Multivariate Time Series Analysis Research Articles

Multilayer quantile graph for multivariate time series analysis and dimensionality reduction

Multilayer quantile graph for multivariate time series analysis and dimensionality reduction

The Impact of Non-Oil Exports on the Economic Growth in Saudi Arabia: An Empirical Analysis

This study aims to investigate the impact of non-oil exports on the economic growth of Saudi Arabia during the period 2000-2022. Since Saudi Arabia targets to transform their economy from dependence to the diversification of economic resources, it is important to evaluate the impact of non-oil exports on the gross domestic product (GDP) in the long run. This study used multivariate time series analysis, including Johansen-Juselius co-integration and Vector Error Correction Model to determine the long-run relationship between them. The findings of the study revealed that non-oil exports have a statistically significant impact on economic growth in the long run. However, oil exports have a negative relationship with economic growth in the long run. Moreover, it also observed that a real effective exchange rate negatively affects economic growth while gross capital formation has a positive impact on economic growth in the long run. It is recommended that the non-oil sectors should be considered as a prime concern regarding infrastructural development due to their instant return to the country and should provide loans at minimal or zero interest to support them in the effective production of non-oil exports. Moreover, also makes legislation in the favor of domestic and foreign stakeholders so that they can encourage them to invest in non-oil exports and expand the non-oil sector. 

Anomaly detection in wind turbine blades based on PCA and convolutional kernel transform models: employing multivariate SCADA time series analysis

With the widespread application of wind power technology, the detection of abnormalities in wind turbine blades has become a key research area. The use of data from monitoring and data acquisition (SCADA) systems for data-driven fault detection research presents new challenges. This study utilizes short-term SCADA data from wind turbine generators to classify the blade abnormal and normal operational states, thereby introducing a new method called PCABSMMR. This strategy integrates principal component analysis (PCA) and borderline-synthetic minority over-sampling technique (Borderline-SMOTE) for data processing and utilizes an improved multi-dimensional time series classification (MTSC) model. It combines one-dimensional convolution from deep learning with shallow learning’s rigid classifiers. PCA is used for dimensionality reduction, while Borderline-SMOTE expands the samples of minority class fault instances. Comparative analysis with various methods shows that the proposed method has an average F1-score of 0.98, outperforming many state-of-the-art MTSC models across various evaluation metrics.

Time and frequency-domain feature fusion network for multivariate time series classification

Multivariate time series classification is a significant research topic in the realm of data mining, which encompasses a wide array of practical applications in domains such as healthcare, energy systems, and traffic. The complex temporal and spatial dependencies inherent in multivariate time series pose challenges to classification tasks. Previous studies have usually focused on the time-domain information of multivariate time series. However, achieving accurate classification using only the time-domain information may be difficult. To address this challenge, a time and frequency-domain feature fusion network (TF-Net) for multivariate time series classification is proposed in this paper. Our model contains two modules, the time-domain module and the frequency-domain module. The time-domain module is used to capture the time-domain features of multivariate time series. It is constructed using CNNs and GCNs, enabling the capture of both temporal and spatial dependencies within the time-domain. The frequency-domain module is used to capture the frequency-domain features of multivariate time series data. In this module, we treat the frequency-domain features as images and innovatively transform the multivariate time series classification task into an image classification task. Our method is able to classify multivariate time series from both the time-domain and frequency-domain, which provides a new perspective for multivariate time series analysis. We conduct extensive experiments on the UAE archive, and the experimental results show that our model achieves the best performance compared to the ten state-of-the-art methods.

Contribution of Population Growth on Economic Growth in Rwanda (1992-2022)

This study examines the impact of changes in population size on economic growth in Rwanda between 1992 and 2022. The research methodology involves the use of secondary data from World Bank development indicators. The key variables analysed include population size, gross capital formation expenditure, and gross domestic product growth rate. A multivariate time series analysis was used to examine the impact of population on economic growth in this study. Diagnostic tests were conducted, and the results indicated that the model was sound. The variables were not significantly affected by heteroskedasticity and serial correlation problems. During the unit root test, it was found that all variables were stationary at the level using intercept and trend. This led to the use of the Ordinary Least Square model. The findings reveal a complex relationship between population dynamics, gross capital formation, and economic growth in Rwanda. The R-squared value was found to be close to one, indicating that population growth and gross capital formation explain economic growth to the greatest extent. The findings from the study showed that population has negative relationship with economic growth. Gross capital formation also plays a crucial role in driving economic growth by facilitating investment activities across different sectors.

