Wavelet Scale Research Articles

Spectral Variations of Reclamation Vegetation in Rare Earth Mining Areas Using Continuous–Discrete Wavelets and Their Impact on Chlorophyll Estimation

Ion-adsorption rare earth mining areas are primarily situated in the hilly regions of southern China. However, mining activities have led to extensive deforestation of the original vegetation. The reclamation vegetation planted for ecological restoration faces significant challenges in surviving under environmental stresses, including heavy metal pollution, ammonia nitrogen contamination, and soil drought. To rapidly and accurately monitor the growth of reclamation vegetation, this study investigates the spectral variations and their impact on the accuracy of chlorophyll estimation, utilizing hyperspectral data and relative chlorophyll content (SPAD). Specifically, continuous–discrete wavelet transforms were applied, along with the original spectra and first derivative spectra, to enhance spectral anomalies in the reclamation vegetation and identify chlorophyll-sensitive spectral features. Additionally, multiple linear stepwise regression and backpropagation neural network models were employed to estimate chlorophyll content. The results revealed the following: (1) the d5 and d6 scales of the discrete wavelet effectively highlighted spectral anomalies in the reclamation vegetation; (2) Salix japonica (Salix fragilis L.), among typical reclamation species, exhibited poor adaptability to the environmental conditions of the rare earth mining area; (3) the backpropagation neural network model demonstrated superior performance in chlorophyll estimation, with the spectral features Fir, Fir_d4, Fir_d5, and Fir_d6 significantly enhancing the accuracy of the model, achieving an R2 of 0.93 for Photinia glabra (Photinia glabra (Thunb.) Maxim.). The application of continuous–discrete wavelet transforms to hyperspectral data significantly improves the precision of chlorophyll estimation, underscoring the potential of this method for the rapid monitoring of reclamation vegetation growth.

Analysis of the Response of Shallow Groundwater Levels to Precipitation Based on Different Wavelet Scales—A Case Study of the Datong Basin, Shanxi

The rise in shallow groundwater levels is typically triggered by precipitation recharge, exhibiting a certain lag relative to precipitation changes. Therefore, identifying the response mechanism of shallow groundwater levels to precipitation is crucial for clarifying the interaction between precipitation and groundwater. However, the response mechanism of groundwater levels to precipitation is complex and variable, influenced by various hydrogeological and geographical conditions, and often exhibits significant nonlinear characteristics. To address this issue, this study employs methods such as continuous wavelet transform, cross wavelet transform, and wavelet coherence to analyze the response patterns of groundwater levels to precipitation at different wavelet scales in the Datong Basin from 2013 to 2022: (i) At short wavelet scales (10.33~61.96 d), the groundwater level dynamics respond almost instantaneously to extreme rainfall; (ii) At medium wavelet scales(61.96~247.83 d), the precipitation-groundwater recharge process shows characteristics of either rapid recovery or significant delay; (iii) At long wavelet scales (247.83~495.67 d), three potential groundwater processes were identified in the Datong Basin, exhibiting long-term lag responses throughout this study period, with lag times of 11.18 days, 148.75 days, and 151.49 days, respectively. Furthermore, the results indicate that the lag response time of shallow groundwater levels to precipitation is not only related to the wavelet scale but also to the identified depth conditions of different groundwater regions, groundwater extraction intensity, precipitation intensity, and aquifer lithology. This study distinguishes the temporal and spatial response mechanisms of shallow groundwater to precipitation at different wavelet scales, and this information may further aid in understanding the interaction between precipitation and groundwater levels.

