Multivariate Autoregressive Model Research Articles

Directional Interactions Between Constituents of the Human Large-Scale Thermoregulatory Network

In humans, dynamic thermoregulation is (presumably) underpinned by a complex hierarchy of functional interactions between constituents of the human thermoregulatory large-scale network. However, these interactions have not been quantified from in vivo fMRI signals acquired during the experimental delivery of whole-body thermal stress. Here, we used directed functional connectivity (dFC) analysis (based on multi-variate autoregressive models) to recover directed interactions within a single thermoregulatory network during an experimental paradigm that involved controlled exposure to whole-body cooling and warming. MRI studies were performed in 30 young adults (15M/15F, mean age 25.1 ± 3.4years). Gradient echo EPI fMRI data were acquired on a 3T Siemens Verio system. The thermoregulatory challenge was applied using a specialized whole-body garment covering the entire body. Tubes lining the innards of the suit were infused with cold (2-4°C) or neutral (31-34°C) water to induce whole-body Cooling or Warming while fMRI data were contemporaneously acquired. dFC was estimated within and between the hierarchically organized homeostatic (midbrain, pons), interoceptive (insula) and executive (anterior cingulate, orbitofrontal and superior parietal cortices) sub-networks using multi-variate autoregressive models applied to the fMRI time series data. Estimates of directed interactions (akin to Granger Causality) between nodes were analyzed to recover ascending (homeostatic sub-network "upward"), descending (executive sub-network "downward"), and lateral (within sub-network) directional ("causal") effects. Both Cooling and Warming induced complex hierarchical interactions in the thermoregulatory large-scale network. Cooling induced ascending interactions from the homeostatic (midbrain) to both the executive (OFC) and interoceptive (insula) sub-networks, particularly to the superior parietal, ACC and the anterior and posterior insulae. In comparison, descending interactions were induced from the posterior insula. Warming induced ascending interactions from the homeostatic sub-network to notably the OFC (executive) and the insulae (interoceptive). Descending interactions were induced from the ACC and the OFC. Sparser effects appear from the executive to the interoceptive sub-network during warming. Our study demonstrates a hierarchical organization of thermoregulatory function between homeostatic, interoceptive and executive sub-networks. The observed information flow between/within these is consistent with a reentrant property of the hierarchical regulatory structure, characterized by the ongoing bi-directional exchange of signals along reciprocal axonal fibers linking the various nodes.

Estimating the burden of the opioid epidemic for adults and adolescents in Ohio counties.

Quantifying the opioid epidemic at the local level is a challenging problem that has important consequences on resource allocation. Adults and adolescents may exhibit different spatial trends and require different interventions and resources so it is important to examine the problem for each age group. In Ohio, surveillance data are collected at the county level for each age group on measurable outcomes of the opioid epidemic, overdose deaths, and treatment admissions. However, our interest lies in quantifying the unmeasurable construct, representing the burden of the opioid epidemic, which drives rates of the outcomes. We propose jointly modeling adult and adolescent surveillance outcomes through a multivariate spatial factor model. A generalized spatial factor model within each age group quantifies a latent factor related to the number of opioid-associated treatment admissions and deaths. By assuming a multivariate conditional autoregressive model for the spatial factors of adults and adolescents, we allow the adolescent model to borrow strength from the adult model (and vice versa), improving estimation. We also incorporate county-level covariates to help explain spatial heterogeneity in each of the factors. We apply this approach to the state of Ohio and discuss the findings. Our framework provides a coherent approach for synthesizing information across multiple outcomes and age groups to better understand the spatial epidemiology of the opioidepidemic.

Structural connectivity to reconstruct brain activation and effective connectivity between brain regions

