Nonlinear Autoregressive Model Research Articles

A non-linear integer-valued autoregressive model with zero-inflated data series

A new non-linear stationary process for time series of counts is introduced. The process is composed of the survival and innovation component. The survival component is based on the generalized zero-modified geometric thinning operator, where the innovation process figures in the survival component as well. A few probability distributions for the innovation process have been discussed, in order to adjust the model for observed series with the excess number of zeros. The conditional maximum likelihood and the conditional least squares methods are investigated for the estimation of the model parameters. The practical aspect of the model is presented on some real-life data sets, where we observe data with inflation as well as deflation of zeroes so we can notice how the model can be adjusted with the proper parameter selection.

Neuro-modelling and fuzzy logic control of a two-wheeled wheelchair system

Two-wheeled wheelchairs have been used as alternatives for the elderly and disabled people to perform physical activities due to their restriction of movement. Significant challenges posed by two-wheeled wheelchairs control due to their inherent instability, resembling that inverted pendulum system. This research addresses these challenges by developing a dynamic non-linear model and stability control using computational algorithms. A neural network-based Nonlinear Autoregressive model with Exogenous Inputs (NARX) was developed, capturing and behaving similar to the complex dynamics of the wheelchair system with the identification on the experimental input–output data. Ensuring stable and responsive control, design of optimized PD-type and PID-type fuzzy logic controllers using Particle Swarm Optimization (PSO) were established and were tested under a simulation environment. The performance was evaluated across various metrics, including Integral Squared Error (ISE), Integral Absolute Error (IAE), Mean Squared (MSE), and Integral Time Absolute Error (ITAE). The result demonstrates that the PSO Optimized PID-type fuzzy logic controller with scaling factor from MSE index performance come out as best overall, significantly outperforms PD-type fuzzy logic controller, reducing its settling time by 12.5% to 35 s, minimizing overshoot to 0.81°, and achieving a negligible steady-state error of 0.046%. These results highlight the significant of integrating fuzzy logic control and PSO to the neural network model in enhancing the stability and performance of two-wheeled wheelchair systems, offering user safety and comfort.

Asymmetric connectedness among BSE SENSEX, INR–USD exchange rate, gold price and crude oil price: fresh evidence from nonlinear ARDL

PurposeThis paper investigates the asymmetric connectedness among the Indian stock market, crude oil price, gold price and the USD–INR exchange rate.Design/methodology/approachWe construct a nonlinear autoregressive distributed lag model that contains the four aforementioned variables. We further used the pairwise Granger causality test to identify the direction of causality.FindingsThe results verify an asymmetrical long-run co-movement between the Indian stock market index, exchange rate, international crude oil prices and gold prices. In the long run, the performance of the Indian stock market is mainly affected by both positive as well as negative shocks in the INR–USD exchange rate, positive shocks in gold prices and positive shocks in crude oil prices. Further, a feedback mechanism is observed between positive shocks in the INR–USD exchange rate and Indian stock market performance.Originality/valueThe research paper revisited the linkage among the variables using a novel methodology proposed by Shin et al. (2014).

The Relationship Between Interest Rates and Agricultural Commodity Price Dynamics

ABSTRACTThe U.S. Federal Reserve has undertaken several interest rate interventions in the past decade. This study explores the relationship between U.S. corn and soybean prices and Federal Reserve monetary policy interventions, in the short and long run. We use a nonlinear autoregressive distributed lag model to capture three key features of agricultural commodity price responses to changes in interest rates. First, we observe that corn and soybean prices initially overreact to changes in interest rates, overshooting their long‐run equilibrium before gradually reverting. Second, in the short run, the relationship between soybean prices and interest rates is asymmetric; the initial price change is more pronounced for an interest rate increase than for a decrease of the same magnitude. Lastly, both corn and soybean prices display symmetry in the long run. These results help to understand how changes in interest rates affect commodity prices. Assessing the relationship between agricultural commodity prices and interest rates can assist farmers and processors in planning investments and loans based on interest rate forecasts.

