ARMAX Model Research Articles

The convenience benefits of the shipping market: Evidence from C3 and C5 FFAs

Forward Freight Agreements (FFAs) are consequential derivatives for risk hedging in the shipping market. This paper presents the first empirical study of convenience yield in the shipping market with a sample of C3 (Tubarao to Qingdao) and C5 (Western Australia to Qingdao) FFAs from 2013 to 2023. First, single-factor and two-factor models are constructed to analyze the random behavior of freight rates in the shipping market, and the existence of convenience yield is empirically tested. The results provide evidence of the existence of convenience yield in the shipping market, with its stochastic variation being a critical factor in shaping the term structure characteristics of FFAs. Second, an ARMAX model is developed for the freight rate index, and the predictive role of the estimated convenience yield and its difference in spot freight rates is analyzed by operating the two-factor model. The findings reveal a significant predictive effect of convenience yield and its difference on spot freight rates. Last but not least, this study emphasizes the importance of convenience yield as a crucial parameter in the shipping market, particularly regarding the transportation of bulk commodities. Changes in the supply and demand of bulk commodities directly impact the fluctuations in shipping market capacity and convenience yield. This study delivers a new explanatory perspective for price formation in the shipping market and is highly valuable for risk management in this sector.

Key SDG7 Factors Shaping the Future of Clean Coal Technologies: Analysis of Trends and Prospects in Poland

This article presents the results of an analysis aimed at verifying the relationship between the implementation of SDG Goal 7 and the use of clean coal technologies in Poland. Clean coal technologies in the United Nations plans will constitute a crucial element of the strategy for sustainable development in the energy context. They are intended to be one of the tools for building an energy system based on renewable energy sources, constituting a bridge that enables the transition of Poland’s energy system from coal to renewable energy sources. To identify whether this relationship exists, the Autoregressive Moving Average with Exogenous Input (ARMAX) model was used. The structure of the model, its correctness, and its accuracy were confirmed using information criteria; statistical tests such as Dickey-Fuller, Doornik-Hansen, Durbin-Watson, and Breusch-Pagan; and measures of prediction accuracy such as MAPE, MAE, and RMSE. The explanatory variables were the Objective 7 indicators adopted by Eurostat. Before being introduced to the ARMAX model, they were standardized using the Compound Annual Growth Rate (CAGR) indicator. The analysis made it possible to indicate which of the explanatory variables has the greatest impact on the development of clean coal technologies in Poland, to determine a synthetic CAGR measure for all the explanatory variables, and to compare the results obtained with the indicator determined by the United Nations.

Real-time nowcasting the monthly unemployment rates with daily Google Trends data

Policymakers often have to make decisions based on incomplete economic data because of the usual delay in publishing official statistics. To circumvent this issue, researchers use data from Google Trends (GT) as an early indicator of economic performance. Such data have emerged in the literature as alternative and complementary predictors of macroeconomic outcomes, such as the unemployment rate, featuring readiness, public availability and no costs. This study deals with extensive daily GT data to develop a framework to nowcast monthly unemployment rates tailored to work with real-time data availability, resorting to Mixed Data Sampling (MIDAS) regressions. Portugal is chosen as a use case for the methodology since extracting GT data requires the selection of culturally dependent keywords. The nowcasting period spans 2019 to 2021, encompassing the time frame in which the coronavirus pandemic initiated. The findings indicate that using daily GT data with MIDAS provides timely and accurate insights into the unemployment rate, especially during the COVID-19 pandemic, showing accuracy gains even when compared to nowcasts obtained from typical monthly GT data via traditional ARMAX models.

Retraction Note: ARX and ARMAX modelling of SBCNC-60 machine for surface roughness and MRR with optimization of system response using PSO

Retraction Note: ARX and ARMAX modelling of SBCNC-60 machine for surface roughness and MRR with optimization of system response using PSO

Pattern-Moving-Modelling and Analysis Based on Clustered Generalized Cell Mapping for a Class of Complex Systems

Considering a class of complex nonlinear systems whose dynamics are mostly governed by statistical regulations, the pattern-moving theory was developed to characterise such systems and successfully estimate the outputs or states. However, since the pattern class variable is not computable directly, this study establishes a clustered generalized cell mapping (C-GCM) to reveal system characteristics. C-GCM is a two-stage approach consisting of a pattern-moving-based description and analysis method. First, a density algorithm, named density-based spatial clustering of applications with noise (DBSCAN), is designed to obtain cell space Ω and the corresponding classification guidelines; this algorithm is initiated after the initial pre-image cells, and the total number of entity cells amounts to Ns. Then, the GCM provides several image cells based on a cell mapping function that refers to the multivariate ARMAX model. The global dynamic analysis employing both searching and storing algorithms depend on the attractor, domain of attraction, and periodic cell groups. At last, simulation results of two examples emphasise the practicality as well as efficacy of the technique suggested. The chief aim of this study was to offer a new perspective for a class of complex systems that could inspire research into nonmechanistic principles modelling and application to nonlinear systems.

