Cross-correlation Structure Research Articles

Scaling Correlation Analysis of Particulate Matter Concentrations of Three South Indian Cities

Analyzing the fluctuations of particulate matter (PM) concentrations and their scaling correlation structures are useful for air quality management. Multifractal characterization of PM2.5 and PM10 of three cities in India wase considered using the detrended fluctuation procedure from 2018 to 2021. The cross-correlation of PM concentration in a multifractal viewpoint using the multifractal cross-correlation analysis (MFCCA) framework is proposed in this study. It was observed that PM2.5 was more multifractal and complex than PM10 at all the locations. The PM–gaseous pollutant (GP) and PM–meteorological variable (MV) correlations across the scales were found to be weak to moderate in different cities. There was no definite pattern in the correlation of PM with different meteorological and gaseous pollutants variables. The nature of correlation in the pairwise associations was found to be of diverse and mixed nature across the time scales and locations. All the time series exhibited multifractality when analyzed pairwise using multifractal cross-correlation analysis. However, there was a reduction in multifractality in individual cases during PM–GP and PM–MV paired analyses. The insights gained into the scaling behavior and cross-correlation structure from this study are valuable for developing prediction models for PMs by integrating them with machine learning techniques.

Auto- and Cross-Correlation Multifractal Analysis of Sea Surface Temperature Variability

In this study, we investigate multiscale auto- and cross-correlation structural characteristics of sea surface temperature (SST) variability using our new methodology, called the multifractal asymmetric cross-correlation analysis (MF-ACCA), incorporating signs of a segment’s detrended covariance and linear trend. SST is greatly affected by air–sea interactions and the advection of water masses with a wide range of spatiotemporal scales. Since these force factors are imprinted on SST variability, their features can be revealed in terms of long-range auto- and cross-correlation structures of SST variability via a multifractal analysis. By applying the MF-ACCA methodology to SST variability in the East/Japan Sea, we have found the following features: (1) the auto- and cross-correlation multifractal features are dependent on several parameters, such as the location, linear trends (rising or falling), level of fluctuations, and temporal scales; (2) there are crossover behaviors that are discrete for small scales (less than 1000 days) but continuous for large scales (more than 1000 days); (3) long-range persistence of auto- and cross-correlations is random for large scales during the falling phase; (4) long-range persistence is stronger during the rising phase than during the falling phase; (5) the degree of asymmetry is greater for large scales than for small scales.

On Comparing and Assessing Robustness of Some Popular Non-Stationary BINAR(1) Models

Intra-day transactions of stocks from competing firms in the financial markets are known to exhibit significant volatility and over-dispersion. This paper proposes some bivariate integer-valued auto-regressive models of order 1 (BINAR(1)) that are useful to analyze such financial series. These models were constructed under both time-variant and time-invariant conditions to capture features such as over-dispersion and non-stationarity in time series of counts. However, the quest for the most robust BINAR(1) models is still on. This paper considers specifically the family of BINAR(1)s with a non-diagonal cross-correlation structure and with unpaired innovation series. These assumptions relax the number of parameters to be estimated. Simulation experiments are performed to assess both the consistency of the estimators and the robust behavior of the BINAR(1)s under mis-specified innovation distribution specifications. The proposed BINAR(1)s are applied to analyze the intra-day transaction series of AstraZeneca and Ericsson. Diagnostic measures such as the root mean square errors (RMSEs) and Akaike information criteria (AICs) are also considered. The paper concludes that the BINAR(1)s with negative binomial and COM–Poisson innovations are among the most suitable models to analyze over-dispersed intra-day transaction series of stocks.

