Nonlinear Autoregressive Model Research Articles

Bootstrap prediction inference of nonlinear autoregressive models

The nonlinear autoregressive (NLAR) model plays an important role in modeling and predicting time series. One‐step ahead prediction is straightforward using the NLAR model, but the multi‐step ahead prediction is cumbersome. For instance, iterating the one‐step ahead predictor is a convenient strategy for linear autoregressive (LAR) models, but it is suboptimal under NLAR. In this article, we first propose a simulation and/or bootstrap algorithm to construct optimal point predictors under an or loss criterion. In addition, we construct bootstrap prediction intervals in the multi‐step ahead prediction problem; in particular, we develop an asymptotically valid quantile prediction interval as well as a pertinent prediction interval for future values. To correct the undercoverage of prediction intervals with finite samples, we further employ predictive – as opposed to fitted – residuals in the bootstrap process. Simulation and empirical studies are also given to substantiate the finite sample performance of our methods.

Natural resource development, economic policy uncertainty and urban residents’ consumption in China: a nonlinear ARDL and time-varying parameter vector autoregressive with stochastic volatility approach

Increased risks of economic policy uncertainty and overexploitation of natural resources exist in China. At the same time, the growth rate of urban residents’ consumption has generally declined. The paper analyses the role of economic policy uncertainty (EPU) and natural resource exploitation on the urban residents’ consumption in China. Based on the data from the first quarter of 2002 to the third quarter of 2021, the paper uses a nonlinear autoregressive distributed lag model to verify the asymmetric effects. Then the paper constructs a time-varying parameter vector autoregressive model with stochastic volatility term to analyze the nonlinear responses. Impulse response analysis was used to further explain the relationship between the three. The negative impact of rising EPU on urban residents’ consumption is larger than its reduction. Negative shocks to natural resource development increase the urban residents’ consumption. Positive shocks reduce the urban residents’ consumption. There is a time-varying non-linear effect of EPU and natural resource development on urban residents’ consumption in China. The negative impact of EPU on urban consumption has been further exacerbated by major crises such as the financial crisis, COVID-19 and the post-crisis period. The negative impact of natural resource development diminished after the government introduced industrial upgrading policies and environmental regulations. This study provides constructive suggestions for the optimization of economic policies and the improvement of urban consumption. This study also enriches consumer theory and provides new evidence for the resource curse hypothesis.

Importance of natural energy, and blue resources to address environmental challenges in view of the Saudi Vision 2030

AbstractThe purpose of this study is to scrutinize the impact of natural resources, energy, and blue economic indicators on the ecological footprint of Saudi Arabia over the period from 1993 to 2022 by employing a nonlinear autoregressive distributed lag model. We have simulated the missing data using the Markov Chain Monte Carlo algorithm. The study encompasses the effects of post‐Vision 2030 and post‐COVID‐19 policies and their assistance in minimizing the environmental footprint. The observed results determine that non‐renewable energy consumption increases the ecological footprint, whereas natural resources and biocapacity drop the ecological footprints in the case of pre‐ and post‐Vision 2030. For variable fisheries production, the post‐ and pre‐Vision 2030 results demonstrate a boosted ecological footprint in Saudi Arabia, with the highest coefficient among all results. This research offers valuable insights into how Saudi Arabia's energy consumption and natural resource management impact its ecological footprint, highlighting the effectiveness of Vision 2030 and post‐COVID policies in promoting environmental sustainability. The study's findings provide crucial guidance for policy making to reduce environmental impact while considering the role of fisheries and biocapacity in ecological balance. Based on empirical findings, this study commends some policy understandings that assist in being effectively implemented towards a sustainable environment.

Relationship between Energy and Economic Growth: Evidence from a Panel Nonlinear ARDL Model

In this article, we study the heterogeneous relationship among energy consumption and economic growth by incorporation gross fixed capital formation, foreign direct investment, international trade and finance development as control variables in a selected sample of 11 countries of the Middle East and North Africa over the period 1980-2020 using a panel nonlinear autoregressive distributed lag model. Empirical results show the presence of an asymmetric long run relationship between energy consumption and economic growth in the group of countries. The Pooled Mean Group estimates indicate that positive and negative changes in energy consumption have positive and significant effects on output growth in the long term, whereas both Mean Group and Difference Fixed Effect estimates report that only negative changes in energy consumption have positive and significant effect on long-term economic growth in the selected sample of countries. In addition, the short run individual effects of energy use on economic growth are positive and significant for only three countries (Jordan, Saudi Arabia, and Tunisia). These results are very important for the design of energy policies and sustainable economic growth. Energy-saving policies are suitable for long-run economic growth for the entire sample, while they are only suitable for eight countries out of eleven in the short-run.

