Autoregressive Moving Average Research Articles

Application of Asymmetric-GARCH Type Models to The Kenyan Exchange Rates

Modelling and forecasting the volatility of a financial time series has become essential in many economic and financial applications like portfolio optimization and risk management. The symmetric-GARCH type models can capture volatility and leptokurtosis. However, the models fail to capture leverage effects, volatility clustering, and the thick tail property of high-frequency financial time series. The main objective of this study was to apply the asymmetric-GARCH type models to Kenyan exchange to overcome the shortcomings of symmetric-GARCH type models. The study compared the asymmetric Conditional Heteroskedasticity class of models: EGARCH, TGARCH, APARCH, GJR-GARCH, and IGARCH. Secondary data on the exchange rate from January 1993 to June 2021 were obtained from the Central Bank of Kenya website. The best fit model is determined based on parsimony of the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Log-Likelihood criterion, and minimisation of prediction production errors (Mean error [ME] and Root Mean Absolute error [RMAE]). The optimal variance equation for the exchange rates data was APARCH (1,1) - ARMA (3,0) model with a skewed normal distribution (AIC = -4.6871, BIC = -4.5860). Volatility clustering was present in exchange rate data with evidence of the leverage effect. Estimated Kenya’s exchange rate volatility narrows over time, indicating sustained exchange rate stability.

The Chen Autoregressive Moving Average Model for Modeling Asymmetric Positive Continuous Time Series

In this paper, we introduce a new dynamic model for time series based on the Chen distribution, which is useful for modeling asymmetric, positive, continuous, and time-dependent data. The proposed Chen autoregressive moving average (CHARMA) model combines the flexibility of the Chen distribution with the use of covariates and lagged terms to model the conditional median response. We introduce the CHARMA structure and discuss conditional maximum likelihood estimation, hypothesis testing inference along with the estimator asymptotic properties of the estimator, diagnostic analysis, and forecasting. In particular, we provide closed-form expressions for the conditional score vector and the conditional information matrix. We conduct a Monte Carlo experiment to evaluate the introduced theory in finite sample sizes. Finally, we illustrate the usefulness of the proposed model by exploring two empirical applications in a wind-speed and maximum-temperature time-series dataset.

PREDIKSI JUMLAH PEMAKAIAN AIR BERSIH MENGGUNAKAN METODE HYBRID SINGULAR SPECTRUM ANALYSIS (SSA) DAN SARIMA DI PDAM TIRTANADI SIBOLANGIT

Clean water is one of the basic human needs that is needed on an ongoing basis. Water has an important role in human life. As the population increases, the use of clean water also increases, resulting in the need for demand for the availability of clean water to continue to increase, this is explained by data from the Central Statistics Agency (2022) that the population growth rate in Sibolangit District from 2021-2022 is 0.25% and that This is also explained by data on the amount of clean water consumption by PDAM Tirtanadi Sibolangit which has increased by 6.5%. The purpose of this study is to apply the SSA-SARIMA hybrid model to predict the amount of clean water consumption in the coming period at PDAM Tirtandi Sibolangit so that there is no shortage and wastage of clean water. Hybrid SSA-SARIMA is a combination of two data analysis methods that take advantage of the advantages of each method, namely Singular Spectrum Analysis (SSA) and Seasonal Autoregressive Moving Average (SARIMA). SSA is a technique used to separate signals into periodic and non-periodic components while SARIMA is used to model time series data with trend and seasonal patterns and make predictions for future periods. SARIMA cannot separate periodic and non-periodic signals in data like SSA did. The data used in this study is monthly data on clean water usage from January 2018 to December 2022. The prediction results for the amount of clean water consumption in PDAM Tirtanadi Sibolangit in 2024 use the SSA-SARIMA(1,1,0)(1,0,0) hybrid model. )12 experienced a decrease in the use of clean water with a level of forecasting accuracy having a MAPE value of 6.920446%.

