Autoregressive Network Models Research Articles

Short-term PM2.5 forecasting using a unique ensemble technique for proactive environmental management initiatives

Particulate matter with a diameter of 2.5 microns or less (PM2.5) is a significant type of air pollution that affects human health due to its ability to persist in the atmosphere and penetrate the respiratory system. Accurate forecasting of particulate matter is crucial for the healthcare sector of any country. To achieve this, in the current work, a new time series ensemble approach is proposed based on various linear (autoregressive, simple exponential smoothing, autoregressive moving average, and theta) and nonlinear (nonparametric autoregressive and neural network autoregressive) models. Three ensemble models are also developed, each employing distinct weighting strategies: equal distribution of weight among all single models (ESME), weight assignment based on training average accuracy errors (ESMT), and weight assignment based on validation mean accuracy measures (ESMV). This technique was applied to daily PM2.5 concentration data from 1 January 2019, to 31 May 2023, in Pakistan’s main cities, including Lahore, Karachi, Peshawar, and Islamabad, to forecast short-term PM2.5 concentrations. When compared to other models, the best ensemble model (ESMV) demonstrated mean errors ranging from 3.60% to 25.79% in Islamabad, 0.81%–13.52% in Lahore, 1.08%–7.06% in Karachi, and 1.09%–12.11% in Peshawar. These results indicate that the proposed ensemble approach is more efficient and accurate for short-term PM2.5 forecasting than existing models. Furthermore, using the best ensemble model, a forecast was made for the next 15 days (June 1 to 15 June 2023). The forecast showed that in Lahore, the highest PM2.5 value (236.00 μg/m3) was observed on 8 June 2023. Other days also displayed higher and poor air quality throughout the 15 days. Conversely, Karachi experienced moderate PM2.5 concentration levels between 50 μg/m3 and 80 μg/m3. In Peshawar, the PM2.5 concentration levels were consistently unhealthy, with the highest peak (153.00 μg/m3) observed on 9 June 2023. This forecasting experience can assist environmental monitoring organizations in implementing cost-effective planning to minimize air pollution.

Integration of Google Trends Data in Predicting New HIV Cases in Western Visayas, the Philippines

Recent studies have demonstrated the capacity of Internet search data to be used for monitoring and tracking infectious diseases. Given that the Philippines has one of the most rapidly expanding human immunodeficiency virus (HIV) epidemics in the globe, it is imperative to enhance the local surveillance and prediction of HIV by utilizing easily accessible web data such as Google Trends. This study aims to [1] evaluate the advantages of utilizing Google Trends data (GTD) in predicting new monthly HIV diagnoses in the Western Visayas and [2] determine the suitable modeling approach that effectively utilizes this tool in forecasting HIV cases in the region. Data on new monthly HIV cases from January 2012–December 2022 in Western Visayas was requested from the Department of Health Region VI Office and HIV-related internet search data was obtained from Google Trends. Data imputations were applied to mitigate the effects of COVID-19 on HIV data. The results of the traditional seasonal autoregressive integrated moving average (SARIMA) model were compared with the results of the neural network autoregression (NNAR) model using cross-validation via rolling forecast origin. GTD have a moderately weak but significant association with HIV case numbers in Western Visayas. NNAR models outperformed the traditional SARIMA models in terms of mean absolute percentage error, mean absolute error, and root mean squared error. The use of Google search data in NNAR models improved the predictive accuracy of the forecasts when using moving average imputation as a replacement for outliers. However, this does not accurately represent the overall NNAR process, as the linear interpolation replacements did not yield comparable outcomes. This study showed that, if suitable models are adopted, utilizing HIV-related web data has the potential to produce real-time surveillance systems for HIV monitoring and forecasting. This presents an opportunity to enhance local surveillance in the country not just for HIV but also for other infectious diseases such as tuberculosis and dengue. Internet search data is free and readily available, and public health agencies can adopt this type of modeling, even with limited funding; however, further study is advised.