Predicting plateau atmospheric ozone concentrations by a machine learning approach: A case study of a typical city on the southwestern plateau of China

Atmospheric ozone (O3) has been placed on the priority control pollutant list in China's 14th Five-Year Plan. Due to their unique meteorological conditions, plateau regions contain high concentrations of atmospheric O3. However, traditional experimental methods for determining O3 concentrations using automatic monitoring stations cannot predict O3 trends. In this study, two machine learning models (a nonlinear auto-regressive model with external inputs (NARX) and a temporal convolution network (TCN)) were developed to predict O3 concentrations in a plateau area in the Kunming region by considering the effects of meteorological parameters, air quality parameters, and volatile organic compounds (VOCs). The plateau O3 prediction accuracy of the machine learning models was found to be much higher than those of numerical models that served as a comparison. The O3 values predicted by the machine learning models closely matched the actual monitoring data. The temporal distribution of plateau O3 displayed a high all-day peak from February to May. A correlation analysis between O3 concentrations and feature parameters demonstrated that humidity is the feature with the highest absolute correlation (−0.72), and was negatively correlated with O3 concentrations during all test periods. VOCs and temperatures were also found to have high positive correlation coefficients with O3 during periods of significant O3 pollution. After negating the effects of meteorological parameters, the predicted O3 concentrations decreased significantly, whereas they increased in the absence of NOx. Although individual VOCs were found to greatly affect the O3 concentration, the total VOC (TVOC) concentration had a relatively small effect. The proposed machine learning model was demonstrated to predict plateau O3 concentrations and distinguish how different features affect O3 variations.

Has competition law enforcement been effective in South Africa?

ABSTRACT The South African Competition Act was crafted on the basis that it could be used to address distortions and inequalities in the market through enforcing competition. A question which has arisen is whether competition enforcement has been effective given that many economic sectors are still largely dominated by monopolies, duopolies or oligopolies. In this study, I assess whether competition enforcement has reduced inequality in South Africa by studying the link between market power and inequality, following a competition intervention in selected product markets. Using the nonlinear autoregressive distributed lag model, I assess whether competition enforcement in the market for bread, maize meal, and sunflower oil, has been effective in increasing consumer welfare, by lowering income inequality through lower prices. The findings of this study suggest that firms in these markets abuse their market power even post-intervention, such that they can raise prices and reduce consumer welfare, increasing inequality indirectly.

Vietnam's exports to Korea and the real exchange rate: Post-crisis evidence from the multiple threshold nonlinear autoregressive distributed lag model

In this study, the asymmetric effects of the real exchange rate on Vietnam's exports to Korea were investigated using the multiple threshold nonlinear autoregressive distributed lag (MTNARDL) model. As a result, the MTNARDL model exhibited enhanced estimation accuracy compared to the single-threshold nonlinear autoregressive distributed lag (NARDL) model. Furthermore, the aggregate bias problem was solved using individual export data for 16 major industries instead of relying on the overall export value data. The results revealed the substantial asymmetric impact of real exchange rate fluctuations in the short and long run. Fluctuations in the real exchange rate boosted Vietnam's exports to the Republic of Korea in the long run, with minimal negative influence. This indicates that the depreciation of the Vietnamese dong against the United States (US) dollar encouraged exports in some industries but limited exports in others. However, the short-term effect of the real exchange rate remains uncertain, as it could be either negative or positive depending on the industry and threshold level. The diverse impacts of the real exchange rate fluctuations on exports across industries were attributed to factors such as the capacity to absorb foreign exchange risks, product heterogeneity, and the ease of adjusting inputs and production for each sector. Therefore, these findings may help policymakers develop Vietnam-specific policies to address long- and short-term changes in the threshold levels of real exchange rate fluctuations.

Can environmental taxes and green technological investment ease environmental pollution in China?

