Multivariate Time Series Analysis Research Articles

Short-Term Traffic Speed Prediction for Multiple Road Segments

Short-term traffic prediction has been an essential part of real-time applications in modern transportation systems for the last few decades. Despite the recent progress in the voluminous models and data sources, many existing studies have focused on prediction for either a single or a few locations. In addition, the spatiotemporal dependency in the traffic data was narrowly accounted for. Therefore, this paper finds a new short-term traffic speed prediction algorithm that can efficiently cope with the complexity and immensity of the prediction process derived from the network size and amount of data in order to provide accurate predictions in real time. This algorithm consists of two modules: (a) principal component analysis (PCA) for data dimensionality reduction and feature selection, and (b) multichannel singular spectral analysis (MSSA) for multivariate time-series data prediction. A large amount of traffic data is efficiently compressed by PCA with high accuracy, then used as an input in the multivariate time-series analysis. The algorithm was compared with a vector autoregressive (VAR) model to predict traffic speeds five minutes ahead for a 21.3-mile-long highway segment, using the traffic detector data, and for 451-mile-long segment, using probe-based speed data in Tennessee. The tested algorithm is found to provide accurate predictions with a computation time of less than one second without training. Furthermore, the algorithm shows a better prediction performance under congested flow conditions, compared to VAR. This indicates that the tested algorithm is suitable for real-time prediction and scalable for a large network analysis.

Bayesian prior modeling in vector autoregressions via the Yule-Walker equations

In multivariate time series analysis, the Yule-Walker method refers to a system of equations relating the cross-covariances of a stationary vector autoregressive (VAR) model with the matrices of the autoregressive coefficients and the covariance matrix of the noise, both of which are unknown to be estimated. In Bayesian inference of VAR models, one of the key problems is the setting of the prior distributions on these unknown parameters. The Yule-Walker equations are used here to develop a novel prior specification that exploits the reparameterization of the unknowns in terms of the mean, the cross-covariances, and the covariance of the process. Further, the cross-covariance matrices are separated out in terms of the standard deviations and the correlations. All these new quantities are easier to handle because it is more common to have prior information on the mean and the correlation structure of a multiple time series rather than the underlying autoregressive coefficients and the white noise process. The proposed prior specification is suitable for both non informative and informative settings. Through the Yule-Walker based prior, parameter estimation and structure learning of the stationary VAR models are performed via Markov chain Monte Carlo methods. The methodology is illustrated via some synthetic data sets, a benchmark example, and an environmental time series.

Multivariate time series data imputation using attention-based mechanism

As the widely deployment of different sensors and Internet of Things, a large volume of multivariate time series has been collected. However, there are many missing values in the multivariate time series due to different reasons, such as sensor damage, environmental intrusion and machine failure. These missing values bring challenges to further analysis of multivariate time series. The existing methods for multivariate time series imputation either destroy the properties of the original data or fail to capture the correlations of the data effectively. In order to solve the problems in existing methods, we propose a novel imputation method for multivariate time series based on Generative Adversarial Networks (GAN). Specifically, we use Auto-Encoder (AE) as the generator (G), Recurrent Neural Networks (RNN) as the discriminator (D). Taking advantages of generative adversarial networks to impute the incomplete multivariate time series data. In addition, Attention Mechanism is integrated to the structure of the Encoder and Decoder to keep the correlations among data. By integrating the advantages of Attention Mechanism, it enables the generator to take advantage of the internal features of the original data when imputing the data. Therefore, the imputed multivariate time series are more reasonable and reliable. Furthermore, we also improve our model by integrating Self-Attention Mechanism to improve the accuracy for multivariate time series imputation. Experimental results on real datasets demonstrate that the performance of the proposed model exceeds existing models and achieves state-of-the-art performance.

