Multivariate Autoregressive Model Research Articles

Estimating brain effective connectivity from EEG signals of patients with autism disorder and healthy individuals by reducing volume conduction effect.

Studying brain connectivity has shed light on understanding brain functions. Electroencephalogram signals recorded from the scalp surface comprise inter-dependent multi-channel signals each of which is a linear combination of simultaneously active brain sources as well as adjacent non-brain sources whose activity is widely volume conducted to the scalp through overlapping patterns. Evaluation of brain connectivity based on multivariate autoregressive (MVAR) model identification from neurological time series can be a proper tool for brain signal analysis. However, the MVAR model only considers the lagged influences between time series while ignoring the instantaneous effects (zero-lagged interactions) among simultaneously recorded neurological signals. Hence predicting instant interactions may result in fake connectivity, which may lead to misinterpreting in results. In this study, we aim to find instantaneous effects from coefficients of the MVAR model acquired using an ADALINE neural network and investigate the efficiency of the proposed algorithm by applying it to a simulated signal. We show that our coefficients are estimated accurately from channels of the simulated signal. Moreover, we apply the proposed method on a dataset of a group of 18 healthy children and 10 children with autism by comparing their effective connectivity estimated by direct directed transfer function method using new and old coefficients. Finally, to show the efficiency of the algorithm we exploit the support vector machine method for classifying the dataset. We show that there is a significant improvement in the results obtained from the proposed method.

Analysis of the impact of electric vehicle policy on supply and demand of U.S. states bioethanol market

This study aims to construct a quantitative model of the dynamic influence of electric vehicle sales in the United States on bioethanol consumption and bioethanol production. The final research results have shown that there is a long-term equilibrium relationship in our multivariate vector autoregression (VAR) model between bioethanol consumption and bioethanol production, gasoline price, corn price, and electric vehicle sales. It can be seen from the impulse response analysis that ethanol demand will strongly respond to one standard deviation of electric vehicle sales, and our new model fits the real data of ethanol supply and demand deviation well. Based on this newly long-term equilibrium relationship, we have constructed a policy simulation model to describe the quantitative relationship between the changes in the electric vehicle policy of each state and the temporal and spatial pattern of the national bioethanol resource allocation among US states. It can help and serve as a reference tool for policy makers to conduct quantitative policy evaluation.

Evaluating the activity of a chemical enterprise based on the comprehensive analysis of trends in technical, economic, and financial indicators

Subject. The article analyzes the economic activity of a large enterprise and forecasts basic technical and economic indicators. Objectives. Our aim is to develop analytical tools for business analysis, based on official reporting data, intended to increase the reliability of knowledge about the business situation at the enterprise. Methods. The study employs methods of analysis of technical and economic indicators, intelligent multidimensional data analysis, forecasting methods, time series models, and multivariate dynamic regression models. Results. We developed tools to evaluate management decisions on the basis of the volatility of income and expenditure indicators, which enable to assess the effectiveness of technical and economic solutions. We also developed a hybrid approach to forecasting the main technical and economic indicators based on models combining the multivariate dynamic regression models, multivariate autoregressive models, and adaptive forecasting models. The presented analytical tools for business analysis were tested on the materials of three large industrial enterprises of the chemical complex. Conclusions. The offered instrumental methods can be integrated into the analysis of enterprise by minority shareholders or potential investors, who do not have access to management statements. We also recommend them as analytical tools in the field of business consulting and business analysis for various purposes, including investment ones, to increase the reliability of knowledge about the condition of business, according to official reports of the enterprise.

Echo state network models for nonlinear Granger causality.