Asymmetric Effect of Oil Price on Economic Activity: Evidence from Lebanon Using NARDL Model

The aim of this paper is to investigate the impact of oil prices on the real economic activity of Lebanon, represented by the Gross Domestic Product (GDP) while controlling for inflation. For this purpose, this study employs a non-linear auto-regressive distributed lag model (NARDL) that enables to take into consideration the asymmetrical nature of the relationship between these two variables. The empirical findings confirm the asymmetric impact of changes in oil prices on economic activity. Notably, reductions in oil prices positively influence GDP in the long term and exert a more pronounced fluctuating effect compared to increases in oil prices, which are statistically insignificant. In other words, the country’s GDP, serving as a measure of the total value of finished goods and services, does not respond significantly to oil price rises but is influenced by oil price reductions. This empirical analysis focuses particularly on Lebanon, and time series data spanning from 1988 to 2021 are used to explore this relationship. This study guides Lebanon's policymakers, revealing the impact of declining oil prices on economic activity. It highlights growth opportunities amidst challenges like economic crises and corruption. Advocating for prudent policies and strategies, it offers a pathway for sustainable development.

Economic growth, structural changes and employment linkages in India

PurposeIndia started economic reforms at a rapid pace to catch up the world economy by following the services-led-growth model during the post-liberalisation period. Over the years, the growing unemployment rate posits a re-look into the dynamics of growth model for wider work force participation. In this backdrop, the paper aims to examine the dynamics of structural changes in employment pattern in view of economic growth led by services-led growth model in India.Design/methodology/approachThe study employs a non-linear autoregressive model (NARDL) to examine the effect of the growth rates in three broad economic sectors namely agriculture and allied, services and industry on work force participation representing the employment opportunities in India.FindingsThe results highlight that the rapid expansion of the service sector has not occurred with enough employment opportunities by the same rate. By contrast, the growth in the industrial sector significantly creates employment opportunities in the short and long run. These results support the industry led growth model over the services for sustainable and inclusive economic growth in the country.Research limitations/implicationsThe study relies on combined labour force participation rates rather than gender-specific rates. Further, the regulatory, working conditions and economic incentives may affect the gender-specific engagement of the labour force in three broad sectors.Practical implicationsThe results offer important insight into changing patterns in employment with policy lessons. A wider workforce force participation calls for expansion of manufacturing activities through pro-industry programmes.Originality/valueThe study makes pioneer efforts to examine the dynamics of labour force participation with respect to the growth of three broad economic sectors of the Indian economy. The results provide new insights with policy implications for the changing employment pattern and policy response.

Platinum and palladium price forecasting through neural networks

To many commodity market participants, forecasts of price series represent a critical task. In this work, nonlinear autoregressive neural network models’ potential is explored for forecasting daily prices series of platinum and palladium over about a fifty-year period. For this purpose, one hundred and twenty model settings are examined, including different training algorithms, numbers of hidden neurons and delays, and ratios used to segment the data. With the analysis, two models leading to stable and accurate forecast results are constructed for the prices of the two commodities. In particular, the models’ performance in terms of the relative root mean square error is 1.86% and 3.61% for platinum and palladium, respectively, for the overall sample. Results in this work could help technical forecasts and policy analysis. The forecast framework might be extended to other different commodities.

Prediction of SO2 emission concentration in industrial flue gas based on deep learning: The ammonia desulfurization system of the Yunnan aluminum carbon plant as the research object

The desulfurization efficiency of flue gas desulfurization (FGD) systems is affected by many operation parameters, and predicting SO2 emission concentration through mechanism models requires a significant number of resources, limiting the process optimization of the overall desulfurization efficiency. Taking the desulfurization system of Yunnan aluminum carbon plant as the research object, based on the inlet flue gas, process control parameters, and pollutants of the discharged flue gas, we constructed the NARX (nonlinear auto-regressive model with external inputs) neural network and TCN (temporal convolutional network) models. Predicted the concentration of SO2 in the discharged flue gas in the next moment from the above three types of historical data, optimized the industrial control parameters, and reduced the concentration of the discharged SO2. The results show that both TCN and NARX models have strong nonlinear dynamic descriptive ability, and both are capable of accurately predicting the SO2 concentration in the emitted flue gas. The TCN neural network model can control the mean absolute percentage error and root mean square error of the dataset within 1.46% and 1.86, respectively. The response relationship established by the model has an important role in guiding the regulation of SO2 emission and process operation parameters, such as reducing the flue gas pressure of the absorber tower inlet or increasing the pressure of the concentration section of the absorber tower, which can effectively improve the desulfurization rate.