Influencer detection meets network autoregression — Influential regions in the bitcoin blockchain

Known as an active global virtual money network, the Bitcoin blockchain, with millions of accounts, has played a continually increasingly important role in fund transition, digital payment, and hedging. We propose a method to Detect Influencers in Network AutoRegressive models (DINAR) via sparse-group regularization to detect regions influencing others across borders. For a granular analysis, we analyse whether the transaction size plays a role in the dynamics of the cross-border transactions in the network. With two-layer sparsity, DINAR enables discovering (1) the active regions with influential impact on the global digital money network and (2) whether changes in the size of the transaction affect the dynamic evolution of Bitcoin transactions. In the analysis of real data of the Bitcoin blockchain from Feb 2012 to December 2021, we find that influence from certain regions is linked to the economic need to use BTC, such as to circumvent sanctions, avoid high inflation, and to carry out transactions through off-shore markets. The effects are robust to different groupings, evaluation periods, and choices of regularization parameters.

1D -FNO - Residual convolutional neural network autoregressive prediction model for deep water wave train evolution based on high-order spectral (HOS) data

Accurate prediction of deep-water wave dynamics is essential for ocean engineering, meteorology, and maritime safety. Traditional physical models, though effective, face significant computational and time challenges with complex nonlinear dynamics. This study introduces an autoregressive prediction model using a one-dimensional adaptive Fourier Neural Operator-Residual Convolutional Neural Network (1D-FNO-ResNet) to enhance prediction accuracy. We developed a high-precision single-step prediction model capable of capturing wave characteristics such as height and fluid particle velocity. A fine-tuning training strategy based on multi-step prediction errors was proposed for autoregressive evolution. Performance comparisons between the ResNet and FNO-ResNet models were made under various fine-tuning steps. A correction model was also introduced to control error accumulation, improving autoregressive prediction steps. The model's generalization performance was validated with modulated and random wave trains under different conditions, optimizing predictive stability and accuracy. This approach demonstrates efficient 1D deep-water wave evolution prediction, offering a novel deep learning solution for wave dynamics prediction in ocean engineering, supporting wave energy conversion device design and optimization.

Optimized Parameter Estimation and Integrating Neural Network Forecasting of Dynamic Plant-Livestock Model for Early Warning in Agro-Environment Control Systems

The research utilizes the Lotka-Volterra prey-predator model to study Plant-Herbivore dynamics, focusing on the relationship between traditional livestock farming and vegetation conditions. Advanced methods are developed to improve the precision and efficiency of parameter estimation in these models. Neural networks are incorporated to enhance forecasting abilities, and an extension of the Plant-Herbivore models includes Botswana's climate and livestock variables. Efficient parameter space exploration is achieved using the Runge-Kutta method along with Multistart and the local solver $fmincon$ in MATLAB. This method improves parameter estimation accuracy. To address the impact of homogeneity assumptions in the data, estimate aggregation through weighting and time conversion is applied. Furthermore, the study investigates the use of nonlinear least squares to further refine the process, allowing for the identification of parameters that best fit observed livestock data, even with non-linearity. By using optimized parameter estimation techniques along with normalized nonlinear least squares, the cumulative error was reduced from an initial 1563.4521 to a final value of 0.0038, well within the specified thresholds (1.0, 0.1, and 0.01). Comparisons between Autoregressive Integrated Moving Average (ARIMA) and Neural Network Auto-Regressive (NNAR) models showed that NNAR models outperformed ARIMA models, with lower variance estimates (0.000004 - 0.000562) compared to ARIMA (0.103 - 0.155). NNAR models displayed Mean Error (ME) values ranging from -0.0012 to 0.0140, indicating a close match between forecasts and actual values with minor deviations. As a result, NNAR forecasting was used for predicting soil moisture, death, and harvest rates, which were integrated into the extended Plant-Herbivore model. This integration enabled the estimation of livestock production trajectories for 2021-2022, along with corresponding interpretations. The study also assessed the uncertainty propagation from NNAR forecasts onto the Plant-Herbivore dynamic model, revealing an increase in uncertainty with longer lead times.

