Multivariate Autoregressive Model Research Articles

An Oracle Inequality for Multivariate Dynamic Quantile Forecasting

I derive an oracle inequality for a family of possibly misspecified multivariate conditional autoregressive quantile models. The family includes standard specifications for (nonlinear) quantile prediction proposed in the literature. This inequality is used to establish that the predictor that minimizes the in-sample average check loss achieves the best out-of-sample performance within its class at a near optimal rate, even when the model is fully misspecified. An empirical application to backtesting global Growth-at-Risk shows that a combination of the generalized autoregressive conditionally heteroscedastic model and the vector autoregression for Value-at-Risk performs best out-of-sample in terms of the check loss.

Trends in COPD severe exacerbations, and all-cause and respiratory mortality, before and after implementation of newer long-acting bronchodilators in a large population-based cohort

BackgroundLittle is known about the trends in morbidity and mortality at the population level that followed the introduction of newer once-daily long-acting bronchodilators for COPD. The purpose of the study was to evaluate whether the availability of new bronchodilators was associated with changes in the temporal trends in severe COPD exacerbations and mortality between 2007 and 2018 in the older population with COPD; and whether this association was homogeneous across sex and socioeconomic status classes.MethodsWe used an interrupted time-series and three segments multivariate autoregressive models to evaluate the adjusted changes in slopes (i.e., trend effect) in monthly severe exacerbation and mortality rates after 03/2013 and 02/2015 compared to the tiotropium period (04/2007 to 02/2013). Cohorts of individuals > 65 years with COPD were created from the nationally representative database of the Quebec Integrated Chronic Disease Surveillance System in the province of Quebec, Canada. Whether these trends were similar for men and women and across different socioeconomic status classes was also assessed.ResultsThere were 130,750 hospitalizations for severe exacerbation and 104,460 deaths, including 24,457 (23.4%) respiratory-related deaths, over the study period (928,934 person-years). Significant changes in trends were seen after 03/2013 for all-cause mortality (-1.14%/month;95%CI -1.90% to -0.38%), which further decreased after 02/2015 (-1.78%/month;95%CI -2.70% to -0.38%). Decreases in respiratory-related mortality (-2.45%/month;95%CI -4.38% to -0.47%) and severe exacerbation (-1,90%/month;95%CI -3.04% to -0.75%) rates were only observed after 02/2015. These observations tended to be more pronounced in women than in men and in higher socioeconomic status groups (less deprived) than in lower socioeconomic status groups (more deprived).ConclusionsThe arrival of newer bronchodilators was chronologically associated with reduced trends in severe exacerbation, all-cause and respiratory-related mortality rates among people with COPD > 65 years. Our findings document population benefits on key patient-relevant outcomes in the years following the introduction of newer once-daily long-acting bronchodilators and their combinations, which were likely multifactorial. Public health efforts should focus on closing the gap between lower and higher socioeconomic status groups.

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.

A novel approach for large-scale characterization of residential cooking-generated PM with computer vision and low-cost sensors

Cooking is one of the major sources of indoor particulate matter (PM), which poses significant health risks and is a severe health hazard. Current studies lack an economical and effective analytical framework for quantifying inhalable particles (PM10) and fine particulate matter (PM2.5) from residential cooking activities on a large scale under real-world scenarios. This study bridges this gap by employing computer vision (CV) technology and readily available sensors. We collected data over a month in real-world settings, including cooking videos and air quality data (indoor PM10, PM2.5, CO2, temperature, relative humidity, and outdoor PM10 and PM2.5 concentrations). To classify high-emission (pan-frying, stir-frying, deep-frying) and low-emission (stewing, steaming, boiling, non-cooking) activities, we developed and validated a robust CV model named “Cooking-I3D.” This model leverages a pre-trained Two-Stream Inflated 3D ConvNet (I3D) architecture. We then assessed the efficacy of the CV-predicted cooking method in PM characterization using a first-order multivariate autoregressive model, controlling for environmental factors. The Cooking-I3D model achieved exceptional performance, boasting an accuracy of 95 % and an Area Under the Curve (AUC) of 0.98. Our results indicate that a single 6-minute high-emission cooking event triggers a 21–25 % increase in indoor PM concentrations and a 23–24 % increase in the indoor/outdoor ratio, with relative errors in these estimates ranging from 10 to 21 %. This innovative method offers a powerful tool for long-term assessment of cooking-related indoor air pollution and facilitates precision exposure assessment in human health studies.