DPDGAD: A Dual-Process Dynamic Graph-based Anomaly Detection for multivariate time series analysis in cyber-physical systems

With the rapid development of cyber–physical systems, an increasing amount of data is stored in the form of multivariate time series. Detecting anomalies within multivariate time series has become a crucial means to ensure the proper functioning of cyber–physical systems. Traditional methods for anomaly detection in multivariate time series often categorize features into temporal and spatial features based on their representative dimensions. However, these approaches tend to overlook the unique characteristics of cyber–physical systems reflected in the multivariate time series. This hinders their ability to perform well in cases with complex multivariate time series data. To overcome this challenge, we introduce a novel approach that classifies the spatiotemporal features of multivariate time series data into steady features (features that remain constant under external variations) and dynamic features (features that respond to external changes), aligning with the nature of cyber–physical systems. Addressing this challenge involves two main aspects: (1) determining how to classify steady and dynamic features in multivariate time series data and (2) leveraging these features for anomaly detection.To address these challenges, we propose a Dual-Process Dynamic Graph-based time series Anomaly Detection (DPDGAD) method. DPDGAD enhances the generalizability of anomaly detection in complex spatiotemporal environments and improves the interpretability of the detected anomalies. We validate the performance of DPDGAD through six real-world datasets generated by cyber–physical systems, achieving F1 scores of 0.7529 and 0.9009 on WADI and SWaT, respectively.

A Study on the Spill Over Effects on Nifty 50 Returns: Evidence from Stock Market Performances of Major Asian Counterparts of India

This study investigates the spillover effects of major Asian stock market performances on the returns of the Nifty 50, India's benchmark index. Employing advanced econometric techniques, we analyze the dynamic relationships between the Nifty 50 and key Asian counterparts, considering both short-term and long-term horizons. Our research delves into return spillovers aiming to comprehensively assess the interconnectedness and transmission of market movements across the region. This study utilizes an extensive dataset covering Nifty 50 returns from April 1, 2013, to March 31, 2023, along with meticulously documented returns from stock market indexes linked to major strategic alliances in India. By applying advanced multivariate time series analysis techniques, encompassing Vector Autoregression (VAR), Granger causality tests, and impulse response functions, we model the intricate dynamics interweaving these indexes with the Nifty 50. The research endeavors to answer fundamental questions, including assessing short- term and long-term effects resulting from major Asian counterparts of India on Nifty returns, as well as exploring noticeable patterns that indicate the direction of causality between these counterparts and Nifty returns. The outcomes of this study carry substantial implications for decision-makers. Investors can make more informed decisions, businesses planning strategic partnerships can refine their strategies, and policymakers can formulate economic and financial regulations that accurately reflect the complexities of these dynamics. By unveiling the ripple effects of these counterparts on the Nifty 50, this research offers valuable insights into the evolving dynamics of India's financial markets and their integration into the global economy.

Spatiotemporal Land Use/Land Cover Changes and Impact on Urban Thermal Environments: Analyzing Cool Island Intensity Variations