Network-based time series modeling for COVID-19 incidence in the Republic of Ireland

Network-based time series models have experienced a surge in popularity over the past years due to their ability to model temporal and spatial dependencies, arising from the spread of infectious disease. The generalised network autoregressive (GNAR) model conceptualises time series on the vertices of a network; it has an autoregressive component for temporal dependence and a spatial autoregressive component for dependence between neighbouring vertices in the network. Consequently, the choice of underlying network is essential. This paper assesses the performance of GNAR models on different networks in predicting COVID-19 cases for the 26 counties in the Republic of Ireland, over two distinct pandemic phases (restricted and unrestricted), characterised by inter-county movement restrictions. Ten static networks are constructed, in which vertices represent counties, and edges are built upon neighbourhood relations, such as railway lines. We find that a GNAR model based on the fairly sparse Economic hub network explains the data best for the restricted pandemic phase while the fairly dense 21-nearest neighbour network performs best for the unrestricted phase. Across phases, GNAR models have higher predictive accuracy than standard ARIMA models which ignore the network structure. For county-specific predictions, in pandemic phases with more lenient or no COVID-19 regulation, the network effect is not quite as pronounced. The results indicate some robustness to the precise network architecture as long as the densities of the networks are similar. An analysis of the residuals justifies the model assumptions for the restricted phase but raises questions regarding their validity for the unrestricted phase. While generally performing better than ARIMA models which ignore network effects, there is scope for further development of the GNAR model to better model complex infectious diseases, including COVID-19.

Consistent two-stage estimation in heterogeneous network autoregressive model

Obtaining consistent estimates of network effects in the heterogeneous network autoregressive model presents significant challenges. These challenges arise from the large number of target parameters, potential endogeneity, and non-identifiability issues. To overcome these challenges, we reformulate the model into a higher-order version. Our proposed two-stage estimation procedure first reduces parameter complexity by screening out nodes with negligible network effects. Then, we employ the ordinary least squares method and the instrumental variables technique for effective post-screening estimation. We further investigate the consistency and asymptotic normality of the estimators under appropriate assumptions and explore the cases of heteroscedasticity. The finite sample performance of the two-stage method is evaluated by simulation studies and an empirical analysis.

Modelling the GDP of KSA using linear and non-linear NNAR and hybrid stochastic time series models.

Gross domestic product (GDP) serves as a crucial economic indicator for measuring a country's economic growth, exhibiting both linear and non-linear trends. This study aims to analyze and propose an efficient and accurate time series approach for modeling and forecasting the GDP annual growth rate (%) of Saudi Arabia, a key financial indicator of the country. Stochastic linear and non-linear time series modeling, along with hybrid approaches, are employed and their results are compared. Initially, conventional linear and nonlinear methods such as ARIMA, Exponential smoothing, TBATS, and NNAR are applied. Subsequently, hybrid models combining these individual time series approaches are utilized. Model diagnostics, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as criteria for model selection to identify the best-performing model. The findings demonstrated that the neural network autoregressive (NNAR) model, as a non-linear approach, outperformed all other models, exhibiting the lowest values of MAE, RMSE and MAPE. The NNAR(5,3) projected the GDP of 1.3% which is close to the projection of IMF benchmark (1.9) for the year 2023. The selected model can be employed by economists and policymakers to formulate appropriate policies and plans. This quantitative study provides policymakers with a basis for monitoring fluctuations in GDP growth from 2022 to 2029 and ensuring the sustained progression of GDP beyond 2029. Additionally, this study serves as a guide for researchers to test these approaches in different economic dynamics.