Blockchain ETFs and the cryptocurrency and Nasdaq markets: Multifractal and asymmetric cross-correlations

Blockchain exchange-traded funds (ETFs) are nascent products in the financial industry. A limited literature focuses on the multifractal analysis of some conventional ETFs, but the multifractal behaviour of the blockchain ETF market has not been studied. In this paper, we investigate the multifractal and asymmetric cross-correlation features between blockchain ETFs and the cryptocurrency and Nasdaq markets. Multifractality exists in the cross-correlations between blockchain ETFs and the cryptocurrency and Nasdaq markets. There is a higher persistence in the cross-correlation behaviours between blockchain ETFs and cryptocurrencies in the uptrend, whereas the persistence between blockchain ETFs and Nasdaq is more pronounced in the downtrend. On one hand, this suggests that large fluctuations in the cryptocurrency markets lead to large fluctuations in blockchain ETF markets. On the other hand, large fluctuations in the Nasdaq index lead to small fluctuations in blockchain ETF markets. These results reflect stronger ties between blockchain ETFs and cryptocurrencies compared to blockchain ETFs and the Nasdaq index. Such heterogeneous behaviour in the cross-correlation structure provides insights for short-term investment, hedging strategies, and market efficiency. Further analysis shows that long-range cross-correlation and fat-tail distributions are sources of multifractality.

Measuring fiscal stress via fiscal vulnerability index: a case of Turkish economy

PurposeThis paper aims to develop a compound measure, which is fiscal vulnerability index, provides early warning signals of fiscal sustainability problems for Türkiye's economy.Design/methodology/approachThe index is constructed using twelve distinct fiscal indicators and applying the portfolio method, which considers the time-varying cross-correlation structure between the subindices.FindingsDynamics of the fiscal vulnerability index indicate that it accurately predicts to the well-known fiscal crisis occurring in Türkiye's recent history. As a result, such a compound measure should be used in the early identification of fiscal vulnerability in Türkiye.Originality/valueThe main contribution of this paper, relative to existing papers, is that a fiscal vulnerability index was constructed by employing the most contemporaneous method and evaluating its performance in terms of capturing historical stress periods.

Fusion of sparse non-co-located measurements from multiple sources for geotechnical site investigation

A profile of geotechnical properties is often needed for geotechnical design and analysis. However, site-specific data might be characterized as MUSIC-X (i.e., Multivariate, Uncertain and Unique, Sparse, Incomplete, and potentially Corrupted with “X” denoting the spatial/temporal variability), posing a significant challenge in accurately interpreting geotechnical property profiles. Different sources, or types, of data are commonly available from a specific site investigation program, and they are usually cross-correlated, and thus can provide complementary information. This leads to an important question in geotechnical site investigation: how to integrate multiple sources of sparse data for enhancing the profiling of different geotechnical properties. To address this issue, this study proposes a novel method, called fusion Bayesian compressive sampling (Fusion-BCS), for integrating sparse and non-co-located geotechnical data. In the proposed method, the auto- and cross-correlation structures of different sources of data are exploited in a data-driven manner through a joint sparse representation. Then, profiles of different geotechnical properties are jointly reconstructed from all measurements under a framework of compressive sampling/sensing. The proposed method is illustrated using simulated and real geotechnical data. The results indicate that the accuracy of the interpreted geotechnical property profiles may be significantly improved by integrating multiple sources of site investigation data.

Data-driven simulation of two-dimensional cross-correlated random fields from limited measurements using joint sparse representation

Cross-correlated random fields are an essential tool for simultaneously modeling both auto- and cross-correlation structures of spatial or temporal quantities in stochastic analysis of structures or systems. Existing cross-correlated random field simulation methods often require explicit information about random field parameters as inputs. However, in engineering practice, site-specific measurements of different quantities are often limited, non-co-located and irregularly distributed within a given site because of time, budget, or space constraints as well as missing data. It is notoriously difficult to properly estimate reliable random field parameters from limited non-co-located measurements with an irregular spatial pattern, particularly the auto-correlation and cross-correlation structures of a two-dimensional (2D) cross-correlated random field. To deal with this issue, this study proposes a novel 2D cross-correlated random field generator for simulating 2D cross-correlated random field samples (RFSs) directly from sparsely measured non-co-located data points with unequal measurement intervals. Using a joint sparse representation, auto- and cross-correlation structures of different spatial/temporal quantities are exploited simultaneously from sparse measurements, followed by the generation of cross-correlated RFSs using Bayesian compressive sampling (BCS) and Markov chain Monte Carlo (MCMC) simulation in a data-driven manner. The proposed generator is demonstrated using 2D data of two correlated geotechnical properties. The results indicate that the RFSs generated using the proposed method from sparse measurements can properly characterize the spatial auto- and cross-correlation structures of different geotechnical properties.