A flexible two-piece normal dynamic linear model

We construct a flexible dynamic linear model for the analysis and prediction of multivariate time series, assuming a two-piece normal initial distribution for the state vector. We derive a novel Kalman filter for this model, obtaining a two components mixture as predictive and filtering distributions. In order to estimate the covariance of the error sequences, we develop a Gibbs-sampling algorithm to perform Bayesian inference. The proposed approach is validated and compared with a Gaussian dynamic linear model in simulations and on a real data set.

Network of compression networks to extract useful information from multivariate time series

Abstract Compression networks are the result of a recently proposed method to transform univariate time series to a complex network representation by using a compression algorithm. We show how a network of compression networks can be constructed to capture relationships among multivariate time series. This network is a weighted graph with edge weights corresponding to how well the compression codewords of one time series compress another time series. Subgraphs of this network obtained by thresholding of the relative compression edge weights are shown to possess properties which can track dynamical change. Furthermore, community structures—groups of vertices more densely connected together—within these networks can identify partially synchronized states in the dynamics of networked oscillators, as well as perform genre classification of musical compositions. An additional example incorporates temporal windowing of the data and demonstrates the potential of the method to identify tipping point behaviour through the analysis of multivariate electroencephalogram time series of patients undergoing seizure.

Enhanced Bayesian Factorization With Variant Scale Partitioning for Multivariate Time Series Analysis

Multivariate time series data (Mv-TSD) portray the evolving processes of the system(s) under examination in a “multi-view” manner. Factorization methods are salient for Mv-TSD analysis with the potentials of structural feature construction correlating various data attributes. However, research challenges remain in the derivation of factors due to highly scattered data distribution of Mv-TSD and intensive interferences/outliers embedded in the source data. The proposed Enhanced Bayesian Factorization approach ( <i>Enhanced-BF</i> ) addresses the challenges in three phases: (1) variant scale partitioning applies to Mv-TSD according to degree of amplitude and obtains the blocks of variant scales; (2) hierarchical Bayesian model for tensor factorization automatically derives the factors of each block with interferences suppressed; (3) Bayesian unification model merges those block factors to construct the final structural features. <i>Enhanced-BF</i> has been evaluated using a case study of brain data engineering with multivariate electroencephalogram (EEG). Experimental results indicate that the proposed method manifests robustness to the interferences and outperforms the counterparts in terms of operation efficiency and error when factorizing EEG tensor. Besides, <i>Enhanced-BF</i> excels in factorization-based analysis of ongoing autism spectrum disorder (ASD) EEG: 3 times speed-up in factorization and <inline-formula><tex-math notation="LaTeX">$87.35\%$</tex-math></inline-formula> accuracy in ASD discrimination. The latent factors (“biomarkers”) can distinctly interpret the typical EEG characteristics of ASD subjects.

Pakistan Stock Market Reactions to Covid-19: Moderating Effect of Government Intervention

COVID-19, also known as coronavirus, is extremely contagious, and it spreads quickly. The Pakistani government has taken the necessary precautions to prevent the spread of COVID-19. This research investigates the moderating effect of government interventions on the association between stock returns and increasing confirmed cases. The Black Swan theory can be linked to this study. To investigate the effect of government intervention during the Covid-19 time on the Pakistan stock market, this study has employed a multivariate time-series analysis. The sample consists of 433 daily observations collected in Pakistan from 10th March 2020 to 13th December 2021. The exchange rate was taken as a control variable for this research. The findings have shown that government social distancing policies have a negative impact, whereas government containment, health response, and income assistance programs are likely to contribute to a positive market reaction by increasing investor confidence and lowering the disease’s negative economic impacts. Regression analysis shows that the SI has a negative relationship with stock return and containment and mitigation and economic support health index has positive relationship with stock return, but they have no effect on movement of return as they are insignificant. However, the results imply that COVID-19 confirmed cases and the exchange rate have a significant negative impact on the movement of the stock return. The findings have important policy implications because they show that government intervention policies have significant economic effects.