Objective. Understanding how brain regions interact to perform a specific task is very challenging. EEG and MEG are two non-invasive imaging modalities that allow the measurement of brain activation with high temporal resolution. Several works in EEG/MEG source reconstruction show that estimating brain activation can be improved by considering spatio-temporal constraints but only few of them use structural information to do so. Approach. In this work, we present a source reconstruction algorithm that uses brain structural connectivity, estimated from diffusion MRI (dMRI), to constrain the EEG/MEG source reconstruction. Contrarily to most source reconstruction methods which reconstruct activation for each time instant, the proposed method estimates an initial reconstruction for the first time instants and a multivariate autoregressive model that explains the data in further time instants. This autoregressive model can be thought as an estimation of the effective connectivity between brain regions. We called this algorithm iterative Source and Dynamics reconstruction (iSDR). Main results. This paper presents the overall iSDR approach and how the proposed model is optimized to obtain both brain activation and brain region interactions. The accuracy of our method is demonstrated using synthetic data in which it shows a good capability to reconstruct both activation and connectivity. iSDR is also tested with real data obtained from (Wakeman D and Henson R 2015 A multi-subject, multi-modal human neuroimaging dataset Scientific Data 2 15001) (face recognition task). The results are in phase with other works published with the same data and others that used different imaging modalities with the same task showing that the choice of using an autoregressive model gives relevant results. Significance. This work shows that complex EEG/MEG datasets can be explained by an initial state and a MAR model for effective connectivity. This is a compact way to describe brain dynamics and offers a direct access to effective connectivity.

Zone specific trends in coral cover, genera and growth-forms in the World-Heritage listed Ningaloo Reef

On coral reefs, changes in the cover and relative abundance of hard coral taxa often follow disturbance. Although the ecological responses of common coral taxa have been well documented, little is known about the ecological responses of uncommon coral taxa or of coral morphological groups across multiple adjacent reef zones. We used Multivariate Auto-Regressive State-Space modelling to assess the rate and direction of change of hard coral cover across a variety of coral genera, growth forms, and susceptibility to bleaching and physical damage covering multiple reef zones at northern Ningaloo Reef in Western Australia. Trends were assessed between 2007 and 2016, during which multiple episodic disturbances occurred including cyclones and a heatwave. We provide evidence of zone specific trends, not only in total hard coral cover, but also in taxonomic and morphological groups of corals at Ningaloo Reef. Declines in total coral cover on the reef flat corresponded with declines in fast growing corals, particularly Acropora. In contrast, total coral cover on the reef slope and inshore (lagoon) did not undergo significant change, despite divergent trajectories of individual genera. Importantly, we also show that changes in the composition of coral assemblages can be detected using a morphological based approach when changes are not evident using a taxonomic approach. Therefore, we recommend that future assessments of coral reef trends incorporate not just standard metrics such as total coral cover, but also metrics that provide for detailed descriptions of trends in common and uncommon taxa and morphological groups across multiple reef zones.

Disordered directional brain network interactions during learning dynamics in schizophrenia revealed by multivariate autoregressive models.

Directional network interactions underpin normative brain function in key domains including associative learning. Schizophrenia (SCZ) is characterized by altered learning dynamics, yet dysfunctional directional functional connectivity (dFC) evoked during learning is rarely assessed. Here, nonlinear learning dynamics were induced using a paradigm alternating between conditions (Encoding and Retrieval). Evoked fMRI time series data were modeled using multivariate autoregressive (MVAR) models, to discover dysfunctional direction interactions between brain network constituents during learning stages (Early vs. Late), and conditions. A functionally derived subnetwork of coactivated (healthy controls [HC] SCZ] nodes was identified. MVAR models quantified directional interactions between pairs of nodes, and coefficients were evaluated for intergroup differences (HC ≠ SCZ). In exploratory analyses, we quantified statistical effects of neuroleptic dosage on performance and MVAR measures. During Early Encoding, SCZ showed reduced dFC within a frontal–hippocampal–fusiform network, though during Late Encoding reduced dFC was associated with pathways toward the dorsolateral prefrontal cortex (dlPFC). During Early Retrieval, SCZ showed increased dFC in pathways to and from the dorsal anterior cingulate cortex, though during Late Retrieval, patients showed increased dFC in pathways toward the dlPFC, but decreased dFC in pathways from the dlPFC. These discoveries constitute novel extensions of our understanding of task‐evoked dysconnection in schizophrenia and motivate understanding of the directional aspect of the dysconnection in schizophrenia. Disordered directionality should be investigated using computational psychiatric approaches that complement the MVAR method used in our work.