A novel fatigue driving detection method based on whale optimization and Attention-enhanced GRU

Fatigue driving has emerged as the predominant causative factor for road traffic safety accidents. The fatigue driving detection method, derived from laboratory simulation data, faces challenges related to imbalanced data distribution and limited recognition accuracy in practical scenarios. In this study, we introduce a novel approach utilizing a gated recurrent neural network method, employing whale optimization algorithm for fatigue driving identification. Additionally, we incorporate an attention mechanism to enhance identification accuracy. Initially, this study focuses on the driver's operational behavior under authentic vehicular conditions. Subsequently, it employs wavelet energy entropy, scale entropy, and singular entropy analysis to extract the fatigue-related features from the driver's operational behavior. Subsequently, this study adopts the cross-validation recursive feature elimination method to derive the optimal fatigue feature index about operational behavior. To effectively capture long-range dependence relationships, this study employs the gated recurrent unit neural network method. Lastly, an attention mechanism is incorporated in this study to concentrate on pivotal features within the data sequence of driving behavior. It assigns greater weight to crucial information, mitigating information loss caused by the extended temporal sequence. Experimental results obtained from real vehicle data demonstrate that the proposed method achieves an accuracy of 89.84% in third-level fatigue driving detection, with an omission rate of 10.99%. These findings affirm the feasibility of the approach presented in this study.

Estimation of Winter Wheat Chlorophyll Content Based on Wavelet Transform and the Optimal Spectral Index

Hyperspectral remote sensing technology plays a vital role in advancing modern precision agriculture due to its non-destructive and efficient nature. To achieve accurate monitoring of winter wheat chlorophyll content, this study utilized 68 sets of chlorophyll content data and hyperspectral measurements collected during the jointing stage of winter wheat over two consecutive years (2019–2020), under various fertilization types and nitrogen application levels. Continuous wavelet transform was applied to transform the original reflectance, ranging from 21 to 210, and the correlation matrix method was utilized to identify the spectral index at each scale, with the highest correlation to winter wheat chlorophyll content as the optimal spectral index combination input. Subsequently, winter wheat chlorophyll content prediction models were developed using three machine learning methods: random forest (RF), support vector machine (SVM), and a genetic algorithm-optimized backpropagation neural network (GA-BP). The results indicate that the spectral data processed through continuous wavelet transform at seven scales, from 21 to 27, show the highest correlation with winter wheat chlorophyll content at a scale of 26, with a correlation coefficient of 0.738, compared with the correlation of 0.611 of the original reflectance, and the accuracy is improved by 20.7%. The average highest correlation value between the spectral index at scale 26 and winter wheat chlorophyll content is 0.752. As the scale of wavelet transform increases, the correlation between the spectral index and winter wheat chlorophyll content and the accuracy of the predictive model show a trend of first increasing and then decreasing. The optimal input variables for predicting winter wheat chlorophyll content and the best machine learning method are the spectral data at a scale of 26 processing combined with the GA-BP model. The optimal predictive model has a validation set coefficient of determination (R2) of 0.859, root mean square error (RMSE) of 1.366, and mean relative error (MRE) of 2.920%. The results show that the prediction model can provide a technical basis for improving the hyperspectral inversion accuracy of winter wheat chlorophyll and modern precision agriculture.

Research on features and localization of AE signals from the mechanical body of industrial robots based on WD-EMD

Abstract In order to reveal the propagation characteristics of acoustic emission (AE) signals in the body of industrial machinery, the characteristic frequencies and wave speeds of AE signals propagated on the interior and exterior surfaces (IS and ES) of the body were extracted. Subsequently, an algorithm utilizing characteristic frequency and time difference of arrival (TDOA) is proposed for the identification and localization of AE sources. Initially, an AE source is induced on the IS and ES of the body using the pencil-lead break method in accordance to ASTM standards, and the AE signal is captured by two piezoelectric sensors at a sampling frequency of 3 MHz. Then, to avoid the limitations of wavelet decomposition using self-selected wavelet scale and the problem that a single indicator cannot properly evaluate the correlation between independent mode functions (IMFs) with the original signal, this paper will conduct 4-layer wavelet decomposition of the original signal according to the response frequency range of the sensor, and select the wavelet details within the stable range of the response frequency of the sensor for preliminary reconstruction,and then the empirical mode decomposition (EMD) method is used to decompose the de-noised AE signal into 7 IMFs, and the AE waveform is reconstructed by the combined information of correlation coefficient and variance accounted for. Secondly, the reconstruction method combined with EMD analysis and a single index is compared with the proposed method in this paper to verify the reliability of the proposed method. In addition, the frequency domain characteristics of AE signal propagation process on the IS and ES of the body are extracted. Finally, based on the TDOA principle, the propagation speed of AE signal on the IS and ES of the body is calculated. Based on the geometric relationship between the AE source and two sensors, an algorithm for the location of the AE source is proposed. The results show that the proposed signal reconstruction method can effectively extract the features of AE signals, and the average positioning accuracy of the localization algorithm based on characteristic frequency and TDOA reaches 0.86%.