Discussion of “Multivariate dynamic modeling for Bayesian forecasting of business revenue”

Discussion of “Multivariate dynamic modeling for Bayesian forecasting of business revenue”

Resource Estimation in Multi-Unit Mineral Deposits Using a Multivariate Matérn Correlation Model: An Application in an Iron Ore Deposit of Nkout, Cameroon

Modeling the spatial dependence structure of metal grades in the presence of soft boundaries between geological domains is challenging in any mineral resource estimation strategy. The aim of this work was to propose a structural model adapted to this type of geological boundary, based on a multivariate Matérn model that fits the observed direct (within domain) and cross (between domains) correlation structures of metal grades. The methodology was applied to a case study of an iron deposit located in southern Cameroon. Cross-validation scores show that accounting for the grade correlation across domain boundaries improved the traditional workflow, where the grade was estimated in each domain separately. The scores were significantly better when we also ensured that the mean grade was locally invariant from one domain to another to reflect the grade continuity across the domain boundary.

Task-dependent fractal patterns of information processing in working memory

We applied detrended fluctuation analysis, power spectral density, and eigenanalysis of detrended cross-correlations to investigate fMRI data representing a diurnal variation of working memory in four visual tasks: two verbal and two nonverbal. We show that the degree of fractal scaling is regionally dependent on the engagement in cognitive tasks. A particularly apparent difference was found between memorisation in verbal and nonverbal tasks. Furthermore, the detrended cross-correlations between brain areas were predominantly indicative of differences between resting state and other tasks, between memorisation and retrieval, and between verbal and nonverbal tasks. The fractal and spectral analyses presented in our study are consistent with previous research related to visuospatial and verbal information processing, working memory (encoding and retrieval), and executive functions, but they were found to be more sensitive than Pearson correlations and showed the potential to obtain other subtler results. We conclude that regionally dependent cognitive task engagement can be distinguished based on the fractal characteristics of BOLD signals and their detrended cross-correlation structure.

A high throughput generative vector autoregression model for stochastic synapses.

By imitating the synaptic connectivity and plasticity of the brain, emerging electronic nanodevices offer new opportunities as the building blocks of neuromorphic systems. One challenge for large-scale simulations of computational architectures based on emerging devices is to accurately capture device response, hysteresis, noise, and the covariance structure in the temporal domain as well as between the different device parameters. We address this challenge with a high throughput generative model for synaptic arrays that is based on a recently available type of electrical measurement data for resistive memory cells. We map this real-world data onto a vector autoregressive stochastic process to accurately reproduce the device parameters and their cross-correlation structure. While closely matching the measured data, our model is still very fast; we provide parallelized implementations for both CPUs and GPUs and demonstrate array sizes above one billion cells and throughputs exceeding one hundred million weight updates per second, above the pixel rate of a 30 frames/s 4K video stream.

Data-Driven Modeling of Vibrations in Turbofan Engines Under Different Operating Conditions

Vibration monitoring in aircraft engines is traditionally performed using order tracking methodology. Currently, there are no representative physics-based models for tracked order vibration in aircraft engines. This gap in research is primarily attributed to the limited understanding of mutual interactions and the nonlinear nature of engine vibrations. The objective of the current study is twofold: 1) to present a preliminary investigation of tracked order vibrations in aircraft engines and to statistically analyze them in the context of their operating environment and 2) to leverage emerging data-driven modeling techniques to develop accurate models for the tracked order vibration in a turbofan engine valid over a wide range of operating conditions. Toward the same, we employ multiscale detrended partial cross-correlation analysis to evaluate the interdependencies and cross-correlation structure between various thermomechanical variables and tracked order vibration across multiple time scales. We leverage the understanding of complex correlation structures and subsequently use them to model tracked order vibrations. We develop data-driven models using state-of-the-art time-delay embedded dynamic mode decomposition and compare its performance with Lasso regression.