This study pioneers the comprehensive evaluation of the spatiotemporal evolution of land use/land cover (LULC) in Hangzhou city, introducing the novel water body shape index (WBSI) to analyze its seasonal impacts on the urban thermal environment and urban cool island (UCI) effects, uncovering distinct patterns of thermal regulation. It particularly investigates how distance gradients and the water body shape index (WBSI) influence land surface temperature (LST) in the urban core. The region’s climate, featuring hot summers and cold winters, highlights significant seasonal LST variations. Addressing a gap in existing UCI research, the analysis extends beyond the typical large-scale planning focus to include small-scale, high-resolution aspects. Employing remote sensing and geographic information system (GIS) analysis techniques, this study analyzes the seasonal dynamics in Hangzhou’s central urban area. High-resolution LST data, obtained through single-channel inversion and resolution enhancement algorithms, are crucial to this analysis. This study employs the maximum likelihood classification method to analyze land use and land cover changes from 1990 to 2020. This analysis reveals potential drivers of urban thermal environment changes, such as the expansion of residential and commercial areas and the reduction in green spaces. Different regions in LST data are delineated to assess the cool island effect, and the complexity of water body boundaries is quantified using the water body shape index. Spatial and temporal patterns of LST changes are investigated using multivariate regression and time-series analysis models. We identified significant changes in LULC over the past 30 years in Hangzhou, closely correlating with a continuous rise in LST. This observation underscores a clear finding: the strategic importance of blue–green infrastructure in mitigating urban heat, a novel insight that extends the current understanding of urban thermal dynamics. A clear and novel finding of this study is that the intensity of the cool island effect from large water bodies not only diminishes with distance but is intricately influenced by the complexity of their shapes, as quantified by the WBSI, whereas the complexity of their boundaries enhances this effect. Additionally, the regulatory role of the cool island effect is observed to vary seasonally, being most pronounced in summer and less so in autumn and winter, thereby demonstrating a positive impact. In conclusion, our findings innovatively highlight how the specific shapes of water bodies, quantified through the water body shape index (WBSI), emerge as critical, yet previously underappreciated, drivers in modulating the urban thermal environment. This underscores a new avenue for urban planning, advocating for the strategic design of water bodies within urban landscapes. It also finds that spatial factors and seasonal variations significantly affect the intensity of the cool island effect. These findings offer valuable evidence for urban planning and climate change adaptation, emphasizing balancing natural elements with the built environment in urban design.

Hard c-means transition network for the analysis of multivariate time series

Hard c-means transition network for the analysis of multivariate time series

A framework for automated landslide dating utilizing SAR-Derived Parameters Time-Series, An Enhanced Transformer Model, and Dynamic Thresholding

Determining the timing of landslide occurrence is crucial for establishing an accurate, comprehensive and systematic landslide inventory while assessing the potential for reducing landslide risk. Unfortunately, many existing landslide inventories lack temporal information such as the precise time of landslide events. Optical and Synthetic Aperture Radar (SAR) sensors are the most commonly used remote sensing technologies for landslide detection. Unlike optical sensors, SAR sensors are not affected by cloudy conditions and provide valuable imagery regardless of sunlight availability. Therefore, SAR-derived parameters, i.e., SAR amplitude, interferometric coherence, and polarimetric features (alpha and entropy), offer a higher temporal resolution for detecting landslide occurrence times compared to optical data. Despite the advantages, there is currently no universally accepted automatic method for determining the time of landslide events using SAR data. This is due to the lack of anomaly labels and the high time-series volatility in detecting landslide occurrence times. Despite advances in deep-learning methods for anomaly detection in time-series, only a few of them can address these challenges in our case. In this paper, we propose an unsupervised multivariate transformed-based deep-learning model to automatically and efficiently estimate landslide occurrence times using multivariate SAR-derived parameters time-series analysis. The designed gated relative position can increase robustness and temporal context information, by learning global temporal trends in the time-series. Subsequently, the time-series of the anomaly score derived from the proposed Transformer model is analyzed using an adaptive thresholding strategy to dynamically and automatically mark anomalies related to the landslide occurrence. Our research focuses on collapsed landslides characterized by dramatic changes in ground surface topography, with a particular attention for the need of a prior knowledge about landslide boundaries. We assess the performance of the proposed methodology for several collapsed landslides including the July 21, 2020 Shaziba and 23 July, 2019 Shuicheng landslides in China, March 19, 2019 Takht landslide in Iran, June 15, 2018 Jalgyz-Jangak and May 25, 2018 Kugart landslides in Kyrgyzstan, July 7, 2018 Hitardalur landslide in Iceland, and January 25, 2019 Brumadinho landslide in Brazil. In comparison to commonly used neural networks like the LSTM algorithm, our proposed framework leads to a more accurate estimate for the time of landslide failure using time-series of SAR-derived parameters. Furthermore, our results suggest the great potential of SAR data to narrow the time period detected from optical data when used in conjunction with them.

Ground air pollutants explanation based on multiple visibility graph of complex network by temporal community division.