NHSMM-MAR-sdNC: A novel data-driven computational framework for state-dependent effective connectivity analysis

The brain exhibits intrinsic dynamics characterized by spontaneous spatiotemporal reorganization of neural activity or metastability, which is associated closely with functional integration and segregation. Compared to dynamic functional connectivity, state-dependent effective connectivity (i.e., dynamic effective connectivity) is more suitable for exploring the metastability as its ability to infer causalities between brain regions. However, methods for state-dependent effective connectivity are scarce and urgently needed. In this study, a novel data-driven computational framework, named NHSMM-MAR-sdNC integrating nonparametric hidden semi-Markov model combined with multivariate autoregressive model and state-dependent new causality, is proposed to investigate the state-dependent effective connectivity. The framework is not constrained by any biological assumptions. Furthermore, state number can be inferred from the observed data directly and the state duration distributions will be estimated explicitly rather than restricted by geometric form, which overcomes limitations of hidden Markov model. Experimental results of synthetic data show that the framework can identify the state number adaptively and the state-dependent causality networks accurately. The dynamics of state-related causality networks are also revealed by the new method on real-world resting-state fMRI data. Our method provides a new data-driven computational framework for identifying state-dependent effective connectivity, which will facilitate the identification and assessment of metastability and itinerant dynamics of the brain.

Negative binomial community network vector autoregression for multivariate integer-valued time series

Modeling multivariate integer-valued time series with appropriate methods is currently a popular research topic. In this paper, we propose a multivariate integer-valued autoregressive time series model based on a fixed network community structure. We use the negative binomial distribution as the conditional marginal distribution and a copula to construct the conditional joint distribution. The newly proposed model introduces the heterogeneity of nodes. Stability conditions are provided for both fixed and increasing dimensions. We estimate the parameters of the proposed model by maximizing the quasi-likelihood function with known and unknown community membership matrices, respectively. Corresponding asymptotic properties of parameter estimates are also provided. A simulation study is conducted to demonstrate the asymptotic behavior of the proposed model, and two real datasets are employed to compare the proposed model with other competitive models.

First-order multivariate integer-valued autoregressive model with multivariate mixture distributions

The univariate integer-valued time series has been extensively studied, but literature on multivariate integer-valued time series models is quite limited and the complex correlation structure among the multivariate integer-valued time series is barely discussed. In this study, we proposed a first-order multivariate integer-valued autoregressive model to characterize the correlation among multivariate integer-valued time series with higher flexibility. Under the general conditions, we established the stationarity and ergodicity of the proposed model. With the proposed method, we discussed the models with multivariate Poisson-lognormal distribution and multivariate geometric-logitnormal distribution and the corresponding properties. The estimation method based on EM algorithm was developed for the model parameters and extensive simulation studies were performed to evaluate the effectiveness of proposed estimation method. Finally, a real crime dataset was analysed to demonstrate the advantage of the proposed model with comparison to the other models.

Synthesis of realistic non-homogeneous non-Gaussian turbulent wind fields

This paper presents a sequential method for generating synthetic non-homogeneous non-Gaussian turbulent wind fields with a prescribed time-space covariance structure. The proposed methodology is based on the optimisation of restricted multivariate autoregressive (VAR) models, and the quantile-to-quantile transform between statistical distributions. The considered case study is a non-homogeneous non-Gaussian turbulent wind field over the roof of a high rise building simulated with LES. Results show a notably good matching in terms of the reproduced wind statistical distributions, Covariance Matrix Function (CMF) and Cross Power Spectral Density Matrix (CPSDM). In addition, the synthetic wind field reproduced accurately the recirculation bubble close to the roof. The main advantages of the proposed method are that, once the VAR model is computed, the synthesis of several realisations is computationally very cheap, which is useful for performing several aeroelastic simulations of the same analysis case, as suggested by the standards. The critical point is that, to characterise the statistical features for a specific case study (such as wind turbine wakes or turbulence due to obstacles), an LES simulation of the wind field is required as input. The software employed in this work is open source and it is available on GitHub.