Structure of cross-correlation between stock and oil markets

We displayed in this paper the structure of cross-correlation between the S&P 500 stock market and the Brent Oil market and its evolutionary behavior. Technically, the ensemble empirical mode decomposition is adopted to separate the two series into components. Let a window slide along the multi-variate series of the components, generating a series of segments. For each segment, one calculates the mutual entropies between the components to describe the coupling strengths, resulting into a network between/within the two markets. The networks corresponding to the successive segments form a temporal network. It is found that the characteristic period of intrinsic mode for each series grows exponentially from several days to more than ten years. The couplings between long-term components (with periods larger than one year) form the stable backbone of the network. The shocks of short-term events on the long-term components determine mainly the evolutionary behavior, especially the changes of the coupling structure. This method can be extended straightforwardly to display the cross-correlation structures and their evolutions for complex systems composed of multi-subsystems.

Simulation of Wave Time Series with a Vector Autoregressive Method

Joint time series of wave height, period and direction are essential input data to computational models which are used to simulate diachronic beach evolution in coastal engineering. However, it is often impractical to collect a large amount of the required input data due to the expense. Based on the nearshore wave records offshore of Littlehampton in Southeast England over the period from 1 September 2003 to 30 June 2016, this paper presents a statistical method to obtain simulated joint time series of wave height, period and direction covering an extended time span of a decade or more. The method is based on a vector auto-regressive moving average algorithm. The simulated times series shows a satisfactory degree of stochastic agreement between original and simulated time series, including average value, marginal distribution, autocorrelation and cross-correlation structure, which are important for Monte Carlo modelling of shoreline evolution, thereby allowing ensemble prediction of shoreline response to a variable wave climate.

The effect of autocorrelation on the diagnostic procedures

Apart from quick detection of abnormal changes in a multivariate process, it is also critical to accurately identify the factors of abnormal changes after an out-of-control signal in multivariate statistical process control. Some diagnostic methods for fault identification were proposed by scholars on which one of the basic assumptions is that the process data are independent. The independent assumption is reasonable for many applications. However, with the development of industrial automation, the process data usually meet the phenomenon of autocorrelation. As it is well known, the autocorrelation affects detection ability of control chart. It is a natural question that is whether the autocorrelation affects the diagnostic performance of the diagnostic procedures. In the article, we propose the method adopted the analogy residual sequences and compare it with the performance of existing diagnostic methods for different shift sizes and various autocorrelation and cross-correlation structures. To limit the complexity, our discussion employs a first-order vector autoregressive process and focuses mainly on bivariate data in this article. The results of the simulation show the performances of diagnostic procedures were affected by autocorrelation and the impacts become greater as autocorrelation increases. On the other hand, the proposed method in the article can be free from the impacts of autocorrelation. Finally, a real example is also presented to demonstrate the implementation of the proposed method.

Severity Estimation of Depression Using Convolutional Neural Network

In the present study, we attempt to estimate the severity of depression using a Convolutional Neural Network (CNN). The method is special because an auto- and cross-correlation structure has been crafted rather than using an actual image for the input of the network. The importance to investigate the possibility of this research is that depression has become one of the leading mental disorders in the world. With its appearance, it can significantly reduce an individual's quality of life even at an early stage, and in severe cases, it may threaten with suicide. It is therefore important that the disorder be recognized as early as possible. Furthermore, it is also important to determine the disorder severity of the individual, so that a treatment order can be established. During the examination, speech acoustic features were obtained from recordings. Among the features, MFCC coefficients and formant frequencies were used based on preliminary studies. From its subsets, correlation structure was created. We applied this quadratic structure to the input of a convolutional network. Two models were crafted: single and double input versions. Altogether, the lowest RMSE value (10.797) was achieved using the two features, which has a moderate strength correlation of 0.61 (between estimated and original).