In air pollution studies, the correlation analysis of environmental variables has usually been challenged by parametric diversity. Such variable variations are not only from the extrinsic meteorological conditions and industrial activities but also from the interactive influences between the multiple parameters. A promising solution has been motivated by the recent development of visibility graph (VG) on multi-variable data analysis, especially for the characterization of pollutants' correlation in the temporal domain, the multiple visibility graph (MVG) for nonlinear multivariate time series analysis has been verified effectively in different realistic scenarios. To comprehensively study the correlation between pollutant data and season, in this work, we propose a multi-layer complex network with a community division strategy based on the joint analysis of the atmospheric pollutants. Compared to the single-layer-based complex networks, our proposed method can integrate multiple different atmospheric pollutants for analysis, and combine them with multivariate time series data to obtain higher temporary community division for ground air pollutants interpretation. Substantial experiments have shown that this method effectively utilizes air pollution data from multiple representative indicators. By mining community information in the data, it successfully achieves reasonable and strong interpretive analysis of air pollution data.

A structural VAR and VECM modeling method for open-high-low-close data contained in candlestick chart

The structural modeling of open-high-low-close (OHLC) data contained within the candlestick chart is crucial to financial practice. However, the inherent constraints in OHLC data pose immense challenges to its structural modeling. Models that fail to process these constraints may yield results deviating from those of the original OHLC data structure. To address this issue, a novel unconstrained transformation method, along with its explicit inverse transformation, is proposed to properly handle the inherent constraints of OHLC data. A flexible and effective framework for structurally modeling OHLC data is designed, and the detailed procedure for modeling OHLC data through the vector autoregression and vector error correction model are provided as an example of multivariate time-series analysis. Extensive simulations and three authentic financial datasets from the Kweichow Moutai, CSI 100 index, and 50 ETF of the Chinese stock market demonstrate the effectiveness and stability of the proposed modeling approach. The modeling results of support vector regression provide further evidence that the proposed unconstrained transformation not only ensures structural forecasting of OHLC data but also is an effective feature-extraction method that can effectively improve the forecasting accuracy of machine-learning models for close prices.

Breast cancer classification through multivariate radiomic time series analysis in DCE-MRI sequences

Breast cancer is the most prevalent disease that poses a significant threat to women’s health. Despite the Dynamic Contrast-Enhanced MRI (DCE-MRI) has been widely used for breast cancer classification, its diagnostic performance is still suboptimal. In this work, the Radiomic workflow was implemented to classify the whole DCE-MRI sequence based on the distinction in contrast agent uptake between benign and malignant lesions. The radiomic features extracted from each of the seven time instants within the DCE-MRI sequence were fed into a multi-instant features selection strategy to select the discriminative features for time series classification. Several time series classification algorithms including Rocket, MultiRocket, K-Nearest Neighbor, Time Series Forest, and Supervised Time Series Forest were compared. Firstly, a univariate classification was performed to find the five most informative radiomic series, and then, a multivariate time series classification was implemented via a voting mechanism. The Multivariate Rocket model was the most accurate (Accuracy = 0.852, AUC-ROC = 0.852, Specificity = 0.823, Sensitivity = 0.882). The intelligible radiomic features enabled model findings explanations and clinical validation. In particular, the Energy and TotalEnergy were among the most important features, and the most descriptive for the change in signal intensity, which is the main effect of the contrast agent.

Causality Between Carbon Dioxide (CO2) Emissions and Economic Growth in Indonesia

Economic growth and environmental protection are two goals that are often considered contradictory. Strong economic growth tends to require high energy consumption, which is often obtained from fossil fuel sources. The aim of this research isthe relationship between carbon dioxide (CO2) emissions and economic growth in Indonesia. This type of research is descriptive qualitative with a quantitative approach, the data source in this research uses 41 year time series data in the period 1980 - 2021 in Indonesia, the research was attempted using Multivariate Time Series Analysis Panel Information on Vector Auto Regression (VAR) combined with Vector Error Correction Form (VECM) uses the statistical application EViews 9. 0. Economic development is the progress of activity in the economy which causes the creation of goods and services in society to increase and the abundance of society to increase, carbonium dioxide (CO2) is a colorless, odorless gas compound that obtained from incomplete combustion of materials containing charcoal or organic matter. Research results show that this lack of connection is also due to the high dependence on fossil fuel sources, which is almost 2 thirds of total energy use, so that increasing energy use can affect carbonium dioxide (CO2) emissions in Indonesia. The ever-increasing number of means of transportation also greatly influences the increase in the use of natural oil, which in the future could disrupt the balance of the area's ecosystem which has an impact on other living creatures.