Wavelet analysis on a generalized helix space curves and its examples

In this paper, wavelet transform on a generalized helix space curves are investigated, including of local continuous wavelet transform at some point and discrete wavelet transform on a class of helix curves. Firstly, a class of helix space curves are introduced and the parameter equations are given. Then the dilation operator and translation on the function ψ(ξ0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi^{{(\\xi_{{0}} )}}$$\\end{document} is properly defined by the local projection at some point from a space curve on the unit sphere onto its tangent line. The local continuous wavelet transform and its reconstruction formula are deduced at some point of a space curve on the unit sphere. On the other hand, According to the discretization of length-preserving projection, discrete wavelet transform is lifted onto a helix space curve, such as a circular helix curve. Based on length-preserving projection, the some properties are discussed, such as two-scale sequences of scaling function and wavelet, orthogonality, decomposition formula and so on. Finally, two examples are given for our discussion. One example is illustrating the application of local continuous wavelet transform at some point of a space curve. The result shows the signal at some point of a space curve can be reconstructed by local continuous wavelet method. The norm of the error is 0.3783 between original signal and reconstructed signal in this example. The other numerical example is given for decomposing and reconstructing with the signal on a circular helix curve. The result shows the signal on a helix space curve can be decomposed and reconstructed by the length-preserving projection. The norm of the error is 8.0741 × 10−11 between original signal and reconstructed signal. The figures are shown for the simulation results.

Tool wear monitoring based on scSE-ResNet-50-TSCNN model integrating machine vision and force signals

In the realm of mechanical machining, tool wear is an unavoidable phenomenon. Monitoring the condition of tool wear is crucial for enhancing machining quality and advancing automation in the manufacturing process. This paper investigates an innovative approach to tool wear monitoring that integrates machine vision with force signal analysis. It relies on a deep residual two-stream convolutional model optimized with the scSE (concurrent spatial and channel squeeze and excitation) attention mechanism (scSE-ResNet-50-TSCNN). The force signals are converted into the corresponding wavelet scale images following wavelet threshold denoising and continuous wavelet transform. Concurrently, the images undergo processing using contrast limited adaptive histogram equalization and the structural similarity index method, allowing for the selection of the most suitable image inputs. The processed data are subsequently input into the developed scSE-ResNet-50-TSCNN model for precise identification of the tool wear state. To validate the model, the paper employed X850 carbon fibre reinforced polymer and Ti–6Al–4V titanium alloy as laminated experimental materials, conducting a series of tool wear tests while collecting pertinent machining data. The experimental results underscore the model’s effectiveness, achieving an impressive recognition accuracy of 93.86%. When compared with alternative models, the proposed approach surpasses them in performance on the identical dataset, showcasing its efficient monitoring capabilities in contrast to single-stream networks or unoptimized networks. Consequently, it excels in monitoring tool wear status and promots crucial technical support for enhancing machining quality control and advancing the field of intelligent manufacturing.

Distinctive Phase Interdependency Model for Retinal Vasculature Delineation in OCT-Angiography Images.