A novel comparative study of NNAR approach with linear stochastic time series models in predicting tennis player's performance

BackgroundPrediction models have gained immense importance in various fields for decision-making purposes. In the context of tennis, relying solely on the probability of winning a single match may not be sufficient for predicting a player's future performance or ranking. The performance of a tennis player is influenced by the timing of their matches throughout the year, necessitating the incorporation of time as a crucial factor. This study aims to focus on prediction models for performance indicators that can assist both tennis players and sports analysts in forecasting player standings in future matches.MethodologyTo predict player performance, this study employs a dynamic technique that analyzes the structure of performance using both linear and nonlinear time series models. A novel approach has been taken, comparing the performance of the non-linear Neural Network Auto-Regressive (NNAR) model with conventional stochastic linear and nonlinear models such as Auto-Regressive Integrated Moving Average (ARIMA), Exponential Smoothing (ETS), and TBATS (Trigonometric Seasonal Decomposition Time Series).ResultsThe study finds that the NNAR model outperforms all other competing models based on lower values of Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE). This superiority in performance metrics suggests that the NNAR model is the most appropriate approach for predicting player performance in tennis. Additionally, the prediction results obtained from the NNAR model demonstrate narrow 95% Confidence Intervals, indicating higher accuracy and reliability in the forecasts.ConclusionIn conclusion, this study highlights the significance of incorporating time as a factor when predicting player performance in tennis. It emphasizes the potential benefits of using the NNAR model for forecasting future player standings in matches. The findings suggest that the NNAR model is a recommended approach compared to conventional models like ARIMA, ETS, and TBATS. By considering time as a crucial factor and employing the NNAR model, both tennis players and sports analysts can make more accurate predictions about player performance.

Empirical likelihood method for detecting change points in network autoregressive models

<p>The network autoregressive model is a super high-dimensional time series model that can fully explain social relationships. This model can fully reflect the complex relationships in reality. Therefore, it plays a vital role in detecting the inflection point problem of this network autoregressive model for economics and finance. In this paper, we proposed the change-point problem of detecting network autoregressive models using empirical likelihood statistics based on the expected error term of the switching rule being 0, using the empirical likelihood method. Moreover, the asymptotic null distribution of the proposed empirical likelihood statistic was investigated. Simulation studies based on different settings were considered, and the results showed that the power of test statistics is significant. In the end, the Chinese stock market was investigated to demonstrate the significance of the proposed method.</p>

Softplus negative binomial network autoregression

AbstractModelling multivariate time series of counts in a parsimonious way is a popular topic. In this paper, we consider an integer‐valued network autoregressive model with a non‐random neighbourhood structure, which uses negative binomial distribution as the conditional marginal distribution and the softplus function as the link function. The new model generalizes existing ones in the literature and has a great flexibility in modelling. Stationary conditions in cases of fixed dimension and increasing dimension are given. Parameters are estimated by maximizing the quasi‐likelihood function, and related asymptotic properties of the estimators are established. A simulation study is conducted to assess performances of the estimators, and a real data example is analysed to show superior performances of the proposed model compared with existing ones.

Forecasting the incidence of dengue fever in Malaysia: A comparative analysis of seasonal ARIMA, dynamic harmonic regression, and neural network models

Currently, no vaccines or specific treatments are available to treat or prevent the increasing incidence of dengue worldwide. Therefore, an accurate prediction model is needed to support the anti-dengue control strategy. The primary objective of this study is to develop the most accurate model to predict future dengue cases in the Malaysian environment. This study uses secondary data collected from the weekly reports of the Ministry of Health Malaysia (MOH) website over six years, from 2017 to 2022. Three forecasting techniques, including seasonal autoregressive integrated moving average (SARIMA), dynamic harmonic regression (DHR), and neural network autoregressive model (NNAR), were first fitted to the estimation part of the data. First, several SARIMA models were run, and the best seasonal model identified was SARIMA (0, 1, 2) (1, 1, 1)52. The best DHR model was obtained with a Fourier term of 2, as this corresponds to the lowest Akaike Information Criteria (AIC) value. The NNAR (9, 1, 6)52 was considered the best choice among the NNAR models due to its superior performance in terms of the lowest error measures. The comparison among the three techniques revealed that the DHR model was the best due to its lowest MAPE and RMSE values. Thus, the DHR model was used to generate future forecasts of weekly dengue cases in Malaysia until 2023. The results showed that the model predicted more than a thousand dengue cases around weeks 27 to 32. The results showed an increase in dengue cases after the end of the monsoon season, which lasted about five months. This technique is proving to be valuable for health administrators in improving preparedness.