Identification of a different design of a photovoltaic thermal collector based on fuzzy logic control and the ARMAX model

This study investigates the effects of absorber design on the performance of a water-based photovoltaic thermal collector (PVT). In this regard, three different absorber designs with the same pipe diameter and length were tested and compared experimentally in Cairo, Egypt, during summer 2021. Furthermore, artificial intelligence techniques were used to create a model to identify the PVT system and define the input–output relationship in state space representation. This is to get a more thorough understanding and deeper evaluation of the PVT performance with various absorber designs to achieve the best possible system performance under varied operating situations and weather. The fuzzy logic control is examined by Autoregression Moving Average using an external input model (ARMAX), which relies on the autoregression moving average to achieve system performance. According to the study's findings, at a maximum water flow rate of 3 L/min, the proposed PVT system can convert solar energy with an overall efficiency of 69.6 %, 64.6 %, and 63.5 %, respectively, with a pressure loss of about 29.5 kPa, 29.33 kPa, and 24.79 kPa for absorbers A, B, and C. Furthermore, the challenging suggested fuzzy control system for the PVT system provides knowledge to comprehend the system complexity since the connection is formed by connecting 5 inputs with 3 outputs through its representation in the state space representation.

The Relationship Between Aging, Economic Development and Healthcare Expenditure in Japan: An Empirical Analysis

This paper investigates the relationship between ageing, economic development, and healthcare expenditure in Japan, considering the challenges posed by an ageing population. The study utilizes a VAR and ARMAX modelling approach to analyse the complex dynamics among these variables. The empirical results reveal interesting findings that contrast with previous literature. While population ageing is often assumed to lead to increased healthcare spending, this study finds no significant correlation between population ageing and healthcare expenditure as a percentage of GDP. The analysis suggests that factors such as advancements in medical technology, healthcare system efficiency, and cultural variations in healthcare utilization patterns may have mitigated the expected rise in healthcare expenditure associated with an ageing population. These findings have implications for policymakers and investors. Policymakers should consider a broader range of factors beyond population ageing when projecting future healthcare expenditures and developing strategies for managing healthcare costs. Investors can benefit from a nuanced understanding of the healthcare sector, focusing on areas such as medical technology, innovation, and healthcare delivery models that are likely to be influenced by population ageing and changing healthcare needs. Overall, this research contributes to the existing knowledge base, offering insights for addressing the challenges of population ageing and healthcare sustainability.

Searching for the Effects of Momentum in Tennis and its Applications

In sports, a team or athlete may feel they have momentum, or “power/strength” during a game, but this phenomenon is difficult to measure. Furthermore, it is not clear how various events during a match create or change momentum. This paper presents an approach to quantifying ‘momentum’ by introducing a composite model integrating a Logistic Regression Model and a LASSO-based Sparse ARMAX Model to predict momentum shifts and guide strategic decisions during games. The combined model addresses both static and dynamic aspects of momentum, culminating in a comprehensive prediction of momentum trends. The model’s robustness is evidenced by its high accuracy rates across different tennis matches and gender scenarios (95.6%, 94.9%, and 95.5%). This paper’s findings confirm momentum’s measurable impact on sports outcomes, offering a scientific basis for tactical decision-making.

Food security, human health, and economy: a holistic approach to sustainable regulation