Automatic detection of retinal vasculature in optical coherence tomography angiography (OCTA) images faces several challenges such as the closely located capillaries, vessel discontinuity and high noise level. This paper introduces a new distinctive phase interdependency model to address these problems for delineating centerline patterns of the vascular network. We capture the inherent property of vascular centerlines by obtaining the inter-scale dependency information that exists between neighboring symmetrical wavelets in complex Poisson domain. In particular, the proposed phase interdependency model identifies vascular centerlines as the distinctive features that have high magnitudes over adjacent symmetrical coefficients whereas the coefficients caused by background noises are decayed rapidly along adjacent wavelet scales. The potential relationships between the neighboring Poisson coefficients are established based on the coherency of distinctive symmetrical wavelets. The proposed phase model is assessed on the OCTA-500 database (300 OCTA images + 200 OCT images), ROSE-1-SVC dataset (9 OCTA images), ROSE-1 (SVC+ DVC) dataset (9 OCTA images), and ROSE-2 dataset (22 OCTA images). The experiments on the clinically relevant OCTA images validate the effectiveness of the proposed method in achieving high-quality results. Our method produces average FScore of 0.822, 0.782, and 0.779 on ROSE-1-SVC, ROSE-1 (SVC+ DVC), and ROSE-2 datasets, respectively, and the FScore of 0.910 and 0.862 on OCTA_6mm and OCT_3mm datasets (OCTA-500 database), respectively, demonstrating its superior performance over the state-of-the-art benchmark methods.

Unsupervised Wavelet-Feature Correlation Ratio Markov Clustering Algorithm for Remotely Sensed Images

The spectrums of one type of object under different conditions have the same features (up, down, protruding, concave) at the same spectral positions, which can be used as primary parameters to evaluate the difference among remotely sensed pixels. The wavelet-feature correlation ratio Markov clustering algorithm (WFCRMCA) for remotely sensed data is proposed based on an accurate description of abrupt spectral features and an optimized Markov clustering in the wavelet feather space. The peak points can be captured and identified by applying a wavelet transform to spectral data. The correlation ratio between two samples is a statistical calculation of the matched peak point positions on the wavelet feature within an adjustable spectrum domain or a range of wavelet scales. The evenly sampled data can be used to create class centers, depending on the correlation ratio threshold at each Markov step, accelerating the clustering speed by avoiding the computation of Euclidean distance for traditional clustering algorithms, such as K-means and ISODATA. Markov clustering applies several strategies, such as a simulated annealing method and gradually shrinking the clustering size, to control the clustering convergence. It can quickly obtain the best class centers at each clustering temperature. The experimental results of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) and Thermal Mapping (TM) data have verified its acceptable clustering accuracy and high convergence velocity.

Geological detection of hard rocks by GPR and signal time-frequency characteristics analysis in urban underground trenchless construction

Abstract The hard rocks in the stratum can pose safety risks and hinder the progress of urban underground tunnel construction using shield and jacking methods, thereby reducing construction efficiency and increasing construction costs. This paper utilizes wavelet scale energy spectrum, wavelet packet theory and statistical methods to conduct research on the detection of special geological formations such as hard rocks and voids, as well as the analysis of their signal time-frequency characteristics based on the ground-penetrating radar (GPR) technique. On the basis of calibrating the permittivity of different types of rock blocks, we established a forward model for detecting hard rocks and voids, and the simulated signals were analyzed in the time and frequency domains. Subsequently, laboratory experiments were conducted to perform GPR tests on different types of hard rocks in natural and water-saturated states and voids, to explore the time-frequency characteristics, frequency band energy variations, and statistical patterns of typical single-trace signals. The results show that the granite detection signal contains more low-frequency components, the sandstone detection signal contains more medium-low frequency components, while the limestone detection signal contains more medium-high frequency components in their natural state; the signal from the karst cave has relatively more low-frequency components than the signal from the empty cavity. The geometric shape of the rock has no influence on the dominant frequency and time-frequency distribution of its reflection signal. Generally, rocks with higher rebound values (hardness) also exhibit larger variance and standard deviation in frequency band energy. The research has important theoretical significance and practical value for the measurement and assessment of special geological features such as hard rocks and voids in urban underground trenchless construction.