Integrated Approach Based on Dual Extended Kalman Filter and Multivariate Autoregressive Model for Predicting Battery Capacity Using Health Indicator and SOC/SOH

To enhance the efficiency of an energy storage system, it is important to predict and estimate the battery state, including the state of charge (SOC) and state of health (SOH). In general, the statistical approaches for predicting the battery state depend on historical data measured via experiments. The statistical methods based on experimental data may not be suitable for practical applications. After reviewing the various methodologies for predicting the battery capacity without measured data, it is found that a joint estimator that estimates the SOC and SOH is needed to compensate for the data shortage. Therefore, this study proposes an integrated model in which the dual extended Kalman filter (DEKF) and autoregressive (AR) model are combined for predicting the SOH via a statistical model in cases where the amount of measured data is insufficient. The DEKF is advantageous for estimating the battery state in real-time and the AR model performs better for predicting the battery state using previous data. Because the DEKF has limited performance for capacity estimation, the multivariate AR model is employed and a health indicator is used to enhance the performance of the prediction model. The results of the multivariate AR model are significantly better than those obtained using a single variable. The mean absolute percentage errors are 1.45% and 0.5183%, respectively.

Realized volatility forecast with the Bayesian random compressed multivariate HAR model

We develop a Bayesian random compressed multivariate heterogeneous autoregressive (BRC-MHAR) model to forecast the realized covariance matrices of stock returns. The proposed model randomly compresses the predictors and reduces the number of parameters. We also construct several competing multivariate volatility models with the alternative shrinkage methods to compress the parameter’s dimensions. We compare the forecast performances of the proposed models with the competing models based on both statistical and economic evaluations. The results of statistical evaluation suggest that the BRC-MHAR models have the better forecast precision than the competing models for the short-term horizon. The results of economic evaluation suggest that the BRC-MHAR models are superior to the competing models in terms of the average return, the Shape ratio and the economic value.

Fully Integrated PET/MR Imaging for the Assessment of the Relationship Between Functional Connectivity and Glucose Metabolic Rate.

In the past, determination of absolute values of cerebral metabolic rate of glucose (CMRGlc) in clinical routine was rarely carried out due to the invasive nature of arterial sampling. With the advent of combined PET/MR imaging technology, CMRGlc values can be obtained non-invasively, thereby providing the opportunity to take advantage of fully quantitative data in clinical routine. However, CMRGlc values display high physiological variability, presumably due to fluctuations in the intrinsic activity of the brain at rest. To reduce CMRGlc variability associated with these fluctuations, the objective of this study was to determine whether functional connectivity measures derived from resting-state fMRI (rs-fMRI) could be used to correct for these fluctuations in intrinsic brain activity. Methods: We studied 10 healthy volunteers who underwent a test-retest dynamic [18F]FDG-PET study using a fully integrated PET/MR system (Siemens Biograph mMR). To validate the non-invasive derivation of an image-derived input function based on combined analysis of PET and MR data, arterial blood samples were obtained. Using the arterial input function (AIF), parametric images representing CMRGlc were determined using the Patlak graphical approach. Both directed functional connectivity (dFC) and undirected functional connectivity (uFC) were determined between nodes in six major networks (Default mode network, Salience, L/R Executive, Attention, and Sensory-motor network) using either a bivariate-correlation (R coefficient) or a Multi-Variate AutoRegressive (MVAR) model. In addition, the performance of a regional connectivity measure, the fractional amplitude of low frequency fluctuations (fALFF), was also investigated. Results: The average intrasubject variability for CMRGlc values between test and retest was determined as (14 ±8%) with an average inter-subject variability of 25% at test and 15% at retest. The average CMRGlc value (umol/100 g/min) across all networks was 39 ±10 at test and increased slightly to 43 ±6 at retest. The R, MVAR and fALFF coefficients showed relatively large test-retest variability in comparison to the inter-subjects variability, resulting in poor reliability (intraclass correlation in the range of 0.11–0.65). More importantly, no significant relationship was found between the R coefficients (for uFC), MVAR coefficients (for dFC) or fALFF and corresponding CMRGlc values for any of the six major networks. Discussion: Measurement of functional connectivity within established brain networks did not provide a means to decrease the inter- or intrasubject variability of CMRGlc values. As such, our results indicate that connectivity measured derived from rs-fMRI acquired contemporaneously with PET imaging are not suited for correction of CMRGlc variability associated with intrinsic fluctuations of resting-state brain activity. Thus, given the observed substantial inter- and intrasubject variability of CMRGlc values, the relevance of absolute quantification for clinical routine is presently uncertain.