While Granger causality (GC) has been often employed in network neuroscience, most GC applications are based on linear multivariate autoregressive (MVAR) models. However, real-life systems like biological networks exhibit notable nonlinear behaviour, hence undermining the validity of MVAR-based GC (MVAR-GC). Most nonlinear GC estimators only cater for additive nonlinearities or, alternatively, are based on recurrent neural networks or long short-term memory networks, which present considerable training difficulties and tailoring needs. We reformulate the GC framework in terms of echo-state networks-based models for arbitrarily complex networks, and characterize its ability to capture nonlinear causal relations in a network of noisy Duffing oscillators, showing a net advantage of echo state GC (ES-GC) in detecting nonlinear, causal links. We then explore the structure of ES-GC networks in the human brain employing functional MRI data from 1003 healthy subjects drawn from the human connectome project, demonstrating the existence of previously unknown directed within-brain interactions. In addition, we examine joint brain-heart signals in 15 subjects where we explore directed interaction between brain networks and central vagal cardiac control in order to investigate the so-called central autonomic network in a causal manner. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Multi-Scale Temporal Patterns in Stream Biogeochemistry Indicate Linked Permafrost and Ecological Dynamics of Boreal Catchments

Temporal patterns in stream chemistry provide integrated signals describing the hydrological and ecological state of whole catchments. However, stream chemistry integrates multi-scale signals of processes occurring in both the catchment and stream. Deconvoluting these signals could identify mechanisms of solute transport and transformation and provide a basis for monitoring ecosystem change. We applied trend analysis, wavelet decomposition, multivariate autoregressive state-space modeling, and analysis of concentration–discharge relationships to assess temporal patterns in high-frequency (15 min) stream chemistry from permafrost-influenced boreal catchments in Interior Alaska at diel, storm, and seasonal time scales. We compared catchments that varied in spatial extent of permafrost to identify characteristic biogeochemical signals. Catchments with higher spatial extents of permafrost were characterized by increasing nitrate concentration through the thaw season, an abrupt increase in nitrate and fluorescent dissolved organic matter (fDOM) and declining conductivity in late summer, and flushing of nitrate and fDOM during summer rainstorms. In contrast, these patterns were absent, of lower magnitude, or reversed in catchments with lower permafrost extent. Solute dynamics revealed a positive influence of permafrost on fDOM export and the role of shallow, seasonally dynamic flowpaths in delivering solutes from high-permafrost catchments to streams. Lower spatial extent of permafrost resulted in static delivery of nitrate and limited transport of fDOM to streams. Shifts in concentration–discharge relationships and seasonal trends in stream chemistry toward less temporally dynamic patterns might therefore indicate reorganized catchment hydrology and biogeochemistry due to permafrost thaw.

Cortical network and connectivity underlying hedonic olfactory perception

Objective. The emotional response to olfactory stimuli implies the activation of a complex cascade of events triggered by structures lying in the limbic system. However, little is known about how this activation is projected up to cerebral cortex and how different cortical areas dynamically interact each other. Approach. In this study, we acquired EEG from human participants performing a passive odor-perception task with odorants conveying positive, neutral and negative valence. A novel methodological pipeline integrating global field power (GFP), independent component analysis (ICA), dipole source localization was applied to estimate effective connectivity in the challenging scenario of single-trial low-synchronized stimulation. Main results. We identified the brain network and the neural paths, elicited at different frequency bands, i.e. , and , involved in odor valence processing. This brain network includes the orbitofrontal cortex (OFC), the cingulate gyrus (CgG), the superior temporal gyrus (STG), the posterior cingulate cortex/precuneus (PCC/PCu) and the parahippocampal gyrus (PHG). It was analyzed using a time-varying multivariate autoregressive model to resolve time-frequency causal interactions. Specifically, the OFC acts as the main node for odor perception and evaluation of pleasant and unpleasant stimuli, whereas no specific path was observed for a neutral stimulus. Significance. The results introduce new evidences on the role of the OFC during hedonic perception and underpin its specificity during the odor valence assessment. Our findings suggest that, after the odor onset different, bidirectional interactions occur between the OFC and other brain regions associated with emotion recognition/categorization and memory according to the stimulus valence. This outcome unveils how the hedonic olfactory network dynamically changes based on odor valence.