Predicting the Torque Demand of a Battery Electric Vehicle for Real-World Driving Maneuvers Using the NARX Technique

An identification technique is proposed to create a relation between the accelerator pedal position and the corresponding driving moment. This step is beneficial to replace the complex physical model of the vehicle control unit, especially when the sufficient information needed to model certain functionalities of the vehicle control unit are unavailable. We utilized the nonlinear autoregressive exogenous model to regenerate the electric motor torque demand, given the accelerator pedal position, the motor’s angular speed, and the vehicle’s speed. This model proved to be extremely efficient in representing this highly complex relationship. The data employed for the identification process were chosen from an actual three-dimensional route with sudden changes of a dynamic nature in the driving mode, different speed limits, and elevations, as an attempt to thoroughly cover the driving moment scope based on the alternation of the given inputs. Analyzing the selected route data points showed the widespread coverage of the motor’s operational scope compared to a standard driving cycle. The training outcome revealed that linear modeling is inadequate for identifying the targeted system, and has a substantial estimation error. Adding the nonlinearity feature to the model led to an exceptionally high accuracy for the estimation and validation datasets. The main finding of this work is that the combined model from the nonlinear autoregressive exogenous and the sigmoid network enables the accurate modeling of highly nonlinear dynamic systems. Accordingly, the maximum absolute estimation error for the motor’s moment was less than 10 Nm during the real-world driving maneuver. The highest errors are found around the maximum motor’s moment. Finally, the model is validated with measurements from an actual field test maneuver. The identified model predicted the driving moment with a correlation of 0.994.

Defect detection and localisation using guided wave images from array data processed by nonlinear autoregressive exogenous model and Gamma statistical operator

Guided wave structural health monitoring (GWSHM) systems, using the delay-and-sum imaging algorithm, are an efficient solution to detect and localise defects in industrial structures. However, the image artifacts caused by either imperfect detection or sensor lay-out limitations make it difficult to identify and locate defects accurately. In order to enhance the performance of defect detection and localisation in GWSHM systems, this paper proposes a three-step procedure for post-processing guided wave signals prior to image formation. In the first step, the signals are processed using the nonlinear autoregressive exogenous model to suppress noise from benign features. The second step calculates the probability of defect presence based on the rescaled Gamma cumulative distribution function. This probabilistic threshold is then determined from the quantile mapping. Finally, a guide wave image is formed using the delay-and-sum imaging algorithm. The experimental validation was performed to inspect a 6 mm-diameter through-thickness circular hole on an aluminium plate and the defects were further scaled as simulated datasets to test its detectability under various amplitudes. In the second procedure step, the detection and localisation performance of the proposed procedure was compared with that of using the signal difference coefficient and the Rayleigh maximum likelihood estimator. It is shown that the proposed procedure can enhance the contrast between damaged and undamaged regions, providing more reliable and accurate guided wave images.

Using Nonlinear Autoregressive Models to Investigate the Impact of Foreign Trade on Economic Growth in Sudan

Foreign commerce is the term for the exchange of goods and services between nations, and it is subject to a wide range of laws, rules, and agreements. The purpose of the study was to evaluate the link between Sudan's economic growth, imports, and exports from 2005 to 2022. Based on a descriptive, analytical, and econometrics methodology, the study estimated the relationship between the study variables using a nonlinear autoregressive model (NARDL). The study's conclusions indicate that, during the study period, exports had a short-term negative influence on the rate of growth in the economy but a positive long-term impact. Additionally, imports have a short-term favorable effect on economic growth rates but a long-term negative one.