Purpose. The research aims to formulate recommendations for sustainable food security regulation taking into account the agriculture intensification’s impact on public health, health-associated economic loss, and regional variations of these effects.
 Methodology / approach. The impact of agricultural intensification on public health was analysed using national and regional (climate zones) data on cancer cases per 100,000 population and mineral fertiliser application per hectare of sown area from the State Statistics Service of Ukraine for 2010–2019. Regression analyses were performed using GRETL 2022c, employing OLS and ARMAX models. Additionally, health-related economic losses from contaminated food consumption in 2020 were estimated based on regional environmental damage assessments and data on environmental damage structure. These assessments informed and guided the suggestions of an organisational and economic framework essential for sustainable food security regulation.
 Results. Based on global research experiences, we identified a notable positive correlation between cancer morbidity and the application of mineral fertilisers in Ukraine, both on a national scale and within four distinct natural geographical zones. These findings highlight the imperative to reconceptualise the notion of food security by incorporating the dimension of human health. Given the eco-destructive nature of the agricultural environment and the socio-ecological and economic factors influencing public health, we articulate the structural and functional elements of an organisational and economic framework essential for the sustainable regulation of food security.
 Originality / scientific novelty. The research results underscore the need to redefine the concept of food security to encompass the dimension of human health. Moreover, it evaluates the economic losses related to health state resulting from consuming contaminated food across various natural and climatic zones. It demonstrates that a harmonious coexistence of food security objectives and the preservation of human health can be achieved by developing a suitable organisational and economic framework for sustainable food security regulation.
 Practical value / implications. The comprehensive assessment of environmental and economic damage to public health caused by contaminated food consumption, considering regional contexts and natural geographical zones, enables determining the scale of environmental, economic and medical risks and, thus, making adequate and optimal management decisions in sustainable food security regulation based on ecologisation of agricultural production.

Stages and main tasks of the century-long control theory and system identification development

The article provides a review of the mathematical description of the dynamics of continuous and discrete linear stationary systems and objects, used at the development stage of the classical theory of automatic control in the form of mathematical models of the «input-output» type. The time and frequency characteristics of continuous and discrete control systems are described, typical links of stationary systems are considered, parametric discrete models of objects as part of typical digital control loops are presented. Stochastic discrete autoregressive models of stationary time series used to describe the dynamic objects in the synthesis of digital control systems are considered. A review of standard control laws for the implementation of continuous and discrete controllers has been completed. A method for synthesizing discrete controllers for multidimensional controlled objects with different, unknown and changing delays is considered, through which variable delays are compensated in the characteristic equation of a closed-loop control system. A common technique for synthesizing one-dimensional and multidimensional controllers for stochastic objects with delays based on ARMAX models is considered. An analysis of approaches to identifying delays in controlled objects is carried out and a method for identifying delays when using input-output models is considered, based on the calculation and comparison of impulse responses for extended and non-extended models of the controlled object. An analysis of the advantages and disadvantages of «input-output» type models is given, as well as the possibilities of their application for solving various classes of control theory problems.

Modeling the Photovoltaic Power Generation in Poland in the Light of PEP2040: An Application of Multiple Regression

This paper presents the results of research on the development of photovoltaic systems in Poland. The authors’ goal was to identify factors that can potentially shape the dynamics of solar energy development in Poland and that will affect the implementation of the PEP2040 goals. The authors also wanted to find a forecasting method that would enable the introduction of many explanatory variables—a set of identified factors—into the model. After an initial review of the literature, the ARMAX and MLR models were considered. Finally, taking into account MAPE errors, multiple regression was used for the analysis, the error of which was 0.87% (minimum 3% for the ARMAX model). The model was verified based on Doornik–Hansen, Breusch–Pagan, Dickey–Fuller tests, information criteria, and ex post errors. The model indicated that LCOE, CO2 emissions, Cu consumption, primary energy consumption, patents, GDP, and installed capacity should be considered statistically significant. The model also allowed us to determine the nature of the variables. Additionally, the authors wrote the WEKR 2.0 program, which allowed to determine the necessary amount of critical raw materials needed to build the planned PV energy generating capacity. Solar energy in Poland currently covers about 5% of the country’s electricity demand. The pace of development of photovoltaic installations has exceeded current expectations and forecasts included in the Polish Energy Policy until 2040 (PEP2040). The built model showed that if the explanatory variables introduced into the model continue to be subject to the same trends shaping them, a dynamic increase in photovoltaic energy production should be expected by 2025. The model indicates that the PEP2040 goal of increasing the installed capacity to 16 GW by 2040 can be achieved already in 2025, where the PV production volume could reach 8921 GWh. Models were also made taking into account individual critical raw materials such as Cu, Si, Ge, and Ga. Each of them showed statistical significance, which means that access to critical raw materials in the future will have a significant impact on the further development of photovoltaic installations.

A Structural Damage Localization Method Based on Empirical Probability Mass Function of ARMAX Model Residual and Kullback–Leibler Divergence

Damage localization is very significant in engineering applications. The existing method based on the chi-square distribution of an autoregressive moving average with exogenous inputs (ARMAX) model residual is not applicable for these realistic excitations except Gaussian excitation. To solve the above problem, this paper presents a structural damage localization method based on the empirical probability mass function (EPMF) of the ARMAX model residual and Kullback–Leibler (KL) divergence. In detail, we employ empirical data analysis (EDA) approach to estimate the EPMF of the ARMAX model residual of the data generated by the arbitrary excitation because EDA does not need any a priori knowledge about the model residual. Moreover, the KL divergence is introduced to measure the dissimilarity of the EPMFs in undamaged and damaged states to prove that our method is effective for arbitrary excitation. Finally, the semi-parametric extreme value theory is used to estimate the reliable threshold for localizing the damage. Numerical simulated and experimental results illustrate that the proposed method localizes the damage under different excitations, respectively.