Mixed-integer second-order cone programming method for active distribution network

Developing a novel type of power system is an important means of achieving the “dual carbon” goals of achieving peak carbon emissions and carbon neutrality in the near future. Given that the distribution network has access to a wide range of distributed and flexible resources, reasonably controlling large-scale and adjustable resources is a critical factor influencing the safe and stable operation of the active distribution network (ADN). In light of this, the authors of this study propose a mixed-integer second-order cone programming method for an active distribution network by considering the collaboration between distributed, flexible resources. First, Monte Carlo sampling is used to simulate the charging load of electric vehicles (EVs), and the auto regressive moving average (ARMA) and the scenario reduction algorithms (SRA) based on probability distance are used to generate scenarios of the outputs of distributed generation (DG). Second, we establish an economical, low-carbon model to optimize the operation of the active distribution network to reduce its operating costs and carbon emissions by considering the adjustable characteristics of the distributed and flexible resources, such as on-load tap changer (OLTC), devices for reactive power compensation, and EVs and electric energy storage equipment (EES). Then, the proposed model is transformed into a mixed-integer second-order cone programming (SOCP) model with a convex feasible domain by using second-order cone relaxation (SOCR), and is solved by using the CPLEX commercial solver. Finally, we performed an arithmetic analysis on the improved IEEE 33-node power distribution system, the results show that ADN’s day-to-day operating costs were reduced by 47.9% year-on-year, and carbon emissions were reduced by 75.2% year-on-year. The method proposed in this paper has significant effects in reducing the operating cost and carbon emissions of ADNs, as well as reducing the amplitude of ADN node voltages and branch currents.

Turbo-shaft engine adaptive neural network control based on nonlinear state space equation

Intelligent Adaptive Control (AC) has remarkable advantages in the control system design of aero-engine which has strong nonlinearity and uncertainty. Inspired by the Nonlinear Autoregressive Moving Average (NARMA)-L2 adaptive control, a novel Nonlinear State Space Equation (NSSE) based Adaptive neural network Control (NSSE-AC) method is proposed for the turbo-shaft engine control system design. The proposed NSSE model is derived from a special neural network with an extra layer, and the rotor speed of the gas turbine is taken as the main state variable which makes the NSSE model be able to capture the system dynamic better than the NARMA-L2 model. A hybrid Recursive Least-Square and Levenberg-Marquardt (RLS-LM) algorithm is advanced to perform the online learning of the neural network, which further enhances both the accuracy of the NSSE model and the performance of the adaptive controller. The feedback correction is also utilized in the NSSE-AC system to eliminate the steady-state tracking error. Simulation results show that, compared with the NARMA-L2 model, the NSSE model of the turbo-shaft engine is more accurate. The maximum modeling error is decreased from 5.92% to 0.97% when the LM algorithm is introduced to optimize the neural network parameters. The NSSE-AC method can not only achieve a better main control loop performance than the traditional controller but also limit all the constraint parameters efficiently with quick and accurate switching responses even if component degradation exists. Thus, the effectiveness of the NSSE-AC method is validated.

Forecasting Model Selection with Variables Impact to Predict Electricity Demand at Rajshahi City of Bangladesh

The purpose of this study is to forecast electricity demand by using the best-selected method which untangles all the factors that affect electricity demand. Three different methods traditional methods (Multiple Regression Model), modified-traditional methods (ARMA), and soft computing method (Fuzzy Linear Regression Model) are selected for prediction. Environmental parameters like temperature, humidity, and wind speed are included as variables as Rajshahi has very impactful weather. The impact of each variable was calculated from their standardized values to know the effect of environmental parameters. The accuracy of the three forecasting models is compared by different statistical measures of errors. Using Mean Absolute Percentage Error (MAPE), the errors of the Multiple Regression Model, ARMA, and Fuzzy Linear Regression (FLR) Model are 6.85%, 22.24%, and 4.45%. The other three measures of error also give the FLR gives the best results. Finally, the electricity demand of Rajshahi City for the next five years is forecasted using the Fuzzy Linear Regression Model.

