerful generalization of the traditional hierarchical basis (HB) finite element method (FEM). A framework based on piecewise polynomial Lagrangian multiwavelets is used to generate customized multiresolution bases that have not only HB properties but also additional qualities.

For the 1D Poisson problem, we propose – for any given order of approximation – a compact closed‐form wavelet basis that block‐diagonalizes the stiffness matrix. With this wavelet choice, all coupling between the coarse scale and detail scales in the matrix is eliminated. In contrast, traditional higher‐order (n>1) HB do not exhibit this property. We also achieve full scale‐decoupling for the 2D Poisson problem on an irregular mesh. No traditional HB has this quality in 2D.

Similar techniques may be applied to scale‐decouple the multiresolution finite element (FE) matrices associated with more general elliptic PDEs.

By decoupling scales in the FE matrix, the wavelet formulation lends itself particularly well to adaptive refinement schemes.

The paper explains second‐generation wavelet construction in a Lagrangian FE context. For 1D higher‐order and 2D first‐order bases, we propose a particular choice of wavelet, customized to the Poisson problem. The approach generalizes to other elliptic PDE problems.

Provides an introduction into wavelets and illustrates their application with two examples. The wavelet transform provides the analyst with a scaleable time‐frequency representation of the signal, which may uncover details not evidenced by conventional signal processing techniques. The signals used in this paper are Doppler ultrasound recordings of blood flow velocity taken from the internal carotid artery and the femoral artery. Shows how wavelets can be used as an alternative signal processing tool to the short time Fourier transform for the extraction of the time‐frequency distribution of Doppler ultrasound signals. Implements wavelet‐based adaptive filtering for the extraction of maximum blood velocity envelopes in the post processing of Doppler signals.

This paper suggests a novel methodology for building robust information processing systems based on wavelets and artificial neural networks (ANN) to be applied either in decision‐making tasks based on image information or in signal prediction and modeling tasks. The efficiency of such systems is increased when they simultaneously use input information in its original and wavelet transformed form, invoking ANN technology to fuse the two different types of input. A quality control decision‐making system as well as a signal prediction system have been developed to illustrate the validity of our approach. The first one offers a solution to the problem of defect recognition for quality control systems. The second application improves the quality of time series prediction and signal modeling in the domain of NMR. The accuracy obtained shows that the proposed methodology deserves the attention of designers of effective information processing systems.

Fueled by the rapid growth of internet, steganography has emerged as one of the promising techniques in the communication system to obscure the data. Steganography is defined as the process of concealing the data or message within media files without affecting the perception of the image. Media files, like audio, video, image, etc., are utilized to embed the message. Nowadays, steganography is also used to transmit the medical information or diagnostic reports. The paper aims to discuss these issues.

In this paper, the novel wavelet transform-based steganographic method is proposed for secure data communication using OFDM system. The embedding and extraction process in the proposed steganography method exploits the wavelet transform. Initially, the cost matrix is estimated by the following three aspects: pixel intensity, edge transformation and wavelet transform. The cost estimation matrix provides the location of the cover image where the message is to be entrenched. Then, the wavelet transform is utilized to embed the message into the cover image according to the cost value. Subsequently, in the extraction process, the wavelet transform is applied to the embedded image to retrieve the message efficiently. Finally, in order to transfer the secret information over the channel, the newly developed wavelet-based steganographic method is employed for the OFDM system.

The experimental results are evaluated and performance is analyzed using PSNR and MSE parameters and then compared with existing systems. Thus, the outcome of our wavelet transform steganographic method achieves the PSNR of 71.5 dB which ensures the high imperceptibility of the image. Then, the outcome of the OFDM-based proposed steganographic method attains the higher PSNR of 71.07 dB that proves the confidentiality of the message.

In the authors’ previous work, the embedding and extraction process was done based on the cost estimation matrix. To enhance the security throughout the communication system, the novel wavelet-based embedding and extraction process is applied to the OFDM system in this paper. The idea behind this method is to attain a higher imperceptibility and robustness of the image.

The purpose of this paper is to present a new hierarchical finite element formulation for approximation in time.

The present approach using wavelets as basis functions provides a global control over the solution error as the equation of motion is satisfied for the entire duration in the weighted integral sense. This approach reduces the semi‐discrete system of equations in time to be solved to a single algebraic problem, in contrast to step‐by‐step time integration methods, where a sequence of algebraic problems are to be solved to compute the solution.

The proposed formulation has been validated for both inertial and wave propagation types of problems. The stability and accuracy characteristics of the proposed formulation has been examined and is found to be energy conserving.

The paper presents a new hierarchical finite element formulation for the solution of structural dynamics problems. This formulation uses wavelets as the analyzing basis for the desired transient solution. It is found to be very well behaved in solution of wave‐propagation problems.