This study examines the complex relationship between environmental taxation, green technology, green investment, real GDP, and environmental pollution by employing the Nonlinear autoregressive distributive lag model for China. The findings indicate that environmental tax policies have significant short- and long-term effects, with positive shocks leading to pollution reductions. The positive and negative shocks to green investment increase pollution levels in the long run. Moreover, the real GDP displays pollution reductions in the short run. The results provide valuable insights into China's environmental and economic situation and offer policy recommendations. These findings were confirmed using the Wald test. The findings emphasize China's need for stronger environmental taxes, green technology adoption, evaluated green investments, and sustainable economic growth to achieve cleaner production and environmental sustainability.

Algeria's pathway to COP28 and SDGs: Asymmetric impact of environmental technology, energy productivity, and material resource efficiency on environmental sustainability

This study examines the asymmetric effects of material resource efficiency (MRE), energy productivity (EP), and environmental technology (ENT) on environmental sustainability (ES) in Algeria from 1990/Q1 to 2022/Q4. Using a nonlinear autoregressive distributed lag model (NARDL), we find that both positive and negative shocks to both MRE and ENT contribute to ES, highlighting their effectiveness. Interestingly, positive EP shocks have a stronger mitigating effect compared to negative shocks. This suggests a magnified benefit during periods of efficiency gains. Additionally, asymmetric causality analysis verifies a causal link between MRE, EP, ENT, and ES. Given these results, it is recommended that Algerian policymakers should prioritize investments in MRE and ENT while emphasizing policies that enhance EP due to its magnified benefit on ES. Asymmetric policy responses for green practices alongside alignment with SDGs 7, 8, 12 and COP-28 objectives will optimize Algeria's ES.

Assessing the Effects of Exchange Rate Volatility on Zambia’s Economic Growth: Evidence from ARDL and NARDL Models

This study investigated the interplay between exchange rate volatility, inflation rates, and real interest rates on Zambia’s economic growth from 1992 to 2022, utilizing annualized time series data. The study was necessitated by the limited published literature and relatively varying findings on the variables’ relationships in resource-dependent countries, such as Zambia. Diagnostic tests, including stationarity and co-integration analyses, were employed to determine integration orders and potential long-run relationships. The linear and nonlinear autoregressive distributed lag models were employed to assess short- and long-run dynamics of the variables on economic growth. The results established a positive short-run relationship between inflation rates and Gross Domestic Product (GDP) growth in the linear autoregressive distributive lag model, while an inverse relationship was observed in the nonlinear autoregressive distributive lag model, suggesting that negative shocks in inflation rates had a highly significant positive impact on economic growth. Furthermore, interest rates exhibited a positive relationship with economic growth, further suggesting that positive shocks had a greater significant direct effect on economic growth in comparison to negative shocks in the short and long run, respectively. Finally, exchange rates in both models exhibited an inverse relationship with economic growth irrespective of positive or negative shocks in the long run, highlighting the adverse effect of exchange rate volatility on economic growth prospects in developing countries, such as Zambia. The speed of adjustment to convergence following any disruptions was determined to be 75.18% (ARDL) and 89.19% (NARDL), highlighting relatively fast speeds of adjustments from any short-run disruptions. Notably, some of the policy recommendations included regular assessments of exchange rate volatility influences on import prices, domestic inflation, and production costs in key sectors. Additionally, the implementation of currency hedging options and forwards as well as bulking of foreign exchange reserves will ensure the stability of exchange rates against other major currencies in various economic conditions.

A novel stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation for modeling and simulating of financial indicators