Forecasting of Crude Oil Prices Using Wavelet Decomposition Based Denoising with ARMA Model

Forecasting of Crude Oil Prices Using Wavelet Decomposition Based Denoising with ARMA Model

IETS: State space model for intermittent demand forecasting

Inventory decisions relating to items that are demanded intermittently are particularly challenging. Decisions relating to termination of sales of product often rely on point estimates of the mean demand, whereas replenishment decisions depend on quantiles from interval estimates. It is in this context that modelling intermittent demand becomes an important task. In previous research, this has been addressed by generalised linear models or integer-valued ARMA models, while the development of models in state space framework has had mixed success. In this paper, we propose a general state space model that takes intermittence of data into account, extending the taxonomy of single source of error state space models. We show that this model has a connection with conventional non-intermittent state space models used in inventory planning. Certain forms of it may be estimated by Croston’s and Teunter–Syntetos–Babai (TSB) forecasting methods. We discuss properties of the proposed models and show how a selection can be made between them in the proposed framework. We then conduct a simulation experiment, empirically evaluating the inventory implications.

ÇEKİRDEK, GIDA VE ENERJİ ENFLASYONLARINDA KALICILIĞIN ARAŞTIRILMASI: ZAMANLA DEĞİŞEN YAKLAŞIMDAN BİR KANIT

This study examines how inflation persistence evolves over time in Euro Area, the UK, the US and OECD countries over the period of 1999:07-2021:09. We consider the persistence of core, energy, and food inflation, as well total inflation. Using an ARMA(1,1) model with time-varying autoregressive parameters based on the Kalman filter (TV-AR), we find that inflation persistence increases significantly during crisis periods and total persistence peaks during the COVID-19 pandemic. However, the persistence of energy inflation decreases due to the economic slowdown during the COVID-19 pandemic. These results highlight how inflation persistence is related to the objectives and conduct of monetary policy. The findings indicate that the various measures taken by the governments such as containment and closure policies, travel restrictions to prevent the spread of COVID-19 cause to increase in total and food inflation persistences. Energy inflation persistence declines due to a slowdown in production during the COVID-19 period.

Sampling Gaussian stationary random fields: A stochastic realization approach

Generating large-scale samples of stationary random fields is of great importance in the fields such as geomaterial modeling and uncertainty quantification. Traditional methodologies based on covariance matrix decomposition have the difficulty of being computationally expensive, which is even more serious when the dimension of the random field is large. This paper proposes an efficient stochastic realization approach for sampling Gaussian stationary random fields from a systems and control point of view. Specifically, we take the exponential and squared exponential covariance functions as examples and make a decoupling assumption when there are multiple dimensions. Then a rational spectral density is constructed in each dimension using techniques from covariance extension, and the corresponding autoregressive moving-average (ARMA) model is obtained via spectral factorization. As a result, samples of the random field with a specific covariance function can be generated very efficiently in the space domain by implementing the ARMA recursion using a Gaussian white noise input. Such a procedure is computationally cheap due to the fact that the constructed ARMA model has a low order. Furthermore, the same method is integrated to multiscale simulations where interpolations of the generated samples are achieved when one zooms into finer scales. Both theoretical analysis and simulation results show that our approach performs favorably compared with covariance matrix decomposition methods.

The impact of long memory in mortality differentials on index-based longevity hedges

AbstractIn multi-population mortality modeling, autoregressive moving average (ARMA) processes are typically used to model the evolution of mortality differentials between different populations over time. While such processes capture only short-term serial dependence, it is found in our empirical work that mortality differentials often exhibit statistically significant long-term serial dependence, suggesting the necessity for using long memory processes instead. In this paper, we model mortality differentials between different populations with long memory processes, while preserving coherence in the resulting mortality forecasts. Our results indicate that if the dynamics of mortality differentials are modeled by long memory processes, mean reversion would be much slower, and forecast uncertainty over the long run would be higher. These results imply that the true level of population basis risk in index-based longevity hedges may be larger than what we would expect when ARMA processes are assumed. We also study how index-based longevity hedges should be calibrated if mortality differentials follow long memory processes. It is found that delta hedges are more robust than variance-minimizing hedges, in the sense that the former remains effective even if the true processes for mortality differentials are long memory ones.