Modeling and monitoring of a multivariate spatio-temporal network system

With the development of information technology, various network systems are created to connect physical objects and people by sensor nodes or smart devices, providing unprecedented opportunities to realize automated interconnected systems and revolutionize people’s lives. However, network systems are vulnerable to attacks, due to the integration of physical objects and human behaviors as well as the complex spatio-temporal correlated structures of the network systems. Therefore, how to accurately and effectively model and monitor a network system is critical to ensure information security and support system automation. To address this issue, this article develops a multivariate spatio-temporal modeling and monitoring methodology for a network system by using multiple types of sensor signals collected from the network system. We first propose a Multivariate Spatio-Temporal Autoregressive (MSTA) model by integrating a Gaussian Markov Random Field and a vector autoregressive model structure to characterize the spatio-temporal correlation of the network system. In particular, we develop an iterative model learning algorithm that integrates the Bayesian inference, least squares, and a sum square error-based optimization method to learn the network structure and estimate parameters in the MSTA model. Then, we propose two spatio-temporal control schemes to monitor the network system based on the MSTA model. Numerical experiments and a real case study of an IoT network system are presented to validate the performance of the proposed method.

Modeling optimization method based on Gamma test and NSGA II for forecast of PV power output

ABSTRACT Forecasting can overcome the shortcomings of volatility and intermittent nature of photovoltaic (PV) power. The PV power output is affected by many factors. To improve the forecasting accuracy, the forecasting model needs considering as many relevant factors as possible, but this makes the input feature vector contain redundant information and leads to high complexity forecasting algorithm, low system stability, and poor application practicability. In this paper, we develop a novel optimization method based on Gamma test and Non-dominated Sorting Genetic Algorithm to optimize the input feature vector space and reduce the information redundancy. Meanwhile, to build targeted models for different weather conditions, a new weather variability and smoothed clearness index are deduced in this paper to measure the weather fluctuation. Based on them, the weather is classified into A and B microweather types. Two sets of input vector for the two types are optimized, and only half of the impact factors (21/51) are selected by this optimization method. Two sets of support vector machine, ELMAN artificial neural network and multivariate autoregressive models, are built. The method can greatly simplify the computational complexity as well as improve the accuracy and efficiency of the models.

Reduced Effective Connectivity in the Motor Cortex in Parkinson's Disease.

Fast rhythms excess is a hallmark of Parkinson’s Disease (PD). To implement innovative, non-pharmacological, neurostimulation interventions to restore cortical-cortical interactions, we need to understand the neurophysiological mechanisms underlying these phenomena. Here, we investigated effective connectivity on source-level resting-state electroencephalography (EEG) signals in 15 PD participants and 10 healthy controls. First, we fitted multivariate auto-regressive models to the EEG source waveforms. Second, we estimated causal connections using Granger Causality, which provide information on connections’ strength and directionality. Lastly, we sought significant differences connectivity patterns between the two populations characterizing the network graph features—i.e., global efficiency and node strength. Causal brain networks in PD show overall poorer and weaker connections compared to controls quantified as a reduction of global efficiency. Motor areas appear almost isolated, with a strongly impoverished information flow particularly from parietal and occipital cortices. This striking isolation of motor areas may reflect an impaired sensory-motor integration in PD. The identification of defective nodes/edges in PD network may be a biomarker of disease and a potential target for future interventional trials.

Forecasting the volatility of agricultural commodity futures: The role of co‐volatility and oil volatility

AbstractWe forecast the realized volatilities of China's agricultural commodity futures (corn, cotton, palm, wheat, and soybean) using a set of multivariate heterogeneous autoregressive (MHAR) models. We consider different error structures to capture the co‐movement of volatility (co‐volatility) between commodity futures to obtain out‐of‐sample forecasts of the realized volatilities of agricultural commodity futures at daily, weekly, and monthly forecast horizons. We also consider global oil volatility as an additional exogenous predictor and assess forecast precision based on both statistical and economic value measures. The results show that the MHAR model with a co‐volatility error structure is superior in predicting the volatility of commodity futures. The most accurate predictions are of corn, cotton, and wheat futures volatility. Interestingly, for all the commodities, the forecasting accuracy noticeably improves as the forecast horizon increases. However, from an investment perspective, the highest economic value is gained from medium‐horizon forecasts, and the economic value of forecasts is highest for less risk‐averse investors.