Spatial Regression with Multiple Dependent Variables: Principal Component Analysis and Spatial Autocorrelation

Simultaneous studies of multiple health conditions over geographic areas can be enhanced by the principal component analysis (PCA). However, the presence of spatial autocorrelation may induce nonlinearity that compromises PCA. This article presents an approach that combines the residual standardization method in PCA with a spatial regression method to account for spatial autocorrelation. It first estimates a multivariate simultaneous autoregressive model for parameter estimates and residuals. It then uses the residuals to formulate a standardized matrix for singular value decomposition. Simulation in various scenarios demonstrates that the proposed approach can effectively remove spatial dependent effects between spatial units to capture pure correlation effects within spatial units. Two case studies examine hospitalization and cancer data in Nebraska. The first demonstrates a way to account for spatial dependency in 39 hospitalization conditions over 156 census tracts. The second applies regression residuals to PCA to evaluate potentially elevated cancer risks near two nuclear power plants. The results show that accounting for spatial dependency and explanatory variables can help reveal information about multiple health outcomes.

Attractor Ranked Radial Basis Function Network: A Nonparametric Forecasting Approach for Chaotic Dynamic Systems

The curse of dimensionality has long been a hurdle in the analysis of complex data in areas such as computational biology, ecology and econometrics. In this work, we present a forecasting algorithm that exploits the dimensionality of data in a nonparametric autoregressive framework. The main idea is that the dynamics of a chaotic dynamical system consisting of multiple time-series can be reconstructed using a combination of different variables. This nonlinear autoregressive algorithm uses multivariate attractors reconstructed as the inputs of a neural network to predict the future. We show that our approach, attractor ranked radial basis function network (AR-RBFN) provides a better forecast than that obtained using other model-free approaches as well as univariate and multivariate autoregressive models using radial basis function networks. We demonstrate this for simulated ecosystem models and a mesocosm experiment. By taking advantage of dimensionality, we show that AR-RBFN overcomes the shortcomings of noisy and short time-series data.

An Autoregressive Distributed-Lag Modeling Approach to Nigeria’s External Reserves Dynamics

The objective of this study was to develop and analyze a regression model that explains the dynamics of foreign exchange reserves in Nigeria by examining the short-run and long-run impacts of some macroeconomic variables (exchange rate, inflation, interest rate, crude oil price, and real gross domestic product) on foreign reserves in Nigeria from 1986 to 2018. The data were sourced from the publications of the Central Bank of Nigeria (CBN) and World Bank. Unit root and co-integration tests were performed on the variables before estimation. An empirical multivariate autoregressive distributed-lag model (ARDL) was identified, specified, and estimated with the aid of EViews econometric software. Diagnostic tests for serial correlation (Breusch-Godfrey serial correlation LM test), normality (Jarque-Bera test), stability (CUSUM-of-squares test), and forecasting performance test were conducted to evaluate the estimated model. The study found that the estimated ARDL model could provide information on the behaviour of foreign exchange reserves in Nigeria. The regression results showed that none of the explanatory variables (exchange rate, inflation rate, interest rate, crude oil price, and real gross domestic product) shared contemporaneous and lagged relationship with foreign reserves dynamics in Nigeria. However, in the long run, only the previous value of foreign reserves was significant in explaining foreign reserves dynamics in Nigeria during the sample period. Given that foreign reserves play an important role in the design and evaluation of current and future macroeconomic policies aimed at achieving trade balance, the study makes the following recommendations: (1) government policies directed at managing and improving foreign reserves should largely consider the short-run and long-run behaviour of foreign reserves and these policies should be pursued with high degree of transparency because foreign reserves dynamics largely find explanation in adaptive expectation in Nigeria, (2) policy makers should ensure the evolution of appropriate exchange rate policies and regimes that will enable the economy build its reserves and adequate and balanced reserves should be accumulated to help to smoothen out the volatility in the exchange rate only in the short run, (3) government and the relevant agencies should block all foreign reserves leakages in the economy by ensuring that foreign exchange allocation and utilization are purely for genuine economic purposes and build fiscal buffers through the replenishment of the Excess Crude Account or the Sovereign Wealth Fund, and (4) the implementation of appropriate policies to facilitate the diversification of the Nigerian economy along areas of key comparative advantage (such as agriculture and small scale labour-intensive manufacturing).

