Vector Time Series Research Articles

Vector time series analysis on economic growth and financial growth based on the oil price

In this paper, we consider the Europe oil prices, Brent, West Texas Intermediate, WTI, American stock market index based on the market capitalizations of 500 large companies having common stock listed on the NYSE or NASDAQ, S & P 500 , and the real gross domestic product, GDP. Based on the rolling test of Granger causality, the Europe oil prices data does Granger-cause the real gross domestic product data and S & P 500 data. So, the vector autoregressive model can be suggested. The one-step prediction method selects the vector autoregressive model as the optimal model for GDP data and S & P 500 data. The main purpose of this paper is to select the optimal model (and variable) based on Vuong’s model selection test. So, we consider the estimation and model selection of the vector autoregressive time series model with Normal innovation. The maximum likelihood method is proposed for the estimation of unknown parameters. We provide Vuong’s test for order and model selection, i.e. for selecting the order and a suitable subset of regressors, in a vector autoregressive model. Our results show that Vuong’s test confirms the causality test for GDP and S & P 500 data. Also, the results of Vuong’s test confirms the results of the predictive method.

Spatio-Temporal Evolution and Interactive Relationship Between Digital Economy and Green Development in China

A digital economy parallel with green development holds profound significance for achieving sustainability. The primary objective of this study was to explore the synergistic interaction effects between the digital economy and green development in China and forecast their future development. This study analyzed the spatio-temporal characteristics of provincial digital economy and green development in China by integrating a combined assignment method, an unconditional spatial kernel density estimation method, and a standard deviation ellipse model. The interplay between the digital economy and green development was examined using a panel vector autoregression model. Additionally, digital economy and green development levels were forecasted using univariate time series and radial basis function kernel ε-support vector regression models. The results indicate that both the digital economy and green development levels in China exhibited an upward trend from 2013 to 2021, with the digital economy increasing at a faster rate. However, both domains demonstrated regional disparities in their development processes. The mutual interaction between the digital economy and green development intensified as the lag period increased. The digital economy contributed 21% to green development, whereas green development contributed 18% to the digital economy. The initial effect of the digital economy on green development was negative, however, this impact gradually diminished over time. Additionally, the influence of green development on the digital economy was shown to follow a consistent trend of transitioning from negative to positive across the eastern, central, and western regions. Therefore, it can be seen that the digital economy exerts a sustainable impact on green development, albeit with a one-phase lag. This research provides a scientific basis for the deep integration of the digital economy and green development, thereby fostering sustainable socioeconomic growth.

PS‐InSAR post‐processing for assessing the spatio‐temporal differential kinematics of complex landslide systems: A case study of DeBeque Canyon Landslide (Colorado, USA)

AbstractThe complex superimposition of different kinematics and nested sectors within landslide systems amplifies the challenge of interpreting their heterogeneous displacement pattern and targeting effective mitigation solutions. As an example of such peculiar spatio‐temporal behaviour, the DeBeque Canyon Landslide (Colorado, USA) is emblematic of the application of interferometric post‐processing analysis for a detailed, remotely‐based investigation. We employed a multi‐geometry Persistent Scatterers (PS) InSAR dataset to provide continuous information on the spatio‐temporal scale and achieve a solid representation of the segmented kinematics and timings. Using an updated geomorphological map of the landslide system, we performed a two‐dimensional decomposition of the Persistent Scatterers (PS) dataset to determine the displacement orientation and inclination for each internal sector of the landslide system. We then conducted statistical analyses on the displacement vector characteristics and time series data. These analyses enabled us to spatially characterize the segmented activity patterns of the landslide system and identify abrupt changes in trends associated with preparatory and triggering factors. A clear differentiation of the rotational or translational kinematics within the landslide system was accomplished solely using surface displacement measures. Moreover, the application of a Bayesian model on the bi‐dimensional vector time series leads to the identification of significant differences in the deformational behaviour of each sector with respect to precipitation and temperature factors. Our approach represents a replicable method for local‐scale characterization and monitoring of landslides exhibiting complex spatio‐temporal displacement patterns and providing an effective, low‐cost solution for transportation agencies from a risk‐reduction perspective.