Analysis of long-term changes in algal bloom pattern and their association with Ocean, atmosphere, and land-based processes across the northern Indian Ocean

Algal blooms are global phenomena in marine and fresh waters. An understanding of the impacts of climate change and anthropogenic activities on marine algal blooms is essential for protecting marine ecosystems. We have studied the long-term changes in the spatial patterns of algal blooms over the northern Indian Ocean and assessed the influence of the ocean, atmosphere, and land-based processes on them. We have analyzed multi-source satellite data (2003 – 2020) of various parameters such as algal concentration, temperature, salinity, sea level, particulate organic carbon, precipitation, wind speed, and river discharge on an open-source cloud computing platform. The seasonality of variables is assessed using a harmonic model, and their spatial trend is estimated using the non-parametric Mann-Kendall test. The spatial relationship between various geophysical parameters and algal bloom concentration is assessed by the cross-correlation test, and the prediction is done using a multivariate autoregression model. Results suggest that each variable exhibits distinguishable seasonal patterns. Algal bloom duration showed a significant increase over time. However, algal bloom coverage showed a significant decline in the coastal waters in all seasons except post-monsoon. The cross-correlation test unveils that lower temperatures, salinity, and sea level promote algal bloom occurrences in coastal waters rather than open waters. Furthermore, the statistical model with a time lag of 2 months shows better performance for prediction of bloom intensity (r2 = 0.86).

Breakdown of effective information flow in disorders of consciousness: Insights from TMS-EEG

BackgroundThe complexity of the neurophysiological mechanisms underlying human consciousness is widely acknowledged, with information processing and flow originating in cortex conceived as a core mechanism of consciousness emergence. Combination of transcranial magnetic stimulation and electroencephalography (TMS-EEG) is considered as a promising technique to understand the effective information flow associated with consciousness. ObjectivesTo investigate information flow with TMS-EEG and its relationship to different consciousness states. MethodsWe applied an effective information flow analysis by combining time-varying multivariate adaptive autoregressive model and adaptive directed transfer function on TMS-EEG data of frontal, motor and parietal cortex in patients with disorder of consciousness (DOC), including 14 vegetative state/unresponsive wakefulness syndrome (VS/UWS) patients, 21 minimally conscious state (MCS) patients, and 22 healthy subjects. ResultsTMS in DOC patients, particularly VS/UWS, induced a significantly weaker effective information flow compared to healthy subjects. The bidirectional directed information flow was lost in DOC patients with TMS of frontal, motor and parietal cortex. The interactive ROI rate of the information flow network induced by TMS of frontal and parietal cortex was significantly lower in VS/UWS than in MCS. The interactive ROI rate correlated with DOC clinical scales. ConclusionsTMS-EEG revealed a physiologically relevant correlation between TMS-induced information flow and levels of consciousness. This suggests that breakdown of effective cortical information flow serves as a viable marker of human consciousness. SignificanceFindings offer a unique perspective on the relevance of information flow in DOC, thus providing a novel way of understanding the physiological basis of human consciousness.

Cross-exchange crypto risk: A high-frequency dynamic network perspective

Cross-exchange crypto trading presents inherent risks, particularly for centralized exchanges. Investors observe exacerbating crypto volatility and counterparty risk and would like to quantify these elements of crypto trades. The multiple exchanges require a multivariate view on the structures of risk spillover across exchanges. Here, a Multivariate Heterogeneous AutoRegression (MHAR) model is designed and analyzed, accommodating the stylized facts of crypto markets, including 24/7 trading and the long-memory effect on return variations. The proposed MHAR approach clearly reveals the intensity of interconnectedness among exchanges during extreme events, e.g., the Bitcoin market. Additionally, one observes extremely volatile eigenvector centralities of Futures Exchange Ltd (FTX), suggesting potential implications for its bankruptcy. Furthermore, portfolios that account for the dynamics of partial correlations or eigenvector centralities offer promising results in terms of risk measures.

A multivariate spatial and spatiotemporal ARCH Model

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects, as they are usually present in geo-referenced data. Furthermore, spatial and temporal cross-variable effects in the conditional variance are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spillovers.

Uncovering the relationship between incidental emotion toward a disaster and stock market fluctuations: Evidence from the US market

Despite having potentially important implications, there has been little research on the relationship between the public's incidental emotion and the stock market. To that end, we construct a valence-based measure of incidental emotion using BERTweet's sentiment analysis and empirically investigate the association between collective incidental emotion toward the COVID-19 pandemic and the U.S. stock market. We employ multivariate time series autoregressive models to test the relationship between emotion polarity and stock market returns or trading volumes. The results reveal that societal sentiment toward the pandemic has a significant effect on the returns of the Dow Jones Industrial Average and S&P 500. In contrast, the macro-level emotion does not significantly affect the return for NASDAQ 100. The findings also suggest a significant association between incidental emotion and trading volumes. We conduct a battery of sensitivity tests that further support our conjecture. The study underscores the robust role of incidental emotion in investment decision-making, highlighting its significance as a distinctive feature that should be incorporated into financial decision support systems.