The main purpose of this study is to develop a new discrete time stochastic ProFiVaS model based on decomposition of stochastic Vasicek differential equation which follows bouncing autoregressive AR1, with fixed variance and trend for modeling and simulating of international financial time series forecasting.This study offers the four discrete time stochastic models. The first model is determined as autoregressive integrated moving average-Arima1,1,1, and the parameter estimates of this model are found using the maximum likelihood method (MLM). Monte Carlo simulation is applied to the obtained parameters. This model is named MoCArima for short. Second, the MoCArima model whose parameters are estimated with particle swarm optimization (PSO) is determined as Proposed Monte Carlo (MC) Arima1,1,1, and is briefly named as ProMoCArima. The third model is determined as Fixed Variance Stochastic Model which has a bouncing autoregressive AR1 structure with constant variance and trend component. This model is briefly named as FiVaS. The parameter estimates are found using the MLM. The fourth model is determined as the Proposed Fixed Variance Stochastic Model. This model is briefly named as ProFiVaS. Structurally the same as the third model. The parameter estimates of both trend and stochastic parts of the FiVaS model are found by the PSO.Proposed models are applied to forecasting international different financial indicators to show its superiority and applicability. The performance and usage efficiency of the proposed four stochastic models are examined on a total of six different international financial data types, five of which are stock index data BIST100 (Türkiye), S&P500 (USA), DAX (Germany), FTSE100 (UK), NIKKEI225 (Japan), and one of which is the exchange rate EURO/USD. The ProFiVaS among all models provides the best performance on the all indices. The ProFiVaS can easily be extended to any real-world time series prediction requirements.The proposed models can be extended to all stationary and non-stationary linear or nonlinear autoregression models opening the door to modeling data types obtained from different sector fields. A part of the future plan of this work is to design a decision support system software that assigns a value of 1 when an investor needs to invest in a financial indicator, and 0 otherwise.

The nonlinear impacts of macroeconomic shocks on the US regional housing markets

ABSTRACT This paper examines the asymmetrical impacts of aggregate macroeconomic shocks on the US regional housing markets by estimating nonlinear Vector Autoregressive models. We show how aggregate output, monetary, inflation, and credit shocks result in heterogenous impulse responses of the housing market volatilities across growing and declining housing market regimes in nine census divisions and 19 metropolitan cities. We find that output and inflation shocks cause qualitatively asymmetrical responses across regimes in majority of regions. A positive output shock and a negative inflation shock reduce (increase) housing price uncertainties when housing markets are in a declining (booming) regime in most regions. The responses of regional housing price volatilities to monetary and credit shocks are quantitatively asymmetrical across regimes in most regions. We also find that aggregate shocks have larger contributions on changing the probabilities of regime switching when a regional housing market is initially expanding than declining. Among aggregate shocks, inflation shock has the most prominent contributions across most regions. It also presents the strongest asymmetrical effects across positive and negative shocks. Our results can help regional decision makers utilize fiscal policies, regulatory measures, and regional planning to mitigate the destabilizing effects of macroeconomic shocks on regional housing markets.

Fusion of Hierarchical Optimization Models for Accurate Power Load Prediction

Accurate power load forecasting is critical to achieving the sustainability of energy management systems. However, conventional prediction methods suffer from low precision and stability because of crude modules for predicting short-term and medium-term loads. To solve such a problem, a Combined Modeling Power Load-Forecasting (CMPLF) method is proposed in this work. The CMPLF comprises two modules to deal with short-term and medium-term load forecasting, respectively. Each module consists of four essential parts including initial forecasting, decomposition and denoising, nonlinear optimization, and evaluation. Especially, to break through bottlenecks in hierarchical model optimization, we effectively fuse the Nonlinear Autoregressive model with Exogenous Inputs (NARX) and Long-Short Term Memory (LSTM) networks into the Autoregressive Integrated Moving Average (ARIMA) model. The experiment results based on real-world datasets from Queensland and China mainland show that our CMPLF has significant performance superiority compared with the state-of-the-art (SOTA) methods. CMPLF achieves a goodness-of-fit value of 97.174% in short-term load prediction and 97.162% in medium-term prediction. Our approach will be of great significance in promoting the sustainable development of smart cities.