Addressing multidimensional highly correlated data for forecasting in precision beekeeping

In recent years, there have been relevant advances in precision beekeeping. These advances are mainly focused on proposing sensor systems that collect crucial information for bee welfare, creating integrated architectures that allow beekeepers to monitor the current state of their hive through real-time data. However, there is a lack of predictive models that would allow beekeepers to anticipate specific events that endanger bee welfare and lead to a decline in productivity. Specifically, predictive approaches accounting for the high correlation among internal variables of beehives have not been developed to date. To address this research gap, multivariate predictive models, including auto-regressive state-space and time series models, have been implemented and applied to four different hives from the we4bee project. These models aim to predict the internal variables of beehives (four different temperatures, humidity, and weight) by utilizing the meteorological conditions to which the hives are exposed. A cross-validation adapted to time series data was employed for model generalization assessment. Prediction models based on vector time series exhibited superior performance in forecasting internal hive variables compared to multivariate auto-regressive state-space models. Overall, the approach based on the vector error correction model yielded the best balance between fit, prediction, and computational cost. The VEC-based approach produces predictions with maximum mean absolute errors of 177 (312)g in weight, 3.366 (3.802)% in humidity, and 1.122 (1.685)°C in temperature at 1 (3)-days ahead when dealing with beehives exhibiting a high degree of correlation in their internal variables. Moreover, the VEC-based approach requires less than a second to perform the time series fitting process, which makes it particularly interesting for application in big data environments. The integration of such models into a decision support system would meet the need of beekeepers to anticipate potential threats to the welfare of their bee colonies, streamlining their monitoring processes while eliminating the need for continuous inspections.

Conditional mean dimension reduction for tensor time series

The dimension reduction problem for a stationary tensor time series is addressed. The goal is to remove linear combinations of the tensor time series that are mean independent of the past, without imposing any parametric models or distributional assumptions. To achieve this goal, a new metric called cumulative tensor martingale difference divergence is introduced and its theoretical properties are studied. Unlike existing methods, the proposed approach achieves dimension reduction by estimating a distinctive subspace that can fully retain the conditional mean information. By focusing on the conditional mean, the proposed dimension reduction method is potentially more accurate in prediction. The method can be viewed as a factor model-based approach that extends the existing techniques for estimating central subspace or central mean subspace in vector time series. The effectiveness of the proposed method is illustrated by extensive simulations and two real-world data applications.

Cutting-edge AI apply un-supervised learning to BDA

In order to take advantage of modern computing power, we shall apply AI to Big Data Analysis (BDA) partially from the so-called Art, Culture, Science, and Technology (ACST) --- “experience of Homosapien”, recorded at the 20 Smithsonian Museums and at the National Library of Medicine affiliated with dozens National Institutes of Medicine as well as non-profit Max-Planck ResearchGate.net. We furthermore define unsupervised learning capability that is innate to the Homosapien based on (1) ionic current responsible for Rational IQ and (2) chemical signals supporting Emotional IQ. Thus, we assume that AI computing tools must incorporate thermal temperature to the computer machine, but not operate at low temperature Electromagnetic physics. We begin by reviewing Homosapien intrinsic characteristics: (1) warm blooded brains that provide steady kinetic transport for efficient cellular operations, and (2) the ‘power of paired sensors’ (pops) which gather vector time series order set data Xp(t) for self-referenced unsupervised learning. Likewise, Homosapien have pair time series sensors (ears, eyes, nostrils, olfactory bulbs, taste buds, limbs extremities) which communicate with each other through the nervous system. The nervous system of human brain must be kept in reference at thermodynamics equilibrium, known in biology as homosapiens= . These are necessary but not sufficient conditions for intelligent beings. A higher temperature does not necessarily imply smarter or quicker learning. For example, the chicken’s brain is in equilibrium at but they lack hands, tools and past experience keeping through evolution to be our growth human beings.

