Flexible Bayesian Product Mixture Models for Vector Autoregressions

A vector autoregressive (VAR) model is a widely used parametric method that captures linear interdependencies between multivariate time series data. However, conventional VAR models are frequently constrained by some assumptions of linearity and stationarity, limiting their ability to capture complex and nonlinearity dynamic observed in real life data. This research aims to develop Multivariate Random Forest Technique for VAR model. Augmented Dickey Fuller (ADF) was applied to test the stationarity of the time series data. Simulated stationary time series data and real time series dataset were applied for modeling VAR model in order to compare their forecast performance. The forecast performance for the proposed technique and existing technique for VAR models were based on Mean Absolute Error and Root Mean Square Error. The proposed multivariate Random Forest technique for VAR model has been developed. The results for unit root test for real life data indicate that all the variables are stationary at level. The result for simulated data in term of forecast performance indicated that the proposed multivariate Random Forest techniques for VAR model outperform existing technique (conventional VAR model) in long term forecasting, while the conventional VAR model outperform proposed multivariate Random Forest technique in short term forecast based on MAE and RMSE. The results for real dataset indicated that the proposed multivariate Random Forest technique for VAR model is superior in terms of forecast performance than that of conventional VAR model in short-term and long-term forecast based on MAE and RMS since the proposed technique has the least value of MAE and RMSE in short and long-term forecasting than the conventional VAR model.

Various analytical techniques are available for modeling multivariate time series data. One such approach is the State Space Model, which can be employed to model this type of data. In this study, the data to be analyzed are data on the Indonesia Rupiah (IDR) exchange rate (ExR) against the US Dollar (USD), oil and gas exports (OGE), money supply (MS) and non-oil and gas exports (non-OGE) from January 2008 to December 2019. The aim of this study is to identify the most suitable state space model for the given data. In this research, the state space method will be applied to multivariate time series data, with the state space represented in the Vector Autoregressive (VAR) model to explore the interrelationships among groups of observed variables. The VAR model is a statistical technique used to analyze the relationships between variables in the dataset, employing the Granger Causality Test. The state space model is utilized to model and forecast multiple interconnected time series, where the variables exhibit dynamic interactions and to examine additional unobserved variables in the time series data. Based on the analysis results and the minimum value of the Akaike Information Criterion (AIC), the optimal VAR model identified is the VAR (6) model. The results of forecasting values using the state space model show that the predicted values and the real values for the state space model are very closed to each other.

This paper is based on the vector autoregressive (VAR) model, and the model optimization is completed by determining the lag order to eliminate the autocorrelation in the error term through model comparison. The variables in the tax-related risk of the betting agreement are formed into a vector form, the parameters are estimated by least squares or maximum likelihood estimation, and the interrelationship of the variables is analyzed by impulse response function. The vector autoregressive model was used to evaluate the tax-related risk of the betting agreement of Company M, and 12 factors were obtained. Among them, the factors that have more than 80% influence on tax-related risk are the lack of research on the betting agreement and the backwardness of the theoretical aspects of the handling of the betting agreement, with the influence of 87.89% and 84.98%, respectively. Therefore, the vector autoregressive model can effectively assess the tax-related risks in corporate betting agreements and provide a reference for companies diversifying into restructuring and mergers.