Count network autoregression

We consider network autoregressive models for count data with a non‐random neighborhood structure. The main methodological contribution is the development of conditions that guarantee stability and valid statistical inference for such models. We consider both cases of fixed and increasing network dimension and we show that quasi‐likelihood inference provides consistent and asymptotically normally distributed estimators. The article is complemented by simulation results and a data example.

The GNAR-edge model: a network autoregressive model for networks with time-varying edge weights

Abstract In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications, such complex systems can be associated with some underlying network describing pairwise relationships among the quantities. Accounting for the underlying network structure for the analysis of this type of multivariate time series is required for assessing estimation error and can be particularly informative for forecasting. Our work is motivated by a dataset consisting of time series of industry-to-industry transactions. In this example, pairwise relationships between Standard Industrial Classification (SIC) codes can be represented using a network, with SIC codes as nodes and pairwise transactions between SIC codes as edges, while the observed time series of the amounts of the transactions for each pair of SIC codes can be regarded as time-varying weights on the edges. Inspired by Knight et al. (2020, J. Stat. Softw., 96, 1–36), we introduce the GNAR-edge model which allows modelling of multiple time series utilizing the network structure, assuming that each edge weight depends not only on its past values, but also on past values of its neighbouring edges, for a range of neighbourhood stages. The method is validated through simulations. Results from the implementation of the GNAR-edge model on the real industry-to-industry data show good fitting and predictive performance of the model. The predictive performance is improved when sparsifying the network using a lead–lag analysis and thresholding edges according to a lead–lag score.

Homogeneous analysis on network effects in network autoregressive model

Network effects are pivotal for understanding the mutual influence of nodes within a network. The homogeneous group structure holds significant importance across networks in various fields. This paper introduces the Classifier-L2 regularized approach for homogeneous analysis of network effects under the network autoregressive model. This approach offers high flexibility with data constraints and provides a completely data-driven procedure. Analysis of international trade data offers meaningful perspectives for refining trade policies. Empirical results derived from Chinese mutual fund data, both before and after the outbreak of the COVID-19 pandemic, provide valuable insights for mitigating potential risks.

Optimizing Cardiovascular Disease Prediction: A Synergistic Approach of Grey Wolf Levenberg Model and Neural Networks

Background: One of the latest issues in predicting cardiovascular disease is the limited performance of current risk prediction models. Although several models have been developed, they often fail to identify a significant proportion of individuals who go on to develop the disease. This highlights the need for more accurate and personalized prediction models. Objective: This study aims to investigate the effectiveness of the Grey Wolf Levenberg Model and Neural Networks in predicting cardiovascular diseases. The objective is to identify a synergistic approach that can improve the accuracy of predictions. Through this research, the authors seek to contribute to the development of better tools for early detection and prevention of cardiovascular diseases. Methods: The study used a quantitative approach to develop and validate the GWLM_NARX model for predicting cardiovascular disease risk. The approach involved collecting and analyzing a large dataset of clinical and demographic variables. The performance of the model was then evaluated using various metrics such as accuracy, sensitivity, and specificity. Results: the study found that the GWLM_NARX model has shown promising results in predicting cardiovascular disease. The model was found to outperform other conventional methods, with an accuracy of over 90%. The synergistic approach of Grey Wolf Levenberg Model and Neural Networks has proved to be effective in predicting cardiovascular disease with high accuracy. Conclusion: The use of the Grey Wolf Levenberg-Marquardt Neural Network Autoregressive model (GWLM-NARX) in conjunction with traditional learning algorithms, as well as advanced machine learning tools, resulted in a more accurate and effective prediction model for cardiovascular disease. The study demonstrates the potential of machine learning techniques to improve diagnosis and treatment of heart disorders. However, further research is needed to improve the scalability and accuracy of these prediction systems, given the complexity of the data associated with cardiac illness. Keywords: Cardiovascular data, Clinical data., Decision tree, GWLM-NARX, Linear model functions