Robust brain causality network construction based on Bayesian multivariate autoregression

BackgroundCognitive processes involve information integration among multiple encephalic regions, which can be measured by causal networks. However, the estimation of causal networks by means of some traditional methods with the least square will lead to distorted networks because of the unexpected outlier noise and the small number of signal samples in real applications. New methodIn this work, we adopted Bayesian inference to estimate parameters in a multivariate autoregression model (MVAR), to restrain the influence of outliers. ResultsThrough the simulation study, we observed that our proposed method can efficiently suppress outlier influence and shows stable performance when sample sizes become small. Application to real motor imagery functional magnetic resonance imaging (fMRI) also revealed that the proposed approach can capture the inherent hemispheric lateralization of motor imagery even with a small number of fMRI samples. Comparison with existing methodsWe compared our proposed Bayesian-based Granger analysis with traditional Granger causality analysis. ConclusionsThe analyses conducted in the current work demonstrate the robustness of Bayesian-based Granger analysis to outlier conditions or physiological signals with small sample sizes.

Multi-Level Clustering of Dynamic Directional Brain Network Patterns and Their Behavioral Relevance.

Dynamic functional connectivity (DFC) obtained from resting state functional magnetic resonance imaging (fMRI) data has been shown to provide novel insights into brain function which may be obscured by static functional connectivity (SFC). Further, DFC, and by implication how different brain regions may engage or disengage with each other over time, has been shown to be behaviorally relevant and more predictive than SFC of behavioral performance and/or diagnostic status. DFC is not a directional entity and may capture neural synchronization. However, directional interactions between different brain regions is another putative mechanism by which neural populations communicate. Accordingly, static effective connectivity (SEC) has been explored as a means of characterizing such directional interactions. But investigation of its dynamic counterpart, i.e., dynamic effective connectivity (DEC), is still in its infancy. Of particular note are methodological insufficiencies in identifying DEC configurations that are reproducible across time and subjects as well as a lack of understanding of the behavioral relevance of DEC obtained from resting state fMRI. In order to address these issues, we employed a dynamic multivariate autoregressive (MVAR) model to estimate DEC. The method was first validated using simulations and then applied to resting state fMRI data obtained in-house (N = 21), wherein we performed dynamic clustering of DEC matrices across multiple levels [using adaptive evolutionary clustering (AEC)] – spatial location, time, and subjects. We observed a small number of directional brain network configurations alternating between each other over time in a quasi-stable manner akin to brain microstates. The dominant and consistent DEC network patterns involved several regions including inferior and mid temporal cortex, motor and parietal cortex, occipital cortex, as well as part of frontal cortex. The functional relevance of these DEC states were determined using meta-analyses and pertained mainly to memory and emotion, but also involved execution and language. Finally, a larger cohort of resting-state fMRI and behavioral data from the Human Connectome Project (HCP) (N = 232, Q1–Q3 release) was used to demonstrate that metrics derived from DEC can explain larger variance in 70 behaviors across different domains (alertness, cognition, emotion, and personality traits) compared to SEC in healthy individuals.

Abstract TP158: Direct Path Functional Connectivity Changes in Stroke Survivors’ Brain Motor Areas Using a Brain Computer Interface Intervention for Upper Extremity Recovery

Objective: This research seeks to identify changes in frequency specific directional flow of information transmission (functional connectivity) as a result of BCI intervention. Direct path functional connectivity (isolated effective coherence (iCOH)) changes between motor-related brain areas (Brodmann areas (BA) 1-7) are thought to relate to electrophysiological signatures of motor learning. Methods: N=16 right hemisphere stroke survivors participated in 9-15 sessions with the BCI. Participants executed hand movements prompted by visual cues on a monitor concordantly with the corresponding audio instructions (e.g., Left, Right, Rest). The ‘screening’ sessions (i.e. pre and post BCI intervention) contained two runs, each consisting of 15 trials for rest, left hand, and right hand movements (i.e., 5 trials for each of the three conditions, the order of trials in a run was random). iCOH is based on formulating a multivariate autoregressive model from time series measurements, and calculating the corresponding partial coherences after setting all irrelevant connections to zero, according to Pascual-Marqui et al. 2014. From the spectral density matrix (including Mu[8-12 Hz] and Beta[18-26 Hz] ranges) obtained from estimated signals in the selected ROI, the partial coherences between any pair of nodes can be calculated. The t-statistics was performed for iCOH values between post and pre of the impaired (left) hand movement trials and thresholded at p=0.05( t=2.13, uncorrected). Results: In the Mu band, iCOH decreased pre to post from contralesional BA 4 to ipsilesional BA 5 and increased from ipsilesional BA 4 to ipsilesional BA 6. In Beta band, iCOH decreased pre to post from ipsilesional BA 5 to contralesional BA 7 and increased from ipsilesional BA 4 and & contralesional BA 7 to ipsilesional BA 6 and also from ipsilesional BA 1,2,3 to contralesional BA 4. Conclusion: There is a consistent change in the direction of information flow, as measured by iCOH, toward the ipsilesional motor and pre-motor areas (BA 4,6). Significant iCOH increases are observed in both Mu and Beta from ipsilesional BA 4 to ipsilesional BA 6 suggesting an increase in participation of motor brain areas associated with motor planning and execution with participation in BCI intervention.