Dynamic Associations Between Centers for Disease Control and Prevention Social Media Contents and Epidemic Measures During COVID-19: Infoveillance Study.

Health agencies have been widely adopting social media to disseminate important information, educate the public on emerging health issues, and understand public opinions. The Centers for Disease Control and Prevention (CDC) widely used social media platforms during the COVID-19 pandemic to communicate with the public and mitigate the disease in the United States. It is crucial to understand the relationships between the CDC's social media communications and the actual epidemic metrics to improve public health agencies' communication strategies during health emergencies. This study aimed to identify key topics in tweets posted by the CDC during the pandemic, investigate the temporal dynamics between these key topics and the actual COVID-19 epidemic measures, and make recommendations for the CDC's digital health communication strategies for future health emergencies. Two types of data were collected: (1) a total of 17,524 COVID-19-related English tweets posted by the CDC between December 7, 2019, and January 15, 2022, and (2) COVID-19 epidemic measures in the United States from the public GitHub repository of Johns Hopkins University from January 2020 to July 2022. Latent Dirichlet allocation topic modeling was applied to identify key topics from all COVID-19-related tweets posted by the CDC, and the final topics were determined by domain experts. Various multivariate time series analysis techniques were applied between each of the identified key topics and actual COVID-19 epidemic measures to quantify the dynamic associations between these 2 types of time series data. Four major topics from the CDC's COVID-19 tweets were identified: (1) information on the prevention of health outcomes of COVID-19; (2) pediatric intervention and family safety; (3) updates of the epidemic situation of COVID-19; and (4) research and community engagement to curb COVID-19. Multivariate analyses showed that there were significant variabilities of progression between the CDC's topics and the actual COVID-19 epidemic measures. Some CDC topics showed substantial associations with the COVID-19 measures over different time spans throughout the pandemic, expressing similar temporal dynamics between these 2 types of time series data. Our study is the first to comprehensively investigate the dynamic associations between topics discussed by the CDC on Twitter and the COVID-19 epidemic measures in the United States. We identified 4 major topic themes via topic modeling and explored how each of these topics was associated with each major epidemic measure by performing various multivariate time series analyses. We recommend that it is critical for public health agencies, such as the CDC, to update and disseminate timely and accurate information to the public and align major topics with key epidemic measures over time. We suggest that social media can help public health agencies to inform the public on health emergencies and to mitigate them effectively.

Catch and release: Testing the effect of a citation release policy on crime in Washington, DC

AbstractResearch summaryThis study investigated the effect of an expanded police station citation release policy enacted in Washington, DC in March 2020 on eight types of crime: homicide, sex abuse, robbery, assault with a dangerous weapon, burglary, motor vehicle theft, theft from motor vehicles, and other theft. Monthly‐level multivariate time series analyses employed data from 2013‐2022 and accounted for the relationship between crime, arrests, and the jail population. The expanded policy was hypothesized to increase certain property crimes based on the new guidelines, but results indicated the policy modification was associated with changes in citywide crime counts for one type of crime: homicide.Policy implicationsEfforts around the United States to decarcerate the pre‐trial jail population should examine potential unintended consequences for public safety. The current study failed to detect a statistically significant increase in seven of the eight types of crime during the expanded use of one jail decarceration approach, police station citation release. In the future, jurisdictions looking to reduce their jail population might consider citation release as a speedy and cost‐effective alternative to release‐on‐recognizance, but they should take care to monitor individual defendants and evaluate their own program.