Unraveling Korea’s Energy Challenge: The Consequences of Carbon Dioxide Emissions and Energy Use on Economic Sustainability

This research delves into the effects of carbon dioxide emissions and energy consumption on economic growth in Korea from 1980 to 2022, employing a sophisticated nonlinear autoregressive distributed lag model. The study unveils pivotal findings, most notably the positive association between carbon dioxide emissions and economic growth, suggesting that periods of economic expansion in Korea have been accompanied by surges in emissions. Furthermore, the investigation highlights a significant, albeit asymmetrical, positive impact of primary energy consumption on economic growth, illuminating the critical role of energy in the nation’s economic trajectory. The analysis also identifies essential economic determinants—namely, the labor force, gross fixed capital formation, and net inflows of foreign direct investment—underscoring their pivotal contributions to economic proliferation. The reliability of these insights is corroborated through advanced econometric techniques, including fully modified ordinary least squares and dynamic ordinary least squares methods. A noteworthy discovery emerges from the Toda–Yamamoto causality test, revealing bidirectional Granger causality between carbon dioxide emissions and economic growth, as well as between energy consumption and economic growth. Moreover, it uncovers a unidirectional causality flowing from labor, capital formation, and foreign direct investment towards economic growth. These findings elucidate the complex interplay between environmental and economic elements, highlighting the critical need for sustainable energy policies and proactive environmental stewardship in Korea. By advocating for a synthesis of economic advancement and environmental sustainability, this study presents indispensable insights for policymakers. It calls for a judicious approach to balancing Korea’s economic ambitions with its ecological responsibilities, thereby charting a sustainable path forward for the nation. Through its comprehensive analysis, this research contributes valuable perspectives to the discourse on economic development and environmental sustainability, offering guidance for Korea’s strategic planning and policy formulation.

Asymmetric Analysis of the Impact of Taxation on Unemployment in Uganda

Uganda, like most developing countries, has one of the highest tax rates not only in Africa but also in the world. This explains the numerous challenges faced in mobilizing sufficient revenues to fight poverty and improve people’s economic welfare. We, therefore, use a more recent nonlinear autoregressive distributed lag model (NARDL) to analyze the impact of higher taxes on the unemployment rate in Uganda. Results indicate that total Unemployment in Uganda is a negative function of both an increase in tax and a negative change in tax. Specifically, if taxes increase, then unemployment decreases by almost 3.9%, and if taxes decrease, then unemployment increases by about 4.9%. Also, the unemployment level decreased by 0.06% with a decrease in the gross capital formation (GFKF). Finally, unemployment also decreases with a rise in GDP and decreases with a decrease in GDP. In a nutshell, Uganda lacks the possibility of making the economy more productive and thus only relies on taxing an already overtaxed economy. Overtaxing an economy kills the possibility of ever building a formidable capital base that can stimulate economic growth and reduce poverty and unemployment. The government, therefore, should cut taxes and level the playing field regarding tax policies for foreign and home-grown investors. Finally, policymakers should also aim to unlock the potential of the informal sector not only to create jobs but also to widen the tax base

Price forecasting through neural networks for crude oil, heating oil, and natural gas

Building price projections of various energy commodities has long been an important endeavor for a wide range of participants in the energy market. We study the forecast problem in this paper by concentrating on four significant energy commodities. Using nonlinear autoregressive neural network models, we investigate the daily prices of WTI and Brent crude oil as well as the monthly prices of Henry Hub natural gas and New York Harbor No. 2 heating oil. We investigate prediction performance resulting from various model configurations, including training techniques, hidden neurons, delays, and data segmentation. Based on the investigation, relatively straightforward models are built that yield quite accurate and reliable performance. Specifically, performance in terms of relative root mean square errors is 1.96%/1.81%/9.75%/21.76%, 1.96%/1.80%/8.76%/14.41%, and 1.87%/1.78%/9.10%/16.97% for model training, validation, and testing, respectively, and the overall relative root mean square error is 1.95%/1.80%/9.51%/20.35% for the whole sample for WTI crude oil/Brent crude oil/New York Harbor No. 2 heating oil/Henry Hub natural gas. The outcomes of this projection might be used in technical analysis or integrated with other fundamental forecasts for policy analysis.