Motor imagery EEG signal classification with a multivariate time series approach

BackgroundElectroencephalogram (EEG) signals record electrical activity on the scalp. Measured signals, especially EEG motor imagery signals, are often inconsistent or distorted, which compromises their classification accuracy. Achieving a reliable classification of motor imagery EEG signals opens the door to possibilities such as the assessment of consciousness, brain computer interfaces or diagnostic tools. We seek a method that works with a reduced number of variables, in order to avoid overfitting and to improve interpretability. This work aims to enhance EEG signal classification accuracy by using methods based on time series analysis. Previous work on this line, usually took a univariate approach, thus losing the possibility to take advantage of the correlation information existing within the time series provided by the different electrodes. To overcome this problem, we propose a multivariate approach that can fully capture the relationships among the different time series included in the EEG data. To perform the multivariate time series analysis, we use a multi-resolution analysis approach based on the discrete wavelet transform, together with a stepwise discriminant that selects the most discriminant variables provided by the discrete wavelet transform analysisResultsApplying this methodology to EEG data to differentiate between the motor imagery tasks of moving either hands or feet has yielded very good classification results, achieving in some cases up to 100% of accuracy for this 2-class pre-processed dataset. Besides, the fact that these results were achieved using a reduced number of variables (55 out of 22,176) can shed light on the relevance and impact of those variables.ConclusionsThis work has a potentially large impact, as it enables classification of EEG data based on multivariate time series analysis in an interpretable way with high accuracy. The method allows a model with a reduced number of features, facilitating its interpretability and improving overfitting. Future work will extend the application of this classification method to help in diagnosis procedures for detecting brain pathologies and for its use in brain computer interfaces. In addition, the results presented here suggest that this method could be applied to other fields for the successful analysis of multivariate temporal data.

Superhighways and roads of multivariate time series shock transmission: Application to cryptocurrency, carbon emission and energy prices

Inferring the heterogeneous connection pattern of a networked system of multivariate time series observations is a key issue. In finance, the topological structure of financial connectedness in a network of assets can be a central tool for risk measurement. Against this, we propose a topological framework for variance decomposition analysis of multivariate time series in time and frequency domains. We build on the network representation of time–frequency generalized forecast error variance decomposition (GFEVD), and design a method to partition its maximal spanning tree into two components: (a) superhighways, i.e. the infinite incipient percolation cluster, for which nodes with high centrality dominate; (b) roads, for which low centrality nodes dominate. We apply our method to study the topology of shock transmission networks across cryptocurrency, carbon emission and energy prices. Results show that the topologies of short and long run shock transmission networks are starkly different, and that superhighways and roads considerably vary over time. We further document increased spillovers across the markets in the aftermath of the COVID-19 outbreak, as well as the absence of strong direct linkages between cryptocurrency and carbon markets.

A COMPARATIVE ANALYSIS OF VECTOR AUTOREGRESSIVE MODEL AND NEURAL NETWORKS

In this work, vector autoregression and neural network approach to multivariate time series analysis is presented. A vector autoregressive model and multilayer perceptron network with back-propagation, gradient descent algorithm have been designed to model the monthly average exchange rates of three international currencies with respect to naira. The series span over the period of January, 2012 to August, 2017. The original series were preprocessed to smoothen the distribution and facilitate fast convergence in the network algorithm. In training the network to learn the combined series of the exchange rates, a remarkable achievement was made. Adding to the beauty of the network model is the fact that the number of units of the input layer was predetermined through the VAR model. Using some model performance measures (RMSE, MBE and R2), it was recorded that the neural network approach performs better than the VAR model as it yielded minimum error of prediction.

Does domestic investment matter? A multivariate time series analysis of the energy-CO2 emission-growth nexus in Ghana.