Visibility-graphlet approach to the output series of a Hodgkin–Huxley neuron

The output signals of neurons that are exposed to external stimuli are of great importance for brain functionality. Traditional time-series analysis methods have provided encouraging results; however, the associated patterns and their correlations in the output signals of neurons are masked by statistical procedures. Here, graphlets are employed to extract the local temporal patterns and the transitions between them from the output signals when neurons are exposed to external stimuli with selected stimulating periods. A transition network is defined where the node is the graphlet and the direct link is the transition between two successive graphlets. The transition-network structure is affected by the simulating periods. When the stimulating period moves close to an integer multiple of the neuronal intrinsic period, only the backbone or core survives, while the other linkages disappear. Interestingly, the size of the backbone (number of nodes) equals the multiple. The transition-network structure is conservative within each stimulating region, which is defined as the range between two successive integer multiples. Nevertheless, the backbone or detailed structure is significantly altered between different stimulating regions. This alternation is induced primarily from a total of 12 active linkages. Hence, the transition network shows the structure of cross correlations in the output time-series for a single neuron.

Real-time fault detection and process control based on multi-channel sensor data fusion

Sensor signals acquired in industrial equipment contain rich information which can be analyzed to facilitate effective monitoring of equipment, early detection of system anomalies, quick diagnosis of fault root causes, and intelligent system design and control. In many mechatronic systems, multiple signals are acquired by different sensor channels (i.e., multi-channel data) which can be represented by high-order arrays (tensorial data). The multi-channel data has a high-dimensional and complex cross-correlation structure. It is crucial to develop a method that considers the interrelationships between different sensor channels. This paper proposes a new equipment monitoring approach based on uncorrelated multilinear discriminant analysis that can effectively model the multi-channel data to achieve a superior monitoring and fault diagnosis performance compared to other competing methods. The proposed method is applied directly to the high-dimensional tensorial data. Features are extracted and combined with multivariate control charts to achieve real-time fault detection of equipment. The effectiveness of the proposed method in quick detection of equipment faults is demonstrated with both the simulation and a real-world case study.

An enhanced co-simulation technique for resource modelling using grade domaining: a case study from an iron ore deposit

ABSTRACT For resource estimation, domains are interpreted in a deposit to define homogenous areas for grade estimation. The conventional approach is to interpret the domains and then to separately model the distribution of the grade (i.e., partial grades) within each domain. The problem is that independent modeling of partial grades ignores the cross-dependency that exists between the partial grades within the defined domains. In this study, an alternative is proposed to first model the grade domains using a stochastic approach and then to model the partial grades within each domain using a co-simulation algorithm that incorporates their cross-correlation structures. The proposed enhanced co-simulation methodology has been applied at an iron deposit and a single grade threshold. This case study shows that the enhanced co-simulation methodology is capable of reproducing the global statistics and spatial continuity characteristics of the partial grades and results in improved domaining, grade estimation and definition of ore.

Feature extraction and process monitoring of multi-channel data in a forging process via sensor fusion

ABSTRACT Sensor signals acquired in the industrial process contain rich information that can be analyzed to detect system anomalies and facilitate effective monitoring of the process. In many processes, multiple signals are acquired by different sensor channels (i.e. multi-channel data) which have high-dimensional and complex cross-correlation structures. When analyzing such signal data, two main issues must be resolved: (1) feature extraction of multi-channel data to reduce the data dimensionality and improve signal analysis efficiency, and (2) the sensor fusion to achieve better monitoring of the process. It is crucial to develop a method that considers the interrelationships between different sensor channels. This paper proposes an improved multilinear feature extraction method with a feature selection strategy to improve the separability of profile data. The proposed method is applied directly to the high-dimensional multi-channel data. Features are extracted and combined with multivariate control charts to monitor multi-channel data. The effectiveness of the proposed method in quick detection of process changes is demonstrated with both the Monte Carlo simulation and a real-world case study. The real multi-channel data in the case study are recorded in a multi-operation forging process for the propose of process monitoring and fault detection.