Automatic muscle impedance and nerve analyzer (AMINA) as a novel approach for classifying bioimpedance signals in intraoperative pelvic neuromonitoring

Frequent complications arising from low anterior resections include urinary and fecal incontinence, as well as sexual disorders, which are commonly associated with damage to the pelvic autonomic nerves during surgery. To assist the surgeon in preserving pelvic autonomic nerves, a novel approach for intraoperative pelvic neuromonitoring was investigated that is based on impedance measurements of the innervated organs. The objective of this work was to develop an algorithm called AMINA to classify the bioimpedance signals, with the goal of facilitating signal interpretation for the surgeon. Thirty patients included in a clinical investigation underwent nerve-preserving robotic rectal surgery using intraoperative pelvic neuromonitoring. Contraction of the urinary bladder and/or rectum, triggered by direct stimulation of the innervating nerves, resulted in a change in tissue impedance signal, allowing the nerves to be identified and preserved. Impedance signal characteristics in the time domain and the time–frequency domain were calculated and classified to develop the AMINA. Stimulation-induced positive impedance changes were statistically significantly different from negative stimulation responses by the percent amplitude of impedance change Amax in the time domain. Positive impedance changes and artifacts were distinguished by classifying wavelet scales resulting from peak detection in the continuous wavelet transform scalogram, which allowed implementation of a decision tree underlying the AMINA. The sensitivity of the software-based signal evaluation by the AMINA was 96.3%, whereas its specificity was 91.2%. This approach streamlines and automates the interpretation of impedance signals during intraoperative pelvic neuromonitoring.

Deep Wavelet Convolutional Neural Networks for Multimodal Human Activity Recognition Using Wearable Inertial Sensors.

Recent advances in wearable systems have made inertial sensors, such as accelerometers and gyroscopes, compact, lightweight, multimodal, low-cost, and highly accurate. Wearable inertial sensor-based multimodal human activity recognition (HAR) methods utilize the rich sensing data from embedded multimodal sensors to infer human activities. However, existing HAR approaches either rely on domain knowledge or fail to address the time-frequency dependencies of multimodal sensor signals. In this paper, we propose a novel method called deep wavelet convolutional neural networks (DWCNN) designed to learn features from the time-frequency domain and improve accuracy for multimodal HAR. DWCNN introduces a framework that combines continuous wavelet transforms (CWT) with enhanced deep convolutional neural networks (DCNN) to capture the dependencies of sensing signals in the time-frequency domain, thereby enhancing the feature representation ability for multiple wearable inertial sensor-based HAR tasks. Within the CWT, we further propose an algorithm to estimate the wavelet scale parameter. This helps enhance the performance of CWT when computing the time-frequency representation of the input signals. The output of the CWT then serves as input for the proposed DCNN, which consists of residual blocks for extracting features from different modalities and attention blocks for fusing these features of multimodal signals. We conducted extensive experiments on five benchmark HAR datasets: WISDM, UCI-HAR, Heterogeneous, PAMAP2, and UniMiB SHAR. The experimental results demonstrate the superior performance of the proposed model over existing competitors.

The green, the dirty and the stable: Diversifying equity portfolios by adding tokens of different nature

In this study we propose to empirically assess the potential diversification benefits of three types of cryptocurrencies (traditional: Bitcoin, green: Cardano and stablecoins: Tether) by including them in equity-based asset allocation strategies. We build monthly rebalanced minimum VaR portfolios based on different wavelet scales or investment horizons. We use the ADCC-GARCH model to fit the dynamic dependence structure. We find that traditional and green cryptocurrencies provide diversification opportunities when considering portfolio strategies based on short-term investment horizons. We also demonstrate that stablecoins may play the role of safe haven assets for those portfolio strategies based on long-term investment horizons.