A Systematic Review of Neural Network Autoregressive Model with Exogenous Input for Solar Radiation Prediction Modelling Development

Neural Network is one of the Machine Learning methods that has been applied in various Artificial Intelligence system development including solar radiation prediction modelling. Since there are multiple approaches had been developed using the Neural Network method, the study has been focusing on the development of a Multi-layer Neural Network model that can handle non-linearities and highly dynamic data. The integration of the Multi-layer Neural Network and the Non-linear Autoregressive Model with Exogenous Input (NARX) developed a compromising non-linear Neural Network model which can be applied in the modelling of solar radiation. This paper develops a systematic review of the Neural Network Autoregressive Model with Exogenous Input (NNARX) for solar radiation prediction modelling starts from the architecture and the comparative selection for the Training Function. The model is developed and analysed using MATLAB R2019a software. Results showed that the Levenberg-Marquardt Training Function performed better with the R2 value of 0.94 for training and 0.91 for testing, making it the most suitable for the NNARX in the development of solar radiation prediction modelling.

A comparative evaluation of streamflow prediction using the SWAT and NNAR models in the Meenachil River Basin of Central Kerala, India.

Reliable and accurate modelling of streamflow is still a challenging task due to their complex behaviour, need for extensive parameter for development as well as lack of complete or accurate data. In this study, the applicability of an emerging data-driven model, specifically a neural network autoregression (NNAR) model, was evaluated for the first time as a substitute to the physically based hydrological model Soil and Water Assessment Tool (SWAT) for predicting streamflow under data-scarce conditions and for immediate high-quality modelling results. The inputs to the NNAR model were the lagged values of the daily streamflow time series data, and the output was the predicted value for the next day. Using streamflow data that was windowed by 20 days, the NNAR model produced the best prediction. The results of the statistical metrics used to evaluate the performance of the NNAR model were satisfactory (R = 0.90, RMSE = 28.27, MAE = 11.92, R2 = 0.83), indicating a high degree of agreement between the predicted and observed streamflow. The NNAR model outputs demonstrated its ability to accurately predict streamflow in the river basin, even without an explicit understanding of the physical processes that govern the system.

A Hybrid Approach Based on Seasonal Autoregressive Integrated Moving Average and Neural Network Autoregressive Models to Predict Scorpion Sting Incidence in El Oued Province, Algeria, From 2005 to 2020.

This study was designed to find the best statistical approach to scorpion sting predictions. Study Design: A retrospective study. Multiple regression, seasonal autoregressive integrated moving average (SARIMA), neural network autoregressive (NNAR), and hybrid SARIMA-NNAR models were developed to predict monthly scorpion sting cases in El Oued province. The root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) were used to quantitatively compare different models. In general, 96909 scorpion stings were recorded in El Oued province from 2005-2020. The incidence rate experienced a gradual decrease until 2012 and since then slight fluctuations have been noted. Scorpion stings occurred throughout the year with peaks in September followed by July and August and troughs in December and January. Sting cases were not evenly distributed across demographic groups; the most affected age group was 15-49 years, and males were more likely to be stung. Of the reported deaths, more than half were in children 15 and younger. Scorpion's activity was conditioned by climate factors, and temperature had the highest effect. The SARIMA(2,0,2)(1,1,1)12, NNAR(1,1,2)12, and SARIMA(2,0,2)(1,1,1)12-NNAR(1,1,2)12 were selected as the best-fitting models. The RMSE, MAE, and MAPE of the SARIMA and SARIMA-NNAR models were lower than those of the NNAR model in fitting and forecasting; however, the NNAR model could produce better predictive accuracy. The NNAR model is preferred for short-term monthly scorpion sting predictions. An in-depth understanding of the epidemiologic triad of scorpionism and the development of predictive models ought to establish enlightened, informed, better-targeted, and more effective policies.

Huber estimation for the network autoregressive model

We propose the Huber estimator for the network autoregressive model, which exhibits both robustness and efficiency under heavy-tailed errors and loses little efficiency compared to OLS under light-tailed errors.