Determinants of Spot and Forward Interest Rates in Brazil in an International Liquidity Scenario: An Econometric Analysis for the Period 2007-2019

Over the last 25 years, Brazil has been among the countries with the highest interest rates globally. High interest rates have been necessary during several recent times, such as in the period from 1997 to 1999, due to the repeated international financial crises that have plagued the country. From 1999, a sustained path of interest rate reduction begun. With the outbreak of the 2008 international financial crisis, the Brazilian monetary authorities promoted a new round of falling domestic interest rates in response to the recessive effects and the threat of a systemic crisis that could hang over the national financial system. In 2012, a set of interventionist nature policies led to a decrease in the Selic rate. Thus, looking at the last 25 years, it appears that many factors have started to influence the trajectory of Brazilian interest rates. In this context, the present work aims to identify, based on empirical research, the determinants of spot and future interest rates. As a methodology, the research uses a multivariate econometric vector autoregressive model (VAR) with error correction (VEC). The analysis covers the years 2017 to 2019, corresponding to the period in the aftermath of the global financial crisis of 2008. The results evidence that both the spot rate and the DI future can be determined by the fluctuations in the level of inflation and by the level of activity and the real exchange rate, in addition to the effects of the lagged variables themselves.

Data-driven models for predicting microbial water quality in the drinking water source using E. coli monitoring and hydrometeorological data

Rapid changes in microbial water quality in surface waters pose challenges for production of safe drinking water. If not treated to an acceptable level, microbial pathogens present in the drinking water can result in severe consequences for public health. The aim of this paper was to evaluate the suitability of data-driven models of different complexity for predicting the concentrations of E. coli in the river Göta älv at the water intake of the drinking water treatment plant in Gothenburg, Sweden. The objectives were to (i) assess how the complexity of the model affects the model performance; and (ii) identify relevant factors and assess their effect as predictors of E. coli levels. To forecast E. coli levels one day ahead, the data on laboratory measurements of E. coli and total coliforms, Colifast measurements of E. coli, water temperature, turbidity, precipitation, and water flow were used. The baseline approaches included Exponential Smoothing and ARIMA (Autoregressive Integrated Moving Average), which are commonly used univariate methods, and a naive baseline that used the previous observed value as its next prediction. Also, models common in the machine learning domain were included: LASSO (Least Absolute Shrinkage and Selection Operator) Regression and Random Forest, and a tool for optimising machine learning pipelines – TPOT (Tree-based Pipeline Optimization Tool). Also, a multivariate autoregressive model VAR (Vector Autoregression) was included. The models that included multiple predictors performed better than univariate models. Random Forest and TPOT resulted in higher performance but showed a tendency of overfitting. Water temperature, microbial concentrations upstream and at the water intake, and precipitation upstream were shown to be important predictors. Data-driven modelling enables water producers to interpret the measurements in the context of what concentrations can be expected based on the recent historic data, and thus identify unexplained deviations warranting further investigation of their origin.

Forecasting with Multivariate Threshold Autoregressive Models


 
 
 An important stage in the analysis of time series is the forecasting. How- ever, the forecasting in non-linear time series models is not straightforward as in linear time series models because an exact analytical of the conditional expectation is not easy to obtain. Therefore, a strategy of forecasting with multivariate threshold autoregressive(MTAR) models is proposed via predictive distributions through Bayesian approach. This strategy gives us the forecast for the response and exogenous vectors. The coverage percentages of the forecast intervals and the variability of the predictive distributions are analysed in this work. An application to Hydrology is presented.
 