Electroencephalographic (EEG) signals recorded from the scalp surface are generally highly correlated. Each channel is a linear mixture of concurrently active brain and non-brain electrical sources whose activities are volume conducted to the scalp electrodes with broadly overlapping patterns (Nunez et al., 1997). This property is particularly relevant to connectivity analyses, which seek to detect and characterize active interactions between brain regions. Therefore, meaningful connectivity patterns can be derived only from measures of cortical source activities and not directly from EEG channel activities (Michel and Murray, 2012). However, this poses a serious problem, since estimating the nature, number, brain (or non-brain) locations, and time courses of the active sources contributing to the scalp EEG is not straightforward (Baillet et al., 2001). Several methods have been proposed to estimate source activities from multi-channel EEG recordings, thereby removing the confounding effects of volume conduction. These methods can be grouped into three categories: (a) simple spatial filters that seek to reduce correlations between scalp channels based on idealized assumptions; (b) more complex spatial filters that seek to estimate net activities within ROIs based on detailed neurophysiological head models; and (c) blind spatial source separation methods that seek to separately identify source signals by exploiting source signal information differences. Whereas simple spatial filters such as bipolar derivations and Laplacian filters can reduce, to some extent, correlations among scalp-recorded channels (Fisch, 2012), more sophisticated spatial filtering methods use inverse imaging methods to estimate the time courses of cortical sources in given or estimated region of interest (ROI) (Baillet et al., 2001). Blind source separation techniques, in particular independent component analysis, by contrast, learn spatial filters from the EEG time courses that separate the data into constituent independent source activities. Their corresponding brain (or non-brain) locations can then be estimated using neurophysiological inverse imaging methods (Makeig et al., 1996; Jung et al., 2001; Delorme et al., 2012). Vector autoregressive (VAR) models are versatile tools for analyzing multivariate time series, including multi-channel EEG or multivariate source activities. VAR models predict current values of time series from their recent past (Lutkepohl, 2005). Importantly, they can be used to derive various electrophysiological connectivity measures (Schlogl and Supp, 2006). Volume conduction in biological tissue can be modeled as instantaneous propagation of activity from sources to recording channels. The resulting zero-phase connectivity may be treated as noise added to lagged connectivity patterns of interest. Although some measures, including the imaginary part of the coherency (Nolte et al., 2004), are insensitive to zero-phase connectivity, measures derived from VAR model coefficients do not include such zero-phase terms. Thus, volume conduction effects are not accounted for by the model and affect the correlation structure of the model residuals, which are normally assumed to be uncorrelated. Popular connectivity measures derived from VAR models include the Directed Transfer Function (DTF) (Kaminski and Blinowska, 1991) and the Partial Directed Coherence (PDC) (Baccala and Sameshima, 2001). Whereas the PDC is defined in terms of the system matrix (a frequency domain representation of the VAR model), the DTF is based on the inverse of the system matrix. Viewing lagged dependencies between source signals as information flow, the DTF may be said to be normalized by the inflow of information to some sink, while the PDC is normalized by the outflow of information from some source. As we will demonstrate below, both the DTF and the PDC are indeed adversely affected by volume conduction from multiple sources to the scalp electrodes, in contrast to the claim of Kaminski and Blinowska in their recent opinion article (Kaminski and Blinowska, 2014). Thus, in general direct application of connectivity measures to scalp EEG signals produces less than accurate results and also does not allow their clear interpretation in terms of underlying source dynamics.

In this paper, a multimodal teaching model based on vector autoregressive (VAR) model is constructed for English teaching in colleges and universities, and the model is optimized and improved. The VAR model can predict the potential future paths of the specified variables in the model, and thus measure the long-term equilibrium relationship of multiple variables in English teaching in colleges and universities. This model was empirically studied in the multimodal teaching of four listening, speaking, reading and writing aspects. The results of the study show that the students in the experimental group significantly improved their performance in the listening test, in which the average scores of Groups A, B, and C were 18.49, 20.265, and 21.99, respectively, with a p-value of 0.000, which is lower than the 0.05 level of significance. Most of the students think that the multimodal English film and video clip teaching mode helps improve English thinking ability and fluency of oral expression. Regarding reading comprehension, the average score of the experimental class reaches 20.89 while the control class is 16.8, with a p-value of 0.001, indicating that the practical class is significantly better than the control class. Regarding writing instruction, most students also preferred multimodal instruction and recognized its positive effects. The application of multimodal teaching mode based on VAR model in English teaching in colleges and universities is practical and can significantly improve students’ listening, speaking, reading and writing abilities.

Very-short-term wind power prediction is of great significance for the safe and stable operation of power system. As a well-known time series model, vector autoregressive (VAR) model is very suitable for very-short-term forecasting, and it can consider the temporal and spatial correlation among multiple wind farms to improve the forecasting accuracy. However, when there are a large number of wind farms, VAR model is prone to over-fitting. Slow calculation speed is also the problem of VAR model. This paper adds regularization terms in estimating coefficients to obtain a sparse coefficient matrix, which helps to avoid over-fitting. Online VAR model is used to improve the calculation speed, and a specific improved online VAR method is proposed for forecasting wind power output from new-built wind farms. This method is tested in a specific case, and the prediction accuracy and calculation speed are better than the traditional VAR model. In addition, the improved online VAR method can accurately predict wind power output of new-built wind farms with little historical data.

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

In this paper, we have estimated vector autoregression (VAR), Bayesian vector autoregression (BVAR) and vector error-correction models (VECMs) using annual time-series data of South Korea for 1950-94. We find evidence supporting the view that growth of real per-capita income has been aided by income, investment and export growth, as well as government spending and exchange rate policies. The VECMs provide better forecasts of growth than do the VAR and BVAR models for both short-term and long-term predictions.