Patient- and area-level predictors of prostate cancer among South Carolina veterans: a spatial analysis.

Racial and socio-economic status (SES) disparities exist in prostate cancer (PrCA) incidence and mortality. Less is known regarding how geographical factors, including neighborhood social vulnerability and distance traveled to receive care, affect PrCA risk. The purpose of this research was to use the Veterans Administration Medical System, which provides a unique means for studying PrCA epidemiology among diverse individuals with ostensibly equal access to healthcare, to determine whether area-level characteristics influence PrCA incidence while accounting for individual-level risk factors. From the US Veteran's Health Administration (VHA) electronic medical records (EMR) database from January 1999 to December 2015, we identified 3,736 PrCA patients and 104,017 cancer-free controls from South Carolina (SC). The VHA EMRs were linked to the US census which provided area-level factors. US census data were used to construct the Social Vulnerability Index which is a continuous composite measure of area-level vulnerability and was divided into tertiles for modeling purposes. Data were analyzed using a Bayesian multivariate conditional autoregressive model (CAR) which accounted for individual-level factors, area-level factors, spatial random effects, and autocorrelation, which were used to identify areas of higher- or lower-than-expected PrCA incidence after controlling for risk factors. As expected, after accounting for age (sixfold and 13-fold increases in men 40-50years and > 50years, respectively), race was an important risk factor, with threefold higher odds among Blacks in the fully adjusted model [ORadj 2.98 (2.77, 3.20)]. After accounting for all other factors, residing in a ZIP code tabulated areas (ZCTA) with the greatest level social vulnerability versus the lowest, least vulnerable ZCTA's, increased PrCA risk by 39% [ORadj 1.39 (1.11, 1.75)]. While accounting for known risk factors for PrCA, including age, race, and marital status, we found geographic areas in SC characterized by higher than average social vulnerability with higher rates of incident PrCA among veterans. Outreach for screening, education, and care coordination may be needed for veterans in these areas.

High-Latitude OTHR Adaptive Beamforming: Preserving Angle-Doppler Coupled Clutter

Over-the-horizon radars (OTHRs) often operate in the presence of interference that is nonstationary over the coherent processing interval (CPI). In this case, effective adaptive beamforming requires intra-CPI updates to the spatial weight vector to track changes in the interference spatial structure. However, these weight vector changes must be constrained to prevent modulating the clutter signal and drastically reducing subclutter visibility. These additional constraints require a model of the clutter signal. Existing adaptive beamforming algorithms either explicitly or implicitly rely on a scalar multivariate autoregressive (MVAR) model, which is based on typical observations made by mid-latitude OTHRs. However, high-latitude OTHRs often observe angle-Doppler coupled clutter, for which the scalar MVAR model does not apply. This article investigates the ramifications of angle-Doppler coupling for spatial adaptive processing (SAP), which results in the proposal of a new SAP algorithm. The efficacy of the new algorithm is compared to existing methods through simulation.

Network connectedness of green bonds and asset classes

We identify network connectedness between green bonds and different asset classes over different investment horizons in the EU and US asset markets. We first focus on dynamic correlations between green bond and asset class price changes in different time scales on the basis of wavelet coherence. We then identify network connectedness by decomposing time series into different frequency components, in each of which we evaluate connectedness on the basis of the error variance decomposition of a multivariate vector autoregressive model. Our empirical evidence reveals strong connectedness between green bonds and treasury and corporate bonds in the short and long run and in both the EU and the USA, with green bonds receiving sizeable spillovers from treasury and corporate bond prices and transmitting negligible effects. Likewise, we find that green bonds are weakly connected with high-yield corporate bond, stock and energy assets over different time scales. These findings have implications for green bond investors regarding portfolio design and hedging decisions, and for the channelling of financial flows to economic activities that are consistent with a decarbonized economy.