The economic cost of greenhouse gas (GHG) emissions to African economies have increased. Therefore, GHG emissions and their concomitant effect on the environment are fast becoming costly for emerging economies like Ghana. Hence, the justification for the growing literature on the subject. This study employed the Autoregressive Distributive Lag (ARDL) bounds test and Granger causality techniques with data from 1983 to 2014. The study examines the dynamic relationship between income growth, power consumption, and carbon dioxide (CO2) emissions in Ghana, capturing the role of domestic investment and foreign direct investment (FDI) in the nexus. All variables were found to be cointegrated in the long run based on the bounds test. The Granger causality test indicates a unidirectional causality from energy consumption to CO2 emissions and economic growth. Furthermore, a unidirectional causality from CO2 to economic growth was found in Ghana. Results from the error correction model and the bounds tests indicate that, while energy consumption increases carbon emissions by more than 44%, the lagged values of domestic investment were found to reduce CO2 emissions by more than 41% in both the short run and the long run. Due to the significant effect of domestic investments on the reduction of CO2 emissions, the study recommends policymakers toadopt policies that may increase domestic capital in place of FDI, which has been proven to exacerbate environmental degradation in host countries.

Time-Series Analysis of Oxygen as an Important Environmental Parameter for Monitoring Diversity Hotspot Ecosystems: An Example of a River Sinking into the Karst Underground

Predicting variations in dissolved oxygen concentration (DO) is important for management and environmental monitoring of aquatic ecosystems. Regression analyses and univariate and multivariate time-series analyses based on autoregressive methods were performed to investigate oxygen conditions in the Pivka River, Slovenia. The monitoring site was established upstream where the river sinks into the karst cave Postojnska jama, which hosts one of the richest subterranean faunas yet studied worldwide. It was found that abnormal variations of DO started to be noticeable at values of DO &lt; 3 mg/L and became more pronounced until the ecosystem reached fully anoxic conditions. The abnormal fluctuations during the critical summer period were due to environmental conditions, organic load and resident biota. Predictions for future detection of anomalies in DO values were made from stable residuals of the measured data, and it was demonstrated that the model could be used to obtain a reliable estimate for a short period, such as one day. The example presented an analysis pipeline based on specific and established threshold DO values, and it is particularly important for ecosystems with diversity hotspots where prolonged low DO values can pose a threat to their biota.

Higher-order organization of multivariate time series

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Several methods have been proposed for the analysis of multivariate time series, yet most of them neglect the effect of non-pairwise interactions on the emerging dynamics. Here, we propose a framework to characterize the temporal evolution of higher-order dependencies within multivariate time series. Using network analysis and topology, we show that our framework robustly differentiates various spatiotemporal regimes of coupled chaotic maps. This includes chaotic dynamical phases and various types of synchronization. Hence, using the higher-order co-fluctuation patterns in simulated dynamical processes as a guide, we highlight and quantify signatures of higher-order patterns in data from brain functional activity, financial markets and epidemics. Overall, our approach sheds light on the higher-order organization of multivariate time series, allowing a better characterization of dynamical group dependencies inherent to real-world data. Most temporal analyses of multivariate time series rely on pairwise statistics. A study combining network theory and topological data analysis now shows how to characterize the dynamics of signals at all orders of interactions in real-world data.

Assessing the Impact of the COVID-19 Pandemic on the Colombian Industrial Sector: A Multivariate Time Series Analysis

The Coronavirus Disease 2019 (COVID-19) pandemic has had a severe impact on the global economy, and Latin America and the Caribbean were no exceptions. Colombia faced unprecedented economic and public health crises, leading to a significant reduction in its gross domestic product (GDP) and exportation rate of goods and services. In this study, we explore the pandemic's effect on the Colombian industrial sector using official data and statistics. We analyze the monthly Industrial Production Index (IPI) measurements taken by the Colombian National Administrative Department of Statistics (DANE, for its Spanish acronym) for 22 national industrial subsectors between January 2005 and December 2021. We apply multivariate statistics and time series techniques to compare forecasts with actual responses of the most affected subsectors after the COVID-19 outbreak. Our findings suggest that the Colombian industrial sector was not well-prepared to face the pandemic, leading to a significant financial loss. We also observe that the developing countries' industrial sectors, like Colombia's, are highly exposed and vulnerable. This information can help policymakers in Colombia to better understand the weaknesses of the industrial sector and develop strategies to mitigate the impact of future crises.