Increasing antibiotic resistance may reciprocally affect consumption and lead to use of broader-spectrum alternatives; a vicious cycle that may gradually limit therapeutic options. Our aim in this study was to demonstrate this vicious cycle in gram-negative bacteria and show the utility of vector autoregressive (VAR) models for time-series analysis in explanatory and dependent roles simultaneously. Monthly drug consumption data in defined daily doses per 100 bed-days and incidence densities of gram-negative bacteria (Escherichia coli, Klebsiella spp., Pseudomonas aeruginosa, and Acinetobacter baumannii) resistant to cephalosporins or to carbapenems were analyzed using VAR models. These were compared to linear transfer models used earlier. In case of all gram-negative bacteria, cephalosporin consumption led to increasing cephalosporin resistance, which provoked carbapenem use and consequent carbapenem resistance and finally increased colistin consumption, exemplifying the vicious cycle. Different species were involved in different ways. For example, cephalosporin-resistant Klebsiella spp. provoked carbapenem use less than E. coli, and the association between carbapenem resistance of P. aeruginosa and colistin use was weaker than that of A. baumannii. Colistin use led to decreased carbapenem use and decreased carbapenem resistance of P. aeruginosa but not of A. baumannii. VAR models allow analysis of consumption and resistance series in a bidirectional manner. The reconstructed resistance spiral involved cephalosporin use augmenting cephalosporin resistance primarily in E. coli. This led to increased carbapenem use, provoking spread of carbapenem-resistant A. baumannii and consequent colistin use. Emergence of panresistance is fueled by such antibiotic-resistance spirals.

The results of forecasting experiments based on an error correction mechanism (ECM) model and various types of vector autoregressive (VAR) and Bayesian vector autoregressive (BVAR) models are presented. A Bayesian error correction mechanism (BECM) model is also tested. This model represents a hybrid of the BVAR and ECM models. The results from experiments using fifty industries and monthly Ohio labor market data demonstrate that the ECM model produces forecasts with much lower errors than any of the alternative VAR or BVAR models when the variables used in the model pass the statistical tests for cointegration. The findings confirm many of the beliefs expressed by Granger (1986) and Engle and Yoo (1987) based on theoretical consideration of the ECM model versus the VAR model. A result contradictory to the contentions of Engle and Yoo is that the BECM model performs well at the longer forecast horizons for both cointegrated and non-cointegrated industries.

SUMMARY & CONCLUSIONSModeling corrosion growth for complex systems such as the oil refinery system is a major challenge since the corrosion process of oil and gas pipelines are inherently stochastic and depends on many factors including exposures to environmental conditions, operating conditions, and electrochemical reactions. Moreover, the number of sensors is usually limited, and sensor data are incomplete and scattering, which hinders the capability of capturing the corrosion growth behaviors. Therefore, this paper proposes Multi-sensor Corrosion Growth Model with Latent Variables to predict the corrosion growth process in oil refinery piping. The proposed model is a combination of the hierarchical clustering algorithm and the vector autoregression (VAR) model. The clustering algorithm aims to find the hidden (i.e., latent) data clusters of the measured time series data, from which the time series from the same cluster will be included in the VAR model to predict the corrosion depth from multiple sensors. The model can capture the relationship between sensor time series data and identify latent variables. A real case study of an oil refinery system, in which in-line inspection (ILI) data were collected, was utilized to validate model. Regarding corrosion growth prediction, the paper compared the prediction accuracy of VAR model with other three forms of power law model, which is widely accepted to expect the time-dependent depth of corrosion such as power function (PF), PF with initiation time of corrosion (PFIT), and PF with initiation time of corrosion and covariates (PFCOV). The results showed that VAR model has the lowest prediction error based on the mean absolute percentage error (MAPE) evaluation for test data. Finally, the proposed model is believed to be useful for dealing with a complex system that has a variety of corrosion growth behaviors, such as the oil refinery system, as well as it can be applied in other real-time applications.