Restored off‐channel pond habitats create thermal regime diversity and refuges within a Mediterranean‐climate watershed

Cool‐water habitats provide increasingly vital refuges for cold‐water fish living on the margins of their historical ranges; consequently, efforts to enhance or create cool‐water habitat are becoming a major focus of river restoration practices. However, the effectiveness of restoration projects for providing thermal refuge and creating diverse temperature regimes at the watershed scale remains unclear. In the Klamath River in northern California, the Karuk Tribe Fisheries Program, the Mid‐Klamath Watershed Council, and the U.S. Forest Service constructed a series of off‐channel ponds that recreate floodplain habitat and support juvenile coho salmon (Oncorhynchus kisutch) and steelhead (O. mykiss) along the Klamath River and its tributaries. We instrumented these ponds and applied multivariate autoregressive time series models of fine‐scale temperature data from ponds, tributaries, and the mainstem Klamath River to assess how off‐channel ponds contributed to thermal regime diversity and thermal refuge habitat in the Klamath riverscape. Our analysis demonstrated that ponds provide diverse thermal habitats that are significantly cooler than creek or mainstem river habitats, even during severe drought. Wavelet analysis of long‐term (10 years) temperature data indicated that thermal buffering (i.e. dampening of diel variation) increased over time but was disrupted by drought conditions in 2021. Our analysis demonstrates that in certain situations, human‐made off‐channel ponds can increase thermal diversity in modified riverscapes even during drought conditions, potentially benefiting floodplain‐dependent cold‐water species. Restoration actions that create and maintain thermal regime diversity and thermal refuges will become an essential tool to conserve biodiversity in climate‐sensitive watersheds.

Driving fatigue detection based on brain source activity and ARMA model.

Fatigue among drivers is a significant issue in society, and according to organizational reports, it substantially contributes to accidents. So accurate fatigue detection in drivers plays a crucial role in reducing the number of people fatalities or injured resulting from accidents. Several methods are proposed for fatigue driver recognition among which electroencephalography (EEG) is one. This paper proposed a method for fatigue recognition by EEG signals with extracted features from source and sensor spaces. The proposed method starts with preprocessing by applying filtering and artifact rejection. Then source localization methods are applied to EEG signals for active source extraction. A multivariate autoregressive (MVAR) model is fitted to selected sources, and a dual Kalman filter is applied to estimate the source activity and their relationships. Then multivariate autoregressive moving average (ARMA) is fitted between EEG and source activity signals. Features are extracted from model parameters, source relationship matrix, and wavelet transform of EEG and source activity signals. The novelty of this approach is the use of ARMA model between source activities (as input) and EEG signals (as output) and feature extraction from source relations. Relevant features are selected using a combination of RelifF and neighborhood component analysis (NCA) methods. Three classifiers, namely k-nearest neighbor (KNN), support vector machine (SVM), and naive Bayesian (NB) classifiers, are employed to classify drivers. To improve performance, the final label for fatigue detection is calculated by combining these classifiers using the voting method. The results demonstrate that the proposed method accurately recognizes and classifies fatigued drivers with the ensemble classifiers in comparison with other methods.

3D convolutional neural network for schizophrenia detection using as EEG-based functional brain network

Schizophrenia (ScZ) is a chronic mental disorder affecting the function of the brain, which causes emotional, social, and cognitive problems. This paper explored the functional brain network and deep learning methods to detect ScZ using electroencephalogram (EEG) signals. Functional brain network analysis was proposed and implemented using a multivariate autoregressive model and coherence connectivity algorithm. The three machine learning techniques and 3D-convolutional neural network (CNN) models were applied to classify the ScZ patients and health control subjects, and then the public LMSU database was utilized to assess the performance. The proposed 3D-CNN method achieved the performance of a 98.47 ± 1.47 % in accuracy, 99.26 ± 1.07 % in sensitivity, and 97.23 ± 3.76 % in specificity. Moreover, in addition to the default mode network region, the temporal and posterior temporal lobes of both right and left hemispheres were found as the significant difference areas in ScZ brain network analysis.