Economic stress affects the human sex ratio: A retest of the Trivers–Willard hypothesis in Poland

This paper contributes to the verification of the Trivers–Willard hypothesis (TWH). Based on the TWH, observed sex (male-to-female) ratio at birth in a population is presumed to decline when parents experience economic stress. The empirical evidence so far is mixed. The research material consisted of data on the total numbers of live male and female births in the Polish population in the years 1995–2020. The data were used to produce semiannual time series for secondary sex ratio (SSR), and the sex ratio at birth (SRB). The variable describing the economic stress of households was percentage change in private consumption. The statistical method proposed by Catalano and Bruckner – expanded to include additional statistical analyses – was applied to retest the economic stress hypothesis. The analysis led to complementary ARMAX models, explaining SSR or SRB variance based on autoregression and the moving average process, as well as private consumption. The results indicate that periods of decreasing consumption favored mothers having daughters, while periods of increasing consumption favored mothers having sons. The number of “additional” male births resulting from improved economic conditions was calculated for the period of study. Consequently, the economic factor was shown to have a positive effect on the human sex ratio. At the same time, it should be noted that SSR and SRB reaction lags to consumption changes were different for Łódzkie Province (one year) and for Poland (two years). The obtained results led to the “correct” verification of the Trivers–Willard hypothesis (TWH): economic stress affected the SSR and SRB in Poland. Both SSR and SRB were useful in analyzing economic stress (a dual solution). The use of a greater density of data points was shown to improve analysis effects and increase the likelihood of a “positive” verification of the economic stress hypothesis.

The Long-Term Relationship between Nasdaq Index and Gold Yield: Analysis Based on ARMAX Model

This article explores the relationship between the gold yield and the Nasdaq index through a detailed understanding of the gold yield and the changes in the Nasdaq index in the past ten years. Will the gold yield be affected by the Nasdaq index, whether there is a correlation between the two, and whether the gold price can be predicted based on the Nasdaq index. In this paper, the ARMA model is used to rank the gold return rate, and four models are used, namely the gold return rate, the gold return rate plus the Nasdaq index, the gold return rate plus the Nasdaq index lagging 1 period and lagging 2 Period to analyze and finally explore the relationship between the two. This paper mainly finds that the return rate of gold is positively correlated with the Nasdaq index, but the prediction efficiency of the model is low. Gold is an effective return to crisis industries. When the stock market is not friendly, gold can play a very good hedging role. This article uses the influential and extensive data of the Nasdaq index to let everyone know how to analyze the yield of gold through existing data. In short, it is when to buy and sell gold. This paper suggests that although the model shows that the prediction effect of the Nasdaq index on the gold return rate is not significant, the two show a positive correlation, and it has a significant effect in the lag period 1 and 2. It is recommended to use the Nasdaq index Investors who watch gold yields give priority to watching lag 1.

A diffusion bias-compensated LMS algorithm for distributed estimation with ARMAX models

In this paper, we study the distributed estimation problem with colored noise over adaptive networks. The nodes estimate and track an identical parameter vector in the network. The colored noise is described by a finite impulse response (FIR) model with an unknown variance, and thus leads to a bias in the diffusion least squares algorithm. Accordingly, we propose a diffusion bias-compensated LMS algorithm to deal with this situation. The performance of the proposed algorithm is analyzed, which shows that it can achieve the mean-square stability on the condition that the step size is sufficiently small. Furthermore, we obtain the corresponding closed mean-square deviation containing the white noise variance. Finally, the given simulations show the effectiveness of our proposed algorithm.

Increasing Liberalization: A Time Series Analysis of the Public’s Mood toward Drugs

Previous research suggests that American drug sentiment is becoming more liberal. However, the absence of a reliable and valid over time measure limits our understanding of changes in drug attitudes. This project utilizes the dyad ratios algorithm and 298 administrations of 66 unique survey indicators to develop a measure of public mood toward drugs from 1969 to 2021. I find that drug mood has trended more liberal since the late 2000s. I then test for the predictors and consequences of drug mood empirically using ARMAX modeling. Results suggest that the violent crime rate, presidential rhetoric on drugs, and college attendance are not significant predictors of drug mood, but punitiveness is significant and negative. Moreover, only drug mood emerges as a significant and negative predictor of punitiveness. Granger causality tests indicate that drug mood Granger causes changes in punitiveness. These results elucidate the socio-political dynamics regarding public opinion toward drug policy.