Multiscale interdependence between economic policy uncertainty and industrial production of Central and Eastern European countries

AbstractThis paper shows how the three economic policy uncertainties (EPUs), namely global economic uncertainty, US economic policy uncertainty and German economic policy uncertainty, impact the industrial production of 8 Central and Eastern European countries. The investigation is done in both time and frequency domains, using the wavelet coherence and wavelet correlation approaches. The US EPU has the strongest effect on all industrial productions, while this effect was recorded during the global financial crisis and the corona virus pandemic. The most intense effect was found in the time-horizon between 4 and 8 months. The Czech Republic and Hungary suffer the strongest impact from EPU, probably because these two economies have relatively high ratio of export (import) vis-à-vis GDP. We fail to find very strong and wide areas of coherence in the Slovakian plot, although Slovakia has the highest level of export (import) to GDP. However, the wavelet correlation findings indicate that Slovakia has relatively high negative correlation at third wavelet scale, which is perfectly in compliance with its high export (import) share in GDP.

A Hybrid Multiwavelet Transform with Grey Wolf Optimization Used for an Efficient Classification of Documents

In machine learning, feature selection is crucial to increase performance and shorten the model's learning time. It seeks to discover the pertinent predictors from high-dimensional feature space. However, a tremendous increase in the feature dimension space poses a severe obstacle to feature selection techniques. Study process to address this difficulty, the authors suggest a hybrid feature selection method consisting of the Multiwavelet transform and Gray Wolf optimization. The proposed approach minimizes the overall downsides while cherry picking the benefits of both directions. This notable wavelet transform development employs both wavelet and vector scaling functions. Additionally, multiwavelets have orthogonality, symmetry, compact support, and significant vanishing moments. One of the most advanced areas of study of artificial intelligence is optimization algorithms. Grey Wolf Optimization (GWO) here produced artificial techniques that yielded good performance results and were more responsive to current needs. Keywords — About four key words or phrases in order of importance, separated by commas, used to compile the subject index for the last issue for the year.

Physics-informed interpretable wavelet weight initialization and balanced dynamic adaptive threshold for intelligent fault diagnosis of rolling bearings

Intelligent fault diagnosis of rolling bearings using deep learning-based methods has made unprecedented progress. However, there is still little research on weight initialization and the threshold setting for noise reduction. An innovative deep triple-stream network called EWSNet is proposed, which presents a wavelet weight initialization method and a balanced dynamic adaptive threshold algorithm. Initially, an enhanced wavelet basis function is designed, in which a scale smoothing factor is defined to acquire more rational wavelet scales. Next, a plug-and-play wavelet weight initialization for deep neural networks is proposed, which utilizes physics-informed wavelet prior knowledge and showcases stronger applicability. Furthermore, a balanced dynamic adaptive threshold is established to enhance the noise-resistant robustness of the model. Finally, normalization activation mapping is devised to reveal the effectiveness of Z-score from a visual perspective rather than experimental results. The validity and reliability of EWSNet are demonstrated through four data sets under the conditions of constant and fluctuating speeds. Source code is available at:https://github.com/liguge/EWSNet.

Time-varying nonlinear parameters identification of high-speed train suspension system based on WMA

The parameters identification of suspension components provides a foundation for health assessment of the high-speed train. Considering the time-varying nonlinearity of suspension parameters caused by changing temperature, this work identifies the time-varying nonlinear parameters based on the wavelet multiresolution analysis (WMA) combined with the proposed improved Akaike information criterion (AIC). Firstly, the parameters variation law against time-temperature are fitted based on test data and the vibration responses of a two-degree-of-freedom suspension model are obtained. Secondly, the time-varying nonlinear parameters are expanded into scale coefficients using WMA. Thus, the identification of time-varying nonlinear parameters is transformed into the identification of time-invariant wavelet scale coefficients. Then the improved AIC is utilized to select the optimal basis functions and decomposition scales in noisy environments. The identified parameters vectors are used by the improved AIC as evaluation index of identification model to reduce the effect of noise. Finally, the time-varying nonlinear parameters are reconstructed based on the optimal wavelet scale coefficients. The results show that the time-varying nonlinear stiffness and damping coefficients can be accurately identified based on the WMA combined with the proposed improved AIC.