On a matrix‐valued autoregressive model

Many data sets in biology, medicine, and other biostatistical areas deal with matrix‐valued time series. The case of a single univariate time series is very well developed in the literature; and single multi‐variate series (i.e., vector time series) though less well studied have also been developed. A class of matrix time series models is introduced for dealing with situations where there are multiple sets of multi‐variate time series data. Explicit expressions for a matrix autoregressive model along with its cross‐autocorrelation functions are derived. Stationarity conditions are also provided. Least squares estimators and maximum likelihood estimators of the model parameters and their asymptotic properties are derived. Results are illustrated through simulation studies and a real data application.

The dominant modes of recent sea level variability from 1993 to 2020 in the China Seas

A better understanding of internal climatic variability is essential for estimating and predicting regional sea level rise in the coming decades. Based on the satellite altimeter data, the cyclostationary empirical orthogonal function (CSEOF) analysis is used to extract and examine the seasonal signal, trend, El Niño-Southern Oscillation (ENSO)-related, and low-frequency mode of sea level anomaly in the China Seas from 1993 to 2020. The interannual changes in the annual cycle of sea level were significantly influenced by the mean surface pressure and the 10-m zonal wind component. Furthermore, strong El Niño events (1997/1998) can significantly affect seasonal fluctuations through precipitation and runoff. By recombining the loading vector and principal component time series of the trend mode, we estimate the sea level trends to be about 3.63 ± 0.37 mm/yr. The South China Sea, followed by the Yellow Sea, is where ENSO's effects on sea level fluctuations are most noticeable. The 2015–2016 El Niño, which was a combination of the Central Pacific (CP) ENSO Eastern Pacific (EP) ENSO, had average sea levels that were much lower than those of the 1997–1998 (CP ENSO) and 2009–2010 (CP ENSO). The Pacific Decadal Oscillation (PDO) can significantly affect the low frequency mode, but other sources also contribute to this mode. The South China Sea, especially to the west of Luzon Island, exhibits the highest level of variability in the low-frequency mode. Finally, our work shows that, in contrast to global or oceanic scales, regional CSEOF analysis does, in fact, capture regional sea level variability more accurately and detailed.

A bicoherence approach to analyze multi-dimensional cross-frequency coupling in EEG/MEG data

We introduce a blockwise generalisation of the Antisymmetric Cross-Bicoherence (ACB), a statistical method based on bispectral analysis. The Multi-dimensional ACB (MACB) is an approach that aims at detecting quadratic lagged phase-interactions between vector time series in the frequency domain. Such a coupling can be empirically observed in functional neuroimaging data, e.g., in electro/magnetoencephalographic signals. MACB is invariant under orthogonal trasformations of the data, which makes it independent, e.g., on the choice of the physical coordinate system in the neuro-electromagnetic inverse procedure. In extensive synthetic experiments, we prove that MACB performance is significantly better than that obtained by ACB. Specifically, the shorter the data length, or the higher the dimension of the single data space, the larger the difference between the two methods.

Vector time series modelling of turbidity in Dublin Bay

Turbidity is commonly monitored as an important water quality index. Human activities, such as dredging and dumping operations, can disrupt turbidity levels and should be monitored and analysed for possible effects. In this paper, we model the variations of turbidity in Dublin Bay over space and time to investigate the effects of dumping and dredging while controlling for the effect of wind speed as a common atmospheric effect. We develop a Vector Auto-Regressive Integrated Conditional Heteroskedasticity (VARICH) approach to modelling the dynamical behaviour of turbidity over different locations and at different water depths. We use daily values of turbidity during the years 2017–2018 to fit the model. We show that the results of our fitted model are in line with the observed data and that the uncertainties, measured through Bayesian credible intervals, are well calibrated. Furthermore, we show that the daily effects of dredging and dumping on turbidity are negligible in comparison to that of wind speed.