A Bayesian transfer sparse identification method for nonlinear ARX systems

SummaryIn this paper, we design a transfer sparse identification algorithm under the Bayesian framework through introducing other system knowledge into the system to be identified. This method provides a new identification solution for a nonlinear autoregressive model with exogenous inputs (NARX). The estimates of the transferred parameters are calculated by adding the transfer correction term to the un‐transferred estimates. To achieve this, a joint prior distribution is devised for the parameters, ultimately enhancing the efficient utilization of existing data, reducing the reliance on new data, and achieving more accurate identification. The maximized marginal likelihood method is used to find the transfer gain and the transfer information matrix in the transfer correction term. Meanwhile, in order to make the algorithm automatically adapt to different data, we design an automatic structure detection method based on the transfer framework. The method automatically determines the sparsity threshold based on the maximum inter‐class variance. Two examples are provided to demonstrate the advantages of our algorithm.

Prediction models to control final control elements for neutralization process in chemical industries

AbstractBACKGROUNDIndustrialization continues to increase in the 21st century, as industries start moving towards automation. Manufacturing of a component/item requires a lot of resources and energy. Usage of water in industries has increased in recent years, as it is used as both a resource and an energy generating source. Neutralization of a processed liquid is carried out by addition of solution through final control elements and most industries are utilizing pneumatic‐based control valves, which have a disadvantage in the regulation of additives.RESULTSA motorized valve system is introduced, which is compared with the pneumatic system in terms of their performance. The proposed system is implemented with different controllers such as proportional–integral controller tuned using linear matrix inequalities, modified internal model controller, model predictive controller and nonlinear autoregressive (NAR) model, where the final control elements are tested for pH neutralization. On implementation of the proposed system the NAR model has proven to be better under the motorized control valve system for the neutralization process, with a peak value of 7.08 (pH), settling time of 75.16 s, rise time of 5.96 s, maximum overshoot of 10.1%, slew rate of 0.21 per second, integral square error of 0.95, integral absolute error of 0.48 and integral time absolute error of 1.88.CONCLUSIONBased on the results obtained it is observed that the NAR controller utilized with motorized control valve has better functionality in neutralizing a solution. © 2024 Society of Chemical Industry (SCI).

Exchange rate and inflation dynamics in Kenya: Does the threshold level matter?

This study empirically examined the threshold effect of exchange rate pass-through (ERPT) on inflation in Kenya, while augmenting the exchange rate depreciation in the monetary policy rate using the Taylor rule. The monthly time series data spanning January 2005 to November 2023 was collected for analysis, in which the non-linear threshold autoregressive (TAR) model was employed as the main econometric model. This study's ERPT results reveal that, exchange rate depreciation has positive and significant effect on inflation only when it raises above the monthly threshold level of 0.51 %. In contrast, the Taylor rule analysis results reveal that the exchange rate depreciation has a positive and significant effect the monetary policy rate regardless of the threshold level of 0.67 %. Therefore, keeping domestic currency depreciation below a monthly growth rate of 0.51 % will control the pass-through effect on inflation, and the exchange rate depreciation at any level should always act as a reaction function for the monetary policy rate setting. This study also found that the relationship between exchange rate depreciation and inflation, as well as monetary policy rate is non-linear, which implies a greater pass-through effect when exchange rate depreciation is high. Therefore, we recommend the monetary authority in Kenya to pay attention to the depreciation of the exchange rate depreciation at any level when adjusting the policy rate to tame inflation.

Dynamic nexus between natural resource rents, economic growth, and environmental quality: A comparative study between China and the US

AbstractEconomic development and environmental sustainability have recently become global priorities. This study utilizes the nonlinear autoregressive distribution lag model (NARDL) to investigate the asymmetric effects of natural resource rents on economic growth and environmental quality in China and the United States from 1970 to 2020. The findings indicate that natural resource rents exert asymmetric effects on economic growth and environmental quality in both countries; however, the impact patterns differ between the two countries. In the short term, a decrease in natural resource rents significantly increases GDP per capita in the US, while an increase in natural resource rents has no effect. Moreover, natural resource rents do not influence the ecological footprint in the US. By contrast, China's GDP per capita remains unaffected by natural resource rents, while the ecological footprint is significantly influenced by both positive and negative changes in natural resource rents, exhibiting asymmetric impacts. In the long run, an increase in natural resource rents significantly impacts both GDP per capita and the ecological footprint in the US, while a decrease only impacts the ecological footprint. By contrast, both increases and decreases in natural resource rents impact per capita GDP and the ecological footprint in China. These findings highlight the importance of tailoring country‐specific policies to facilitate sustainable economic development and enhance environmental quality.