Factors associated with different types of freight crashes: A macro-level analysis

Introduction: Despite evidence showing higher fatality rates in freight-related crashes, there has been limited exploration of their spatial distribution and factors associated with such distribution. This gap in the literature primarily stems from the focus of existing studies on micro-level factors predicting the frequency or severity of injuries in freight crashes. The present study delves into the factors contributing to freight crashes at the neighborhood level, particularly focusing on different types of freight crashes: collisions involving a freight vehicle and a passenger vehicle, crashes between freight vehicles, and freight vehicle–non-motorized crashes. Method: This study analyzes traffic crash data from the urbanized region of Seoul, collected between 2016 and 2019. To effectively deal with spatial autocorrelation and model different types of crashes in a unified framework, a Bayesian multivariate conditional autoregressive model was employed. Results: Findings show substantial differences in the factors associated with various types of freight crashes. The predictors for crashes between freight vehicles diverge significantly from those for freight vehicle–non-motorized crashes. Crashes between freight vehicles are relatively more influenced by road network structure, while freight crashes involving non-motorized users are relatively more affected by the built environment and freight facilities than the other crash types examined. Freight vehicle–passenger vehicle crashes fall into an intermediate category, sharing most predictors with either of the other two types of freight crashes. Conclusions and Practical Applications: The findings of this study offer valuable lessons for transportation practitioners and policymakers. They can guide the formulation of effective land use policies and infrastructure planning, specifically designed to address the unique characteristics of different types of freight crashes.

The vector error correction index model: representation, estimation and identification

Summary This paper extends the multivariate index autoregressive model to the case of cointegrated time series of order (1,1). In this new modelling, namely the vector error-correction index model (VECIM), the first differences of series are driven by some linear combinations of the variables, namely the indexes. When the indexes are significantly fewer than the variables, the VECIM achieves a substantial dimension reduction with reference to the vector error correction model. We show that the VECIM allows one to decompose the reduced-form errors into sets of common and uncommon shocks, and that the former can be further decomposed into permanent and transitory shocks. Moreover, we offer a switching algorithm for optimal estimation of the VECIM. Finally, we document the practical value of the proposed approach by both simulations and an empirical application, where we search for the shocks that drive the aggregate fluctuations at different frequency bands in the US.

Are ride-hailing services safer than taxis? A multivariate spatial approach with accommodation of exposure uncertainty

Despite many research efforts on ride-hailing services and taxis, limited studies have compared the safety performance of the two modes. A major challenge is the need for reliable mode-specific exposure data to model their safety outcomes. Moreover, crash frequencies of the two modes by injury severities tend to be spatially and inherently correlated. To fully address these issues, this study proposes a novel multivariate conditional autoregressive model considering measurement errors in mode-specific exposures (MVCARME). More specially, a classical measurement error structure accommodates the uncertainty of estimated mode-specific exposures, and a multivariate spatial specification is adopted to capture potential spatial and inherent correlations. The model estimation is accelerated by an integrated nest Laplace approximation method. The census tracts in the city of Chicago are set as the spatial analysis unit. The mode-specific exposures (vehicle-mile-traveled) in each census tract are estimated by trip assignments using ride-hailing and taxi trip data in 2019. The modeling results indicate that both ride-hailing crashes and taxi crashes are positively associated with transportation factors (e.g., vehicle-mile-traveled, mode-specific vehicle-mile-traveled, and traffic signal numbers), land use factors (i.e., number of educational and alcohol-related sites), and demographic factors (e.g., median household income, transit ratio, and walk ratio). By comparison, the proposed model outperforms the others (i.e., negative binomial models and multivariate conditional autoregressive model) by yielding the lowest deviance information criterion (DIC), Watanabe-Akaike information criterion (WAIC), mean absolute error (MAE), and root-mean-square error (RMSE). According to the results of t-tests, ride-hailing services are found to be prone to a higher risk of minor injury crashes compared with taxis, despite no significant difference between the risks of severe injury crashes. Methodologically, this study adds a robust safety evaluation approach for comparing crash risks of different modes to the literature. At the same time, practically, it provides researchers, practitioners, and policy-makers insights into the safety management of various mobility alternatives.

Multivariate spatial modelling for predicting missing HIV prevalence rates among key populations

Abstract Ending the HIV/AIDS pandemic is among the sustainable development goals for the next decade. To overcome the problem caused by the imbalances between the need for care and the limited resources, we shall improve our understanding of the local HIV epidemics, especially for key populations at high risk of HIV infection. However, HIV prevalence rates for key populations have been difficult to estimate because their HIV surveillance data are very scarce. This paper develops a multivariate spatial model for predicting unknown HIV prevalence rates among key populations. The proposed multivariate conditional auto-regressive model efficiently pools information from neighbouring locations and correlated populations. As the real data analysis illustrates, it provides more accurate predictions than independently fitting the sub-epidemic for each key population. Furthermore, we investigate how different pieces of surveillance data contribute to the prediction and offer practical suggestions for epidemic data collection.