Fault Diagnosis of PV Array Based on Time Series and Support Vector Machine

This paper proposes a diagnosis method based on time series and support vector machine (SVM) to improve the timeliness, accuracy, and feasibility of fault diagnosis for photovoltaic (PV) arrays. It obtains the nominal output power of the PV array based on real-time collected data such as voltage, current, radiation, and temperature and normalizes the power values at different time points throughout the day to form a time series. Using the time series values as input data for a “one-to-one” multiclass classifier, we can identify and classify typical operational faults such as random shading, fixed shading, and aging degradation of PV arrays. The developed algorithmic model is trained and tested for different fault conditions using the data sets generated by the PV array simulation device. The experimental results show that our model has fairly good reliability and accuracy, and to some extent, it solves the problem of classifying shading and aging faults, two of which exhibit rather similar degradation characteristics.

Comparison of climate time series – Part 5: Multivariate annual cycles

Abstract. This paper develops a method for determining whether two vector time series originate from a common stochastic process. The stochastic process considered incorporates both serial correlations and multivariate annual cycles. Specifically, the process is modeled as a vector autoregressive model with periodic forcing, referred to as a VARX model (where X stands for exogenous variables). The hypothesis that two VARX models share the same parameters is tested using the likelihood ratio method. The resulting test can be further decomposed into a series of tests to assess whether disparities in the VARX models stem from differences in noise parameters, autoregressive parameters, or annual cycle parameters. A comprehensive procedure for compressing discrepancies between VARX models into a minimal number of components is developed based on discriminant analysis. Using this method, the realism of climate model simulations of monthly mean North Atlantic sea surface temperatures is assessed. As expected, different simulations from the same climate model cannot be distinguished stochastically. Similarly, observations from different periods cannot be distinguished. However, every climate model differs stochastically from observations. Furthermore, each climate model differs stochastically from every other model, except when they originate from the same center. In essence, each climate model possesses a distinct fingerprint that sets it apart stochastically from both observations and models developed by other research centers. The primary factor contributing to these differences is the difference in annual cycles. The difference in annual cycles is often dominated by a single component, which can be extracted and illustrated using discriminant analysis.

Multilevel Pain Assessment with Functional Near-Infrared Spectroscopy: Evaluating ΔHBO2 and ΔHHB Measures for Comprehensive Analysis.

Assessing pain in non-verbal patients is challenging, often depending on clinical judgment which can be unreliable due to fluctuations in vital signs caused by underlying medical conditions. To date, there is a notable absence of objective diagnostic tests to aid healthcare practitioners in pain assessment, especially affecting critically-ill or advanced dementia patients. Neurophysiological information, i.e., functional near-infrared spectroscopy (fNIRS) or electroencephalogram (EEG), unveils the brain's active regions and patterns, revealing the neural mechanisms behind the experience and processing of pain. This study focuses on assessing pain via the analysis of fNIRS signals combined with machine learning, utilising multiple fNIRS measures including oxygenated haemoglobin (ΔHBO2) and deoxygenated haemoglobin (ΔHHB). Initially, a channel selection process filters out highly contaminated channels with high-frequency and high-amplitude artifacts from the 24-channel fNIRS data. The remaining channels are then preprocessed by applying a low-pass filter and common average referencing to remove cardio-respiratory artifacts and common gain noise, respectively. Subsequently, the preprocessed channels are averaged to create a single time series vector for both ΔHBO2 and ΔHHB measures. From each measure, ten statistical features are extracted and fusion occurs at the feature level, resulting in a fused feature vector. The most relevant features, selected using the Minimum Redundancy Maximum Relevance method, are passed to a Support Vector Machines classifier. Using leave-one-subject-out cross validation, the system achieved an accuracy of 68.51%±9.02% in a multi-class task (No Pain, Low Pain, and High Pain) using a fusion of ΔHBO2 and ΔHHB. These two measures collectively demonstrated superior performance compared to when they were used independently. This study contributes to the pursuit of an objective pain assessment and proposes a potential biomarker for human pain using fNIRS.

A study of the price situation of sailboats based on a comprehensive evaluation model

In order to optimize the price evaluation of used sailboats, this paper collects and analyzes a large amount of relevant data, and adopts principal component analysis, multiple linear regression and neural network model to establish the linkage between price and each variable. The non-numerical data are quantified and processed, and the comprehensive evaluation model is constructed by entropy value method and linear weighting method. The TOPSIS method was used to revalue the price and optimize the model. The geographic location is quantified by spherical coordinates and analyzed by clustering to build a geographic-price model. Finally, taking Hong Kong as an example, the time series and support vector machine models are used for pricing.