Impact of foreign direct investment on Rwandan economic growth from the period

This study is intended to assess the impact of Foreign Direct Investment on Rwandan economic growth, such determinants are gross domestic saving, population, and gross domestic product and to confirm if it has an impact on Rwandan economic growth. To achieve this study a multivariate time series analysis was used to analyze the impact of Foreign Direct Investment on economic growth.In this study, diagnostic tests and the results confirmed (proved) that the model was good and the results from the tests suggest that the variables were not seriously affected by heteroskedasticity and serial correlation problems. The results showed a long-run relationship of variables based on the results from the unit root test of residuals of variables. The results also showed that the coefficient of ECM (-1) is positive and statistically significant, leading the model to be co-integrated between their variables and errors were corrected in the long run and some of the variables were statistically significant which showed that there are short-run relationships between variables where an increase in foreign direct investment decreased economic growth holding other factors constant.

Graphical Principal Component Analysis of Multivariate Functional Time Series

In this paper, we consider multivariate functional time series with a two-way dependence structure: a serial dependence across time points and a graphical interaction among the multiple functions within each time point. We develop the notion of dynamic weak separability, a more general condition than those assumed in literature, and use it to characterize the two-way structure in multivariate functional time series. Based on the proposed weak separability, we develop a unified framework for functional graphical models and dynamic principal component analysis, and further extend it to optimally reconstruct signals from contaminated functional data using graphical-level information. We investigate asymptotic properties of the resulting estimators and illustrate the effectiveness of our proposed approach through extensive simulations. We apply our method to hourly air pollution data that were collected from a monitoring network in China.

Navigating Complexity: Harnessing AI for Multivariate Time Series Forecasting in Dynamic Environments

Multivariate Time Series Analysis (MTSA) plays a pivotal role in forecasting within diverse domains by addressing the complexities arising from interdependencies among multiple variables. This exploration delves into the fundamentals, methodologies, and applications of MTSA, elucidating its role in enhancing predictive capabilities. The key concepts in MTSA, including Vector Autoregression, Cointegration, Error Correction Models, and Granger Causality, form the foundation for understanding dynamic relationships among variables. The methodology section outlines the critical steps in MTSA, such as model specification, estimation, diagnostics, and forecasting. Additionally, the abstract explores the capabilities of Artificial Intelligence (AI) in time-series forecasting, emphasizing improved accuracy, long-term trend recognition, dynamic pattern recognition, and the handling of seasonality and anomalies. Specific AI models, such as Recurrent Neural Networks (RNNs) with Long Short-Term Memory (LSTM), Echo State Networks (ESNs), and Online Learning Algorithms, are discussed in detail, along with practical implementation examples. Furthermore, the abstract introduces the benefits and challenges associated with MTSA. The benefits include comprehensive insights, improved forecast accuracy, and real-world relevance, while challenges encompass data and model complexity, explicability, and the validity of assumptions. The discussion emphasizes the need for innovative approaches to explain the predictions of complex models and highlights ongoing research in developing explanability frameworks.

Multivariate time series analysis of COVID-19 Pandemic and gold price by using Error Corrections Model

Coronavirus (COVID-19) severe acute respiratory syndrome is an infectious disease that has a direct influence on the world’s population, as is obvious from the prevalence of COVID-19. However, as the COVID-19 virus continues to proliferate, its impact is becoming more and more significant and extensive. Accordingly, the study’s goal is to use the Error Corrections Model (ECM) to examine the relationships between the COVID-19 pandemic and gold prices. An Error Corrections Model was used by the researchers in this investigation. Error Correction Models and long-term equilibrium can be found for non-stationary time series that have been cointegrated together. Two-step estimation can be used to estimate the ECM since a proportion of the imbalance from one period is adjusted in the succeeding period, the system returns to equilibrium. The calculated cointegrating relations are used to create the error correction terms, and the estimation of VAR is done by a first differencing process, and then appears in the model as an explanatory variable, with the term of error correction. The COVID-19 pandemic and gold price data were made available to the general public in a sample data. For the year 2020, it includes data on daily observations for the relevant variables. R-language results show that the COVID-19 pandemic and gold prices have been demonstrated to have a long-term causal relationship. During the most recent period of variance decomposition, 99.76 percent of the variance in covid-19 explains only 0.24 percent of the variance in gold price. This explains that there is no short-term causal relationship between covid-19 and gold price, as indicated by the Wald test results, the granger causality results have shown that the gold price is influenced not only by itself but also by the Covid-19 pandemic. Finally, there is a positive relationship between the Covid-19 pandemic and the price of gold, and this has a negative impact on human life during 2020.