Accurate forecasting of agricultural commodity prices, particularly vegetables, is essential for comprehending market dynamics and maintaining economic stability among stakeholders. Effective price forecasting fosters agricultural sustainability and economic resilience. This study aims to identify the optimal model for forecasting wholesale eggplant prices in the Lucknow market, comparing the traditional vector autoregressive (VAR) model with the Artificial Neural Network (ANN) model. The most commonly used evaluation metrics were applied to compare and assess model performance. For model building, 204 monthly observations from January 2008 to December 2024, comprising a dataset of wholesale prices and total arrival of eggplant in the Lucknow center, were utilized. In the modeling process, the entire dataset was partitioned into two subsets, training and testing data, with a split of 80:20. To check stationarity, the Augmented Dickey-Fuller test was conducted, and the lag order for the VAR model was selected based on the minimum AIC value, with [5] as the optimal lag order. Similarly, the ANN model was created using [5] lags of the variables, as independent variables. The findings indicate that the ANN [10: 3: 2: 1] model surpasses the VAR (5) model in forecasting wholesale prices within the test dataset. However, both models exhibit overfitting, likely attributable to the VAR model's inadequacy in capturing the heteroscedasticity effect and the ANN model's dependence on a limited dataset and the number of lag variables incorporated as inputs. These methods can be applied to model and forecast prices of other agricultural commodities and have potential in broader agricultural research, as their utilization in this field remains limited.

Customers’ evaluations, in terms of text or ratings, are important sources of information for online shops to decide products and marketing strategies. In this paper, we discuss methods to conclude and predict merchants’ performance and characteristics of customers’ behavior of target products based on Amazon dataset. First, we design a Natural Language Processing (NLP) model, Amazon-BERT, to predict text to rating based on transfer learning. We improve the model accuracy by 20% compared to the original pre-trained BERT, and we use the predicted rating in our following steps of modeling. Second, we use PCA to extract 5 principle components, which estimate review’ s popularity, product’s reputation and so on. And then, for pacifier, we find that vector auto regression (VAR) model fits better, we apply it to the regression and doing a Granger causality test. Finally, we looked at the impulse response and variance decomposition. All 3 factors included do have a small impact.

Recent oil price changes have significantly influenced the macroeconomic activities of both oil importing and exporting economies. It has shifted the external balances of many economies. This study investigates the short and long run effects of oil price changes on macroeconomic activities of small open economy of Oman. The short-run changes in oil prices affect the economy via exchange rate and terms of trade channels, which in turn, affect the aggregate demand and supply aspects. While in long run, if the shocks remain persistent, the economy experiences the significant revenue windfalls and positive external balances. However, the degree of external shocks to domestic economy depends on the domestic response to external shocks. Vector Auto Regression (VAR) model is used to trace out those dynamics. VAR model is considered suitable methodological option in identifying the structural shocks through generalized innovations of impulse response functions and variance decompositions. The vector of six key macroeconomic variables is expressed in VAR framework. The framework establishes the joint behaviour of key variables through time and determines the structural dynamics of Oman economy. The variance decompositions are generated from a moving average representation of the VAR system and show the forecast error variance for each variable in the system attributable to both of its own innovations and those comes from other variables. Results suggest that changes in oil prices significantly affect the real exchange rate, output and external balances. Impulse response functions and variance decompositions results confirm positive effect of oil price changes on real effective exchange rates, real - output and consumer prices. To contain the inflationary expectations both in short and long run, the governments are usually resorting towards expansionary policies. The long run changes in oil prices is the key determining factor of output growth and subsequent changes in fiscal and monetary policy adaptations. The results further indicate that innovations in real output largely influenced by changes in prices. Innovations in money supply induce by changes in real output. Real output innovations positively affect by crude oil prices. Money supply is positively influenced by real output. In short run, the expansionary policies are consistent and have served well in containing the inflationary expectations and by maintaining the positive external balances. However, in long run, over reliance on stabilization policies in pegged exchange rate economies like of Oman economy may provide fewer options to contain the external shocks.

Tests for error autocorrelation (AC) are derived under the assumption of independent and identically distributed errors. The tests are not asymptotically valid if the errors are conditionally heteroskedastic. In this article we propose wild bootstrap (WB) Lagrange multiplier tests for error AC in vector autoregressive (VAR) models. We show that the WB tests are asymptotically valid under conditional heteroskedasticity of unknown form. WB tests based on a version of the heteroskedasticity-consistent covariance matrix estimator are found to have the smallest error in rejection probability under the null and high power under the alternative. We apply the tests to VAR models for credit default swap prices and Euribor interest rates. An important result that we find is that the WB tests lead to parsimonious models while the asymptotic tests suggest that a long lag length is required to get white noise residuals.