Modeling Time Series Poison Count Data: An Application to COVID 19 Confirmed Cases in Nigeria

Time series events are counted within time intervals usually for convenience and practical reasons. Time series data involving counts frequently follows Poison distribution. Integrated Autoregressive Moving Average (ARIMA) models were studied on simulated Poison data of different parameter and sample sizes. These models were used to capture Poison data with different phenomena. Data set were simulated from Poison process with ARIMA (p, d, q) were then fitted to the simulated data so as to examine the effect of the changes in parameter value of the Poison on the models’ performance across the sample size. Thereafter, the same models were used to fit and forecast the daily Covid-19 data, confirmed cases from inception to February 2023. It was concluded that ARIMA (2, 1, 2) and ARIMA (1, 1, 1) are obviously the best Models at different sample sizes respectively. Based on the Covid-19 analysis, the estimated coefficient values of all ARIMA (p,d,q) strictly conforms to the bounds of the parameter between -1 and 1 and this had made the model to be stationary comparing the ARIMA models in terms of the AIC, BIC and MSE. It is clearly preferred ARIMA (1, 0, 2) to other models since their estimated AIC, BIC and MSE are smaller as compared to other models. The forecast is quite accurate, and hereby confirms what was expected. It seems that ARIMA (1, 0, 2) does a very good job in capturing the dynamic nature of the data and forecasting. It was observed that the confirmed cases increase, and then keep stationary throughout the future times.

Damage identification in steel plate structures considering bending and torsion moments using estimated seismic responses

This paper proposes a model-free damage identification method and suggests an effective index for damage diagnosis in steel plate-like structures considering both the torsion and bending moments using only acceleration data, with no need for geometric characteristics. The basis for damage detection is the difference between healthy and damaged structural responses to different ground accelerations. In doing so, two Peak Ground Acceleration (PGA) scales, 0.05 (g), and 0.5 (g), labeled for the Loma Prieta ground motion, are considered. Four-node meshes are applied to reflect the torsion moments in the steel plate behavior. A multi-objective function, Fisher Information Matrix, is utilized, and four sensor locations are optimized to identify the locations most sensitive to damage. AutoRegressive Moving Average with exogenous input (ARMAX) system identification method is employed to obtain the structural displacement from the acceleration data and, subsequently, the displacement state equations of the nodes. With the aid of the structural displacement and its derivatives obtained through the central finite difference approximation method, damage to the plate structure is detected at PGA = 0.05 (g) and PGA = 0.50 (g) considering thickness changes based on the peak values manifested in the proposed damage detection index. Furthermore, the recorded structural acceleration responses at the desired scales of PGAs are fed into the 2D wavelet transform to detect damage imposed on the plate structure using the diagonal component of the wavelet transform. The results confirm that the proposed nonmodel-based approach successfully detects the single and multiple damage scenarios and can be used for a quick and judicious assessment of the steel plate behavior immediately after damage.

Simulation of a virtual liver iron overload model and R2 * estimation using multispectral fat-water models for GRE and UTE acquisitions at 1.5 Tand 3 T.

R2 *-MRI has emerged as a noninvasive alternative to liver biopsy for assessment of hepatic iron content (HIC). Multispectral fat-water R2 * modeling techniques such as the nonlinear least squares (NLSQ) fitting and autoregressive moving average (ARMA) models have been proposed for the accurate assessment of iron overload by also considering fat, which can otherwise confound R2 *-based HIC measurements in conditions of coexisting iron overload and steatosis. However, the R2 * estimation by these multispectral models has not been systematically investigated for various acquisition methods in iron overload only conditions and across the full clinically relevant range of HICs (0-40 mg Fe/g dry liver weight). The purpose of this study is to evaluate the R2 * accuracy and precision of multispectral models for various multiecho gradient echo (GRE) and ultrashort echo time (UTE) imaging acquisitions by constructing virtual iron overload models based on true histology and synthesizing MRI signals via Monte Carlo simulations at 1.5 T and 3 T, and comparing their results with monoexponential model and published in vivo R2 *-HIC calibrations. The signals were synthesized with TE1 = 1.0 ms for GRE and TE1 = 0.1 ms for UTE acquisition for varying echo spacing, ΔTE (0.1, 0.5, 1, 2 ms), and maximum echo time, TEmax (2, 4, 6, 10 ms). An iron-doped phantom study is also conducted to validate the simulation results in experimental GRE (TE1 = 1.2 ms, ΔTE = 0.72 ms, TEmax = 6.24 ms) and UTE (TE1 = 0.1 ms