A Machine Learning Predictive Model for Determining Daily Exchange Rate Movement in Sierra Leone

"Prophet is an advanced machine learning tool designed for accurate time series forecasting. Utilizing a Bayesian additive regression model, it employs statistical techniques to analyze historical data and capture underlying patterns, trends, seasonality, and holiday effects. With its ability to handle uncertainties, anomalies, missing data, outliers, and changes in trends or seasonality, Prophet is a versatile solution for both univariate and multivariate time series analyses. In the context of the Sierra Leone currency market, our analysis using Prophet reveals valuable insights into the nominal exchange rates between the Leones and the dollar. On an annual basis, there is an observed upward trend in the nominal exchange rates. Weekly patterns indicate that the Leones tends to experience a slight depreciation on Tuesdays, while showing marginal stabilization or appreciation on Fridays. Additionally, the model highlights a tendency for marginal appreciation in the Leones from April to June, with a slight depreciation around September to October. These findings provide crucial information for risk management, economic planning, and decision-making in the Sierra Leone currency market. By understanding the identified trends in the Leones dollar exchange rates, stakeholders can make informed decisions regarding investments, currency trading, and overall economic strategies. This knowledge contributes to improving investor confidence and enables effective measures for mitigating risks. In summary, Prophet's Bayesian-based forecasting model offers probabilistic insights into future predictions, empowering decision-makers with accurate forecasts and valuable knowledge for strategic planning and risk management. "

Hypertension Monitoring by a Real Time Management System for Patients in Community and Its Data Mining by Vector Autoregressive Model

Blood pressure has a 24-hour repetitive and regular variation which shows circadian rhythm. Using the multivariate time series analysis method of vector autoregressive model, we could realize the simultaneous prediction for both systolic and diastolic blood pressures. We choose blood pressure from 6 AM to 10 AM in 3 weeks as an episode to construct a prediction model. Missing values were imputed by regression models. Subsequently, we defined segments as positive or negative segments according to blood pressure measurements. The predictions were accomplished by vector autoregressive model (VAR). Both positive and negative segments were randomly selected from each patient to summarize the effect of prediction models. In this study, the MAPE (Mean Absolute Percentage Error) of systolic blood pressure and diastolic blood pressure were both less than 10%, indicating that the VAR model was adaptable in predicting the blood pressure of hypertensive patients. Based on VAR, we could provide early warning to breakthrough of blood pressure thresholds. The sensitivity, specificity, and accuracy for patients in the training sets were 77.50%, 81.58 %, and 79.49% respectively, and the sensitivity, specificity, and accuracy for patients in the training sets were 76.92%, 80.00% and 78.43% respectively. This research took information of both systolic and diastolic blood pressures at the same time to establish the VAR models and enabled simultaneous prediction for systolic and diastolic blood pressure.

Comparing bivariate and multivariate timeseries analysis in joint action using cross-recurrence quantification analysis

Comparing bivariate and multivariate timeseries analysis in joint action using cross-recurrence quantification analysis

Multi-variate Time-series Analysis Using VECM Identifies the Best Set of Exogenous Predictors for Rainfall and Temperature in India: A Data Analytical Approach

The complex nature of climate change with multitude of underlying factors poses a major hindrance in data analysis and decision making by policy makers. Here, we utilize data analytic techniques to identify the best set of climate change indicator variables that could predict precipitation and temperature data for India. The observed values of important climatic parameters namely, rain, maximum temperature, minimum temperature, and mean temperature in India were analyzed along with the observed values of selected socio-environmental indicators featured by WHO for climate change as exogenous variables for a period of 61 years. Data were pre-processed to identify ten exogenous indicators which were then modelled using Vector Error Correction Model (VECM). 1024 VECM models were built and evaluated for the prediction of the four endogenous variables using all possible combinations of the selected indicators. Seven exogenous variables were determined as the best set of indicators based on the AIC of the different models. The model built using the identified variables was compared to others to illustrate the probable impact of this combination of variables. The study thus demonstrates a simple but rational data-driven approach for use in decision making.