A Scoring Rule for Factor and Autoregressive Models Under Misspecification

Factor models (FM) are now widely used for forecasting with large set of time series. Another class of models, which can be easily estimated and used in a large dimensional setting, is multivariate autoregressive models (MAR), where independent autoregressive processes are assumed for the series in the panel. We compare the forecasting abilities of FM and MAR models when assuming both models are misspecified and the data generating process is a vector autoregressive model. We establish which conditions need to be satisfied for a FM to overperform MAR in terms of mean square forecasting error. The condition indicates in presence of misspecification that FM is not always overperforming MAR and that the FM predictive performance depends crucially on the parameter values of the data generating process. Building on the theoretical relationship between FM and MAR predictive performances, we provide a scoring rule which can be evaluated on the data to either select the model, or combine the models in forecasting exercises. Some numerical illustrations are provided both on simulated data and on wel-known large economic datasets. The empirical results show that the frequency of the true positive signals is larger when FM and MAR forecasting performances differ substantially and it decreases as the horizon increases.

Global Cortical Network Distinguishes Motor Imagination of the Left and Right Foot

Conventional passive lower limb rehabilitation is suboptimal since the brain is not actively involved in the training. An autonomous motor imagery brain-computer interface (MI-BCI) could potentially improve rehabilitation outcomes. However, motor cortex regions associated with the individual feet are anatomically close to each other. This presents a difficulty in distinguishing the left and right foot MI during rehabilitation therapy. To overcome this difficulty, we extracted functional connectivity to measure the global cortical network via electroencephalography (EEG) signals. Fourteen spatial connections (P3-Fp1, P3-F3, P3-F7, P3-C3, T5-F7, T5-C3, T5-T3, Fp2-T5, Fp2-P3, T6-Fp2, T6-T4, Cz-Fp1, Cz-F7 and Fp2-F7) found across twelve subjects significantly differed between the left and right foot MI, evidencing nonlocalized brain activity during MI. Foot MI were distinguished using machine learning algorithms in terms of the time- and frequency-domain connectivities extracted from Pearson's correlation, multivariate autoregression (MVAR), bandpass correlation, and partial directed coherence (PDC) models. The results showed that connectivity extracted by pairwise Pearson's correlation could be distinguished with 86.26 ± 9.95%, while in the frequency-domain, the gamma band presented the best classification accuracy of 73.55 ± 17.11%. We attempted to simulate asynchronous real-time classification paradigms in order to evaluate the classification performance of connectivity features compared to common spatial pattern (CSP) and band power (BP). The results indicate correlation-connectivity has the best outcome, attaining an accuracy of 80.75 ± 9.51% in asynchronous classification.

Directed Connectivity Analysis of the Neuro-Cardio- and Respiratory Systems Reveals Novel Biomarkers of Susceptibility to SUDEP.

Sudden unexpected death in epilepsy (SUDEP) is the leading cause of epilepsy-related mortality and its pathophysiological mechanisms remain unknown. Goal: We set to record and analyze for the first time concurrent electroencephalographic (EEG), electrocardiographic (ECG), and unrestrained whole-body plethysmographic (Pleth) signals from control (WT - wild type) and SUDEP-prone mice (KO- knockout Kcna1 animal model). Methods: Employing multivariate autoregressive models (MVAR) we measured all tri-organ effective directional interactions by the generalized partial directed coherence (GPDC) in the frequency domain over time (hours). Results: When compared to the control (WT) animals, the SUDEP-prone (KO) animals exhibited (p < 0.001) reduced afferent and efferent interactions between the heart and the brain over the full frequency spectrum (0-200Hz), enhanced efferent interactions from the brain to the lungs and from the heart to the lungs at high (>90 Hz) frequencies (especially during periods with seizure activity), and decreased feedback from the lungs to the brain at low (<40 Hz) frequencies. Conclusions: These results show that impairment in the afferent and efferent pathways in the holistic neuro-cardio-respiratory network could lead to SUDEP, and effective connectivity measures and their dynamics could serve as novel biomarkers of susceptibility to SUDEP and seizures respectively.