Spectral Estimation of Electroencephalogram Signal using ARMAX Model and Particle Swarm Optimization

Electroencephalogram (EEG) signal is short-length time series data. Parametric and non-parametric methods are used to estimate the power spectral density (PSD) of the time series data. While the non-parametric approach of spectrum estimate of short-length data is unreliable, the parametric approach of spectrum estimate is widely suggested. In the presented work, a parametric autoregressive moving average with exogenous input (ARMAX) model was implemented to find the PSD of the EEG signal. The performance of the implemented ARMAX model was contrasted with other parametric methods like autoregressive AR) and autoregressive moving average (ARMA) and nonparametric methods like periodogram. Coefficients of ARMAX and (ARMA) were estimated using the particle swarm optimization (PSO) technique based on swarm intelligence. The PSO algorithm adapted with the system identification technique and statistics yielded highly satisfactory results in finding the coefficients of the ARMAX model. All the programming and visualization were performed in a MATLAB environment.

Long-Term Modeling and Monitoring of Neuromusculoskeletal System Performance Using Tattoo-Like EMG Sensors

This paper introduces stretchable, long-term wearable, tattoo-like dry surface electrodes for highly repeatable electromyography (EMG). The tattoo-like sensors are hair thin, skin compliant and can be laminated on human skin just like a temporary transfer tattoo, which enables multiday noninvasive but intimate contact with the skin even under severe skin deformation. The new electrodes were used to facilitate a system-based approach to tracking of long-term fatiguing and recovery processes in a human neuromusculoskeletal (NMS) system, which was based on establishing an autoregressive moving average model with exogenous inputs (ARMAX model) relating signatures extracted from the surface electromyogram (sEMG) signals collected using the tattoo-like sensors, and the corresponding hand grip force (HGF) serving as the model output. Performance degradation of the relevant NMS system was evaluated by tracking the evolution of the errors of the ARMAX model established using the data corresponding to the rested (fresh) state of any given subject. Results from several exercise sessions clearly showed repeated patterns of fatiguing and resting, with a notable point that these patterns could now be quantified via dynamic models relating the relevant muscle signatures and NMS outputs.

Substructural damage identification using autoregressive moving average with exogenous inputs model and sparse regularization

Substructuring approaches possess many superiorities over traditional global approaches in damage identification because large-size global structures are replaced by small and manageable substructures. This paper proposes a substructural time series model for locating and quantifying the damage in complex systems. A substructural autoregressive moving average with exogenous inputs (ARMAX) model is established to extract the frequencies and mode shapes of substructures as indicators for damage detection. The detection of structural damage is essentially an inverse problem, and the damage in structure bears sparse properties. The inverse problem of substructural damage identification is efficiently solved via sparse regularization, and structural damage can be located and quantified through the nonzero terms in the solution vector. The accuracy of the proposed method is demonstrated by the numerical simulation of a frame structure and shaking table test of a shear building structure. As the substructural properties are more sensitive to local structural damage than the global properties, the substructural ARMAX model is quite accurate and efficient to be used in the damage identification of a complex system.

Analysis and Modeling of the Impact of Macroeconomic Factors on the Commissioning of Residential Real Estate in Russia

The system of statistical indicators, which is necessary for the construction of mathematical and statistical models that reflect modern domestic trends in the development of the residential real estate market is explained. The official data from the Federal State Statistics Service (Rosstat), the Unified Interdepartmental Information and Statistical System (EMISS), the Central Bank of the Russian Federation (CBR), and the Unified Housing Construction Information System (UIIS) served as information sources for the empirical component of the study.Based on quarterly data for 2010–2021 using ARIMA and SARIMA models, a time series of residential real estate commissions in the Russian Federation was modeled and predicted for 2022. Both models make it possible to account for the influence of the seasonal component. Based on results of the time series regression analysis, the authors selected a mathematical and statistical model with the best approximating characteristics. To model the volume of commissioning of residential real estate in the Russian market, with due regard to the influence of macroeconomic factors, the ARMAX model was used, which has significant explanatory power.The results of the study presented in the article may be of interest to analytical agencies, developers, banking professionals, financiers, economists, analysts of the real estate market or related areas, as well as authorities for strategic planning of the development of the real estate market.