Financial fragility, regime change, and monetary policy in an open economy – A model and empirical application to emerging market countries

July 20, 2023 (Revised April 15, 2024) The experiences of the 1997–98 Asian Financial Crisis and the 2008–09 Global Financial Crisis encouraged economists to develop new open-economy dynamic finance-macro models. Such models allow for nonlinearities -- to study the effects of contractionary currency devaluation -- in contrast to models of expansionary currency devaluation. The generic dynamic model of the finance-macro link in this paper includes the dynamics of the inflation rates, output gap, and financial variables (credit flows, risk premia, and exchange rates). The theoretical model with nonlinearities shows that there can be resilient or non-resilient outcomes of the dynamics. The level of resilience is however dependent on some empirical vulnerabilities. Relevant empirics show the risk premium is related not only to domestic real macro and financial variables, but also to the exchange rate and the foreign currency reserves. Econometrically, this paper explores the regime-dependent interaction of the output gap and financial variables in a two-regime non-linear Logistic Vector Smooth Transition Auto-Regressive (LVSTAR) model with a logistic-type transition function. This empirical study reveals that the financial variables of emerging economies show regime-dependent responses to external shocks. Therefore, a positive shock to the risk premia in a negative output gap regime entails an exchange rate depreciation, and accelerating contractions. Overall, however, a diversity of EM economies are examined in terms of their response to external shocks and their resilience levels. This research also has implications for international portfolio holdings.

The impacts of forest resources, green investment, healthcare, and education on environmental pollution: China Carbon neutrality program

This study delves into the complex connections between forest rent, forest extraction, green investment, health expenditure, education expenditure, and environmental pollution, specifically focusing on carbon dioxide emissions. Utilizing a Nonlinear Autoregressive Model, this study analyzes data from China's Carbon Neutrality Program for the period 1970–2022. The results indicate asymmetric cointegration between the variables under investigation. In the short term, sustainable forest rent, green investment, and educational expenditure have a significant impact on CO2 emissions. Negative shocks to forest rent, green investment, and education expenditures negatively affect CO2 emissions in the long run, while positive shocks to forest rent, green investment, and education expenditures have a positive impact on CO2 emissions in the long run. Additionally, health expenditures have a negative impact on CO2 emissions in the long run. These findings provide actionable policy recommendations for China's Carbon Neutrality Program, emphasizing the need for comprehensive approaches that prioritize sustainability, resource conservation, and emission reduction.

An Empirical Analysis of the Asymmetric Association of Public Investment with Private Investment: Revisiting Crowding-In/Out Effect

The crowding-in/out effect of government spending on private investment has been a much-debated topic. As the controversy surrounding this topic persists, the subject is revisited using an improved nonlinear autoregressive distributed lag model for the Indian economy using the sample period 1980–2022. In the framework of the flexible accelerator model, the present study considers the positive and negative shocks in the two public investment series and positive and negative shocks in other macroeconomic variables (such as FDI, lending rate and credit availability to the private sector) as determinants of private investment. The results depict strong nonlinear short-run and long-run cointegrating linkages establishing the tendency of the Indian economy to converge to a long-run and short-run equilibrium threshold. The long-run estimation shows that private investment decreases at a much higher rate when public investment falls as compared to its tendency to rise when public investment increases. Further, contrary to our expectations, public investment in the non-infrastructure sector crowds in private investments, while public investment flowing into the infrastructure crowds out private sector investments, possibly because of the long gestation period of public investments. An important policy implication is to channel investments in the non-infrastructure and infrastructure segments of the public sector that boost private investments aligned with sustainable development goals. Efficient qualitative fiscal and monetary policy measures are recommended to encourage private investments.