Internet-of-Things Traffic Analysis and Device Identification Based on Two-Stage Clustering in Smart Home Environments

Smart home environments, which consist of various Internet of Things (IoT) devices to support and improve our daily lives, are expected to be widely adopted in the near future. Owing to a lack of awareness regarding the risks associated with IoT devices and challenges in replacing or the updating their firmware, adequate security measures have not been implemented. Instead, IoT device identification methods based on traffic analysis have been proposed. Since conventional methods process and analyze traffic data simultaneously, bias in the occurrence rate of traffic patterns has a negative impact on the analysis results. Therefore, this paper proposes an IoT traffic analysis and device identification method based on two-stage clustering in smart home environments. In the first step, traffic patterns are extracted by clustering IoT traffic at a local gateway located in each smart home and subsequently sent to a cloud server. In the second step, the cloud server extracts common traffic units to represent IoT traffic by clustering the patterns obtained in the first step. Two-stage clustering can reduce the impact of data bias, because each cluster extracted in the first clustering is summarized as one value and used as a single data point in the second clustering, regardless of the occurrence rate of traffic patterns. Through the proposed two-stage clustering method, IoT traffic is transformed into time series vector data that consist of common unit patterns and can be identified based on time series representations. Experiments using public IoT traffic datasets indicated that the proposed method could identify 21 IoTs devices with an accuracy of 86.9%. Therefore, we can conclude that traffic analysis using two-stage clustering is effective for improving the clustering quality, device identification, and implementation in distributed environments.

Research on a multilevel scheduling model for multi variety and variable batch production environments based on machine learning

Traditional manufacturing enterprises cannot adjust their production line structure in the short term. They face significant challenges in adapting to the rapidly changing market environment and meeting various variable batch production requirements. Building a suitable and convenient multi-layer planning and scheduling model is an important goal to solve the efficient operation of manufacturing enterprises. This paper proposes a planning and scheduling design that meets the needs of enterprise and the production workshop using the APERT-VC model through a top-down design methodology. APERT is an enterprise-level plan that uses attention mechanisms to collect job plan time and decomposes project plans into workshop plans through PERT technology. virtual command is workshop level plan management, which converts workshop plans into time series vectors and achieves rapid and comprehensive guidance of workshop resource planning for enterprises through multiple classification and decision-making. Through experiments, the algorithm achieved production scheduling accuracy improvement of over 30% compared to previous algorithms and a decision accuracy rate of over 90%. The first half of the new model solves the problem of collecting work time for multi variety and variable batch products, and improves the accuracy of algorithm input. The second half of the new algorithm innovatively combines image recognition technology with dispatcher behavior, achieving efficient simulation results.

Fluctuation of Exchange Rates Caused by Monetary Policy Divergence: Empirical Analysis between China and USA

In the past ten years, because of the differences in economic history and social political scenarios between China and the US, the two countries have already experienced a divergence in monetary policy. Asides the domestic macroeconomic implications, the divergence would potentially cause changes and fluctuations between the exchange rates of the two currencies. Through theoretical analysis on macro and international economics as well as econometrics modelling utilizing Python and Stata-17, this research constructed a time series vector autoregression model quantifying the relationship between the USD/CNY exchange rate and monetary policy changes of both the US and China. This research found that the monetary policy changes in the two countries would not fundamentally change the USD/CNY exchange rate level but would cause fluctuations. Based on the findings, the article made recommendations for both central bankers and investors participating in the foreign exchange market to deal with the monetary policy divergence of the two major global economic entities.