Active flow control for bluff body drag reduction using reinforcement learning with partial measurements

Active flow control for drag reduction with reinforcement learning (RL) is performed in the wake of a two-dimensional square bluff body at laminar regimes with vortex shedding. Controllers parametrised by neural networks are trained to drive two blowing and suction jets that manipulate the unsteady flow. The RL with full observability (sensors in the wake) discovers successfully a control policy that reduces the drag by suppressing the vortex shedding in the wake. However, a non-negligible performance degradation ( $\sim$ 50 % less drag reduction) is observed when the controller is trained with partial measurements (sensors on the body). To mitigate this effect, we propose an energy-efficient, dynamic, maximum entropy RL control scheme. First, an energy-efficiency-based reward function is proposed to optimise the energy consumption of the controller while maximising drag reduction. Second, the controller is trained with an augmented state consisting of both current and past measurements and actions, which can be formulated as a nonlinear autoregressive exogenous model, to alleviate the partial observability problem. Third, maximum entropy RL algorithms (soft actor critic and truncated quantile critics) that promote exploration and exploitation in a sample-efficient way are used, and discover near-optimal policies in the challenging case of partial measurements. Stabilisation of the vortex shedding is achieved in the near wake using only surface pressure measurements on the rear of the body, resulting in drag reduction similar to that in the case with wake sensors. The proposed approach opens new avenues for dynamic flow control using partial measurements for realistic configurations.

Does agricultural trade respond asymmetrically to oil price shocks? Evidence from New Zealand

AbstractDo rising oil prices affect agricultural trade differently from falling oil prices? We answer this question using data on New Zealand, a net importer of oil and a net exporter of agricultural commodities. We consider a disaggregated approach, analysing exports and imports of five key commodity classes; nonlinear autoregressive lag models are employed to conduct the analysis. We find considerable evidence suggesting asymmetries in the effects of oil price shocks on agricultural trade in the long and the short run. Furthermore, in the long run, agricultural exports and imports appear to be largely insensitive to foreign and domestic real income, respectively; there is limited evidence for imports and exports being associated with the real effective exchange rate. In the short run, however, income and exchange rates are associated with imports and exports.

Multi-task learning using non-linear autoregressive models and recurrent neural networks for tide level forecasting

Tide level forecasting plays an important role in environmental management and development. Current tide level forecasting methods are usually implemented for solving single task problems, that is, a model built based on the tide level data at an individual location is only used to forecast tide level of the same location but is not used for tide forecasting at another location. This study proposes a new method for tide level prediction at multiple locations simultaneously. The method combines nonlinear autoregressive moving average with exogenous inputs (NARMAX) model and recurrent neural networks (RNNs), and incorporates them into a multi-task learning (MTL) framework. Experiments are designed and performed to compare single task learning (STL) and MTL with and without using non-linear autoregressive models. Three different RNN variants, namely, long short-term memory (LSTM), gated recurrent unit (GRU) and bidirectional LSTM (BiLSTM) are employed together with non-linear autoregressive models. A case study on tide level forecasting at many different geographical locations (5 to 11 locations) is conducted. Experimental results demonstrate that the proposed architectures outperform the classical single-task prediction methods.

Nonlinear causal network learning via Granger causality based on extreme support vector regression.

For complex networked systems, based on the consideration of nonlinearity and causality, a novel general method of nonlinear causal network learning, termed extreme support vector regression Granger causality (ESVRGC), is proposed. The nonuniform time-delayed influence of the driving nodes on the target node is particularly considered. Then, the restricted model and the unrestricted model of Granger causality are, respectively, formulated based on extreme support vector regression, which uses the selected time-delayed components of system variables as the inputs of kernel functions. The nonlinear conditional Granger causality index is finally calculated to confirm the strength of a causal interaction. Generally, based on the simulation of a nonlinear vector autoregressive model and nonlinear discrete time-delayed dynamic systems, ESVRGC demonstrates better performance than other popular methods. Also, the validity and robustness of ESVRGC are also verified by the different cases of network types, sample sizes, noise intensities, and coupling strengths. Finally, the superiority of ESVRGC is successful verified by the experimental study on real benchmark datasets.

Economic Cycles and Employment Growth in the WAEMU Zone: An Analysis Using a Non-Linear ARDL Panel Model

The West African Economic and Monetary Union (WAEMU) is facing frequent and diverse crises that are affecting economic stability and employment opportunities in the region. It is important to analyze the impact of economic cycles on employment, as the response of employment supply differs during economic growth and contraction. This article uses a lagged non-linear auto-regressive model (NARDL) on panel data from 1990 to 2022, along with various filters, to examine the relationship between employment and business cycles. The study found that there is an asymmetric relationship between economic growth and employment, with the impact of economic recessions being stronger on long-term employment than on short-term employment. The study suggests that countries have not fully utilized their economic potential to benefit employment. To achieve sustainable economic growth and reduce the proliferation of the informal sector, economies should focus their efforts on translating their potential into action.

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.