 
 
 
 
 
 
 
 

Delineating between-subject heterogeneity in alpha networks with Spatio-Spectral Eigenmodes

Between subject variability in the spatial and spectral structure of oscillatory networks can be highly informative but poses a considerable analytic challenge. Here, we describe a data-driven modal decomposition of a multivariate autoregressive model that simultaneously identifies oscillations by their peak frequency, damping time and network structure. We use this decomposition to define a set of Spatio-Spectral Eigenmodes (SSEs) providing a parsimonious description of oscillatory networks. We show that the multivariate system transfer function can be rewritten in these modal coordinates, and that the full transfer function is a linear superposition of all modes in the decomposition. The modal transfer function is a linear summation and therefore allows for single oscillatory signals to be isolated and analysed in terms of their spectral content, spatial distribution and network structure. We validate the method on simulated data and explore the structure of whole brain oscillatory networks in eyes-open resting state MEG data from the Human Connectome Project. We are able to show a wide between participant variability in peak frequency and network structure of alpha oscillations and show a distinction between occipital ’high-frequency alpha’ and parietal ’low-frequency alpha’. The frequency difference between occipital and parietal alpha components is present within individual participants but is partially masked by larger between subject variability; a 10Hz oscillation may represent the high-frequency occipital component in one participant and the low-frequency parietal component in another. This rich characterisation of individual neural phenotypes has the potential to enhance analyses into the relationship between neural dynamics and a person’s behavioural, cognitive or clinical state.

Simple and Instantaneous Causality in A Multivariate Auto-Regressive Models: An Application On Some Monetary Variables of the Egyptian Economy

Granger`s (1969) concept and definitions of causality, feedback, and instantaneous causality and Akaike final prediction error criterion and extended by Chan et al (1982) to fit a multivariate autoregressive model are used. The objective of the paper is to distinguish between simple, feedback and instantaneous causality. The notion of feedback between endogenous and exogenous variables in the bivariate AR model and its extension to the tri-variate AR models is presented. As an application to these Causality notions, the paper aimed to reach the optimal lag structure in forecasting some monetary variables in the Egyptian economy from 2005 to 2018. Variables selected were “current deposits of local currency”, “loan totals” and “quasi-money”. The three variables were correlated, and each variable was used as an endogenous function of itself lagged and the other two variables as exogeneous. The study also aimed to test if prediction is improved if current values and previous values are used in the prediction equation. .. The analysis showed that a one-way simple causal model exists from “loans total” to “current deposits of local currency”, and from “quasi-money” to “loans total”. Instantaneous causality and feedback occur between the three variables.

Predicting total electron content in ionosphere using vector autoregression model during geomagnetic storm

Abstract The ionospheric total electron content (TEC) severely impacts the positional accuracy of a single frequency Global Positioning System (GPS) receiver at the equatorial latitudes. The ionosphere causes a frequency-dependent group delay in the GPS-ranging signals, which reduces the receiver’s accuracy. Further, the variations in TEC due to various space weather phenomena make the ionosphere’s behaviour nonhomogeneous and complex. Hence, developing an accurate forecast model that can track the dynamic behaviour of the ionosphere remains a challenge. However, advances in emerging data-driven algorithms have been found helpful in tracking non-stationary behavior in TEC. These models help forecast the delays in advance. The multivariate Vector Autoregression model (VAR) predicts the Ionospheric TEC in the proposed model. The prediction model uses input data compiled in real-time from the lag values of incoming TEC data and features extracted from TEC. The TEC is predicted in real-time and tested for different prediction intervals. The metrics – Mean Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) are used for testing and validating the accuracy of the model statistically. Testing the predicted output accuracy is also done with the dynamic time warping (DTW) algorithm by comparing it with the actual value obtained from the dual-frequency receiver. The model is tested for storm days of the year 2015 for Bangalore and Hyderabad stations and found to be reliable and accurate. A prediction interval of twenty-minute shows the highest accuracy with an error within 10 TECU for all the storm days.