ADVANCED DEMOGRAPHIC SITUATIONS BASED ON LAG MODELS

Research and forecasting of time series based on models with lags is offered, as well as calculation of a reliable forecast based on data on birth rates in Ukraine. Economic modeling is one of the important modern tools for assessing the impact of technologies on the economic sector in order to obtain an optimal solution. Economic evaluations can be based on several different modeling approaches, each with its own strengths and weaknesses. The relevance of the use of economic and mathematical models for the purpose of studying demography is connected with the need to study population and migration processes, as well as for further planning and implementation of the country's economic and social development. In every sphere of the economy, there are phenomena that are interesting and important to study in their development, as they evolve over time. Prices, economic conditions, industrial processes, and demographic data tend to change over time. The set of measurements of this kind of indicators depending on time is a time series. The goals of studying time series can be different. It is possible, for example, to try to predict the future on the basis of knowledge of the past, to control the process that generates the series, to try to find out the mechanism underlying the process, to clear the series of components that obscure its dynamics, or simply to briefly describe the characteristic features of the series. When studying the relationships between indicators or when analyzing their development over time, not only the current value of the variables, but also some previous values in time, as well as time itself, are used as explanatory variables. Models of this type are called dynamic. In economic analysis, dynamic models are used quite widely. This is quite natural, because in many cases the influence of some economic factors on others is not carried out immediately, but with some delay − a lag. The object of research is the mathematical model of the interdependence of the vector time series "Births in Ukraine for January 2005 − July 2012." The data are chosen quite relevantly, because without a preliminary demographic forecast it is impossible to imagine the prospects of industry and consumption of goods and services, housing construction, development of social infrastructure, health care and education, pension system and solutions to geopolitical problems.

Disentangling Trend Risk and Basis Risk with Functional Time Series

In recent multi-population stochastic mortality models, one critical scientific issue is the vague distinction between trend risk and population basis risk. In particular, the cross- and auto-correlations between the innovations of the latent factors representing the common trend and the population-specific trends are often assumed to be non-existent, although they are possibly statistically significant. While it is theoretically possible to capture such correlations by treating the latent factors as a vector time series, the resulting model would contain a large number of parameters, which may in turn lead to robustness problems. In this paper, we address these issues by the use of the product–ratio model. Contrary to the prevalent assumption of non-existent correlations, the latent factors under the product–ratio model are approximately uncorrelated. This permits us to disentangle trend risk and population basis risk, thereby sparing us from the need to use a heavily parameterized vector time-series process. Compared to the augmented common factor model, our approach demonstrates improved robustness in terms of correlation structures and hedging performance, offering a new perspective on treating cross- and auto-correlations between latent factors in mortality modeling.

Granger causality based on vector time series and quaternion algebra with possible applications to molecular dynamics data analysis.

Causal analysis plays a significant role in physics, chemistry, and biology. Dynamics of complex (bio)molecular and nanosystems, from the microscopic to the macroscopic scale, are characterized by time-dependent vectors such as positions, forces, momenta, angular momenta, or torques. Identification and analysis of causal relationships between these time-dependent signals is an important problem in the multidimensional time-series analysis and is of great practical importance in describing the properties of such dynamical systems, and to understanding their functionality. For linear stochastic systems characterized by multidimensional scalar signals, Granger proposed a simple procedure to detect causal relationships, called Granger causality. In this study we extended this formalism to vector signals representing physical vector quantities. For this purpose, we used quaternion algebra, where vector signals are treated as time-dependent quaternions. The developed analytical model is based on the autoregressive formalism. This formalism (Q-MVAR) and its numerical implementation were validated using two simple dynamic models: a rigid body model represented by a benzenelike molecular fragment, interacting with a short-range harmonic potential with a wall, as well as a system of three model atomic balls moving inside a soft spherical surface and interacting with long range electrostatic forces. Although the motivation to these studies was the analysis of classical motions in complex (bio)molecular systems, described with a mechanical model and based on molecular dynamics (MD) simulations, in particular coarse-grained ones, it should be noted that the developed extended formalism can be applied to any system composed of many rigid elements that interact with arbitrary potentials and are characterized by complex internal motions. A description of the detailed procedure for calculating causality measures is provided in the Appendicesof the Supplemental Material. This formalism and the prototype of its numerical implementation can be further developed and applied in many different fields of physical, natural, and engineering sciences.