Construction and validation of a COVID-19 pandemic trend forecast model based on Google Trends data for smell and taste loss.

To explore the role of smell and taste changes in preventing and controlling the COVID-19 pandemic, we aimed to build a forecast model for trends in COVID-19 prediction based on Google Trends data for smell and taste loss. Data on confirmed COVID-19 cases from 6 January 2020 to 26 December 2021 were collected from the World Health Organization (WHO) website. The keywords "loss of smell" and "loss of taste" were used to search the Google Trends platform. We constructed a transfer function model for multivariate time-series analysis and to forecast confirmed cases. From 6 January 2020 to 28 November 2021, a total of 99 weeks of data were analyzed. When the delay period was set from 1 to 3 weeks, the input sequence (Google Trends of loss of smell and taste data) and response sequence (number of new confirmed COVID-19 cases per week) were significantly correlated (P < 0.01). The transfer function model showed that worldwide and in India, the absolute error of the model in predicting the number of newly diagnosed COVID-19 cases in the following 3 weeks ranged from 0.08 to 3.10 (maximum value 100; the same below). In the United States, the absolute error of forecasts for the following 3 weeks ranged from 9.19 to 16.99, and the forecast effect was relatively accurate. For global data, the results showed that when the last point of the response sequence was at the midpoint of the uptrend or downtrend (25 July 2021; 21 November 2021; 23 May 2021; and 12 September 2021), the absolute error of the model forecast value for the following 4 weeks ranged from 0.15 to 5.77. When the last point of the response sequence was at the extreme point (2 May 2021; 29 August 2021; 20 June 2021; and 17 October 2021), the model could accurately forecast the trend in the number of confirmed cases after the extreme points. Our developed model could successfully predict the development trends of COVID-19. Google Trends for loss of smell and taste could be used to accurately forecast the development trend of COVID-19 cases 1-3 weeks in advance.

Deep learning-based predictions of older adults' adherence to cognitive training to support training efficacy.

As the population ages, the number of older adults experiencing mild cognitive impairment (MCI), Alzheimer's disease, and other forms of dementia will increase dramatically over the next few decades. Unfortunately, cognitive changes associated with these conditions threaten independence and quality of life. To address this, researchers have developed promising cognitive training interventions to help prevent or reverse cognitive decline and cognitive impairment. However, the promise of these interventions will not be realized unless older adults regularly engage with them over the long term, and like many health behaviors, adherence to cognitive training interventions can often be poor. To maximize training benefits, it would be useful to be able to predict when adherence lapses for each individual, so that support systems can be personalized to bolster adherence and intervention engagement at optimal time points. The current research uses data from a technology-based cognitive intervention study to recognize patterns in participants' adherence levels and predict their future adherence to the training program. We leveraged the feature learning capabilities of deep neural networks to predict patterns of adherence for a given participant, based on their past behavior. A separate, personalized model was trained for each participant to capture individualistic features of adherence. We posed the adherence prediction as a binary classification problem and exploited multivariate time series analysis using an adaptive window size for model training. Further, data augmentation techniques were used to overcome the challenge of limited training data and enhance the size of the dataset. To the best of our knowledge, this is the first research effort to use advanced machine learning techniques to predict older adults' daily adherence to cognitive training programs. Experimental evaluations corroborated the promise and potential of deep learning models for adherence prediction, which furnished highest mean F-scores of 75.5, 75.5, and 74.6% for the Convolution Neural Network (CNN), Long Short-Term Memory (LSTM) network, and CNN-LSTM models respectively.