EEG-based motor imagery classification using digraph Fourier transforms and extreme learning machines

Motor imagery patterns are extensively exploited in brain-computer interface systems in order to control outer devices without using peripheral nerves or muscles. Classification of these patterns can be based on the associated electroencephalogram (EEG) signals. Recent approaches addressed this classification problem through techniques exploiting mainly information from one or two EEG channels. However, these approaches overlook correlations between multiple EEG channels. In this paper, we create motor-imagery classification systems based on graph-theoretic models of multichannel EEG signals. In particular, multivariate autoregressive models are used to establish the relations between the EEG channels and construct directed graph signals. Also, we constructed undirected graph signal models with Gaussian-weighted distances between graph nodes. Then, a novel variant of the graph Fourier transform is applied to the directed and undirected graph models with and without edge weights. Distinctive features were thus extracted from the transform coefficients. Additional features were computed using common spatial patterns, polynomial representations and principal components of EEG signals. Significant performance improvements were achieved using extreme learning machine (ELM) classifiers. For Dataset Ia of the BCI Competition 2003, our approach led to a classification accuracy of 96.58% with fully-connected weighted directed graph features computed on the delta-band EEG signals. For the six subjects of the Dataset 1 of the BCI Competition IV, our approach compared well with other state-of-the-art methods in the alpha and beta EEG bands.

Fatigue level detection using multivariate autoregressive exogenous nonlinear modeling based on driver body pressure distribution

Prolonged driving causes symptoms of fatigue in drivers and changes their physical condition during driving. The purpose of this paper is to use a force measurement system located in the driver’s seat by force-sensitive resistance pressure sensors in order to record the received information to predict fatigue by learning regression-based models. This system is designed with 16 FSR (Force Sensing Resistor) sensors mounted on the seat and its backrest that records the driver’s body’s data, based on the force exerted by the driver on the seat in standard mode and during driving at various times. Fatigue level prediction is based on the trained nonlinear autoregressive exogenous model. In this procedure, models based on multivariate regression are first trained, and then correctness is checked. In this paper, the fatigue index is divided into five parts from 0 to 100 included fully conscious, slightly tired, moderately tired, very tired, and extremely tired, so the criterion for diagnosis is crossing the 75% of fatigue index and entering the extremely tired range. The results show that nonlinear models based on exogenous autoregressive have better performance than the linear mode, and even in the nonlinear model of NARX neural network, the fatigue of one step ahead is well predictable. A flopped state will be predictable when the body is immersed in the seat due to fatigue, so is far from the standard sitting position and will be in the extremely tired warning range.

Multivariate Markov-switching score-driven models: an application to the global crude oil market

Abstract A new class of multivariate nonlinear quasi-vector autoregressive (QVAR) models is introduced. It is a Markov switching score-driven model with stochastic seasonality for the multivariate t-distribution (MS-Seasonal-t-QVAR). As an extension, we allow for the possibility of having common-trends and nonlinear co-integration. Score-driven nonlinear updates of local level and seasonality are used, which are robust to outliers within each regime. We show that VAR integrated moving average (VARIMA) type filters are special cases of QVAR filters. Using exclusion, sign, and elasticity identification restrictions in MS-Seasonal-t-QVAR with common-trends, we provide short-run and long-run impulse response functions for the global crude oil market.

Relating Competitive Golfers' Perceived Emotions and Performance.

The present study examined relationships between golfers’ self-perceived emotions (e.g., irritability, nervousness, tension), task-oriented coping, perceived control, and performance during a golf competition. We implemented a process-oriented golf analysis in which competitors rated these variables hole-by-hole in a competitive golf round. Within a two-level Bayesian multivariate autoregressive model, we showed that (a) within persons, emotions and task-oriented coping were reactions that stemmed from performance on the previous hole; and (b) between persons, player skill level predicted both better scores and the ability to limit the influence of negative affect on performance. These findings highlight the complex nature of the relationship between emotions and performance. Future studies might use a similarly ecologically valid research design to more precisely measure aspects of time and potentially moderating effects of player skill level and personality. An increased understanding of the dynamic relationship between emotions and performance can promote the development of effective psychological interventions for optimal performance outcomes.