Genetic Algorithm-Wavelet Transform Feature Extraction for Data-Driven Acoustic Resonance Spectroscopy

Acoustic Resonance Spectroscopy enables highly accurate measurement of the properties (geometry/material) of a structure based on the structure's natural vibrational resonances. In general, measuring a specific property in multibody structures presents a significant challenge due to the complex overlapping peaks within the resonance spectrum. We present a technique for extracting useful features from a complex spectrum by isolating resonance peaks that are sensitive to the measured property and insensitive to other properties (noise peaks). We isolate specific peaks by selecting frequency regions of interest and performing wavelet transformation, where the frequency regions and wavelet scales are tuned via a Genetic Algorithm. This contrasts greatly from traditional wavelet transformation/decomposition techniques, which use a large number of wavelets at different scales to represent the signal, including the noise peaks, and results in a large feature size, thus decreasing Machine Learning generalizability. We provide a detailed description of the technique and demonstrate the feature extraction technique for example regression and classification problems. We observe reductions of 95% and 40% in regression and classification errors, respectively, when using the Genetic algorithm/Wavelet Transform feature extraction, compared to using no feature extraction, or using Wavelet Decomposition, which is common in optical spectroscopy. The feature extraction has potential to significantly increase the accuracy of spectroscopy measurements based on a wide range of Machine Learning techniques. This would have significant implications for ARS, as well as other data-driven methods for other types of spectroscopy, e.g. optical.

The Wavelet Multi-Scale Analysis of Exchange Rate Exposure: An Application to Malaysian Consumer Products and Services Sector

Objective – Past efforts in assessing foreign exchange rate exposure assume homogeneity in the level of exposure across time horizons which seems to be impractical due to the dynamic nature of comovement between firm value and exchange rate. Methodology – Given this, the study aimed to investigate the multi-scale relationships between changes in exchange rates and firm values of 56 multinational corporations in the consumer products and services sector from January 2000 to December 2020. Findings – The novelty of the study lies upon the application of Maximal Overlap Discrete Wavelet Transformation (MODWT) method which allows decomposition of a single time series domain into different time domains. The fragmentation into multiple time domains allows the measurement of scale-dependent foreign exchange exposure. As a result, the study discovered a non-monotonic trend for wavelet scale j of currency exposure across time scales. In particular, there was a gradual increase in the magnitude of beta exchange exposure and the proportion of exposed firms from low to high time scales. This finding suggested that firm value is more sensitive to changes in the exchange rate within a widened time domain. Novelty – The study demonstrated on how the wavelet technique can be used to measure foreign exchange risk and aided firm managers and market participants in managing foreign exchange risk for a specific time interval. Type of Paper: Empirical JEL Classification: E42, F31, F39 Keywords: Currency exposure; multi-horizon exchange rate; Malaysian Sectors; Wavelet Analysis; MODWT. Reference to this paper should be made as follows: Wahab, H.A; Nasir, N.A.M. (2023). The Wavelet Multi-scale Analysis of Exchange Rate Exposure: An Application to Malaysian Consumer Products and Services Sector, J. Fin. Bank. Review, 8(1), 58 – 72. https://doi.org/10.35609/jfbr.2023.8.1(3)

Wavelet Monte Carlo: a principle for sampling from complex distributions

We present Wavelet Monte Carlo (WMC), a new method for generating independent samples from complex target distributions. The methodology is based on wavelet decomposition of the difference between the target density and a user-specified initial density, and exploits both wavelet theory and survival analysis. In practice, WMC can process only a finite range of wavelet scales. We prove that the resulting L_1 approximation error converges to zero geometrically as the scale range tends to (-infty ,+infty ). This provides a principled approach to trading off accuracy against computational efficiency. We offer practical suggestions for addressing some issues of implementation, but further development is needed for a computationally efficient methodology. We illustrate the methodology in one- and two-dimensional examples, and discuss challenges and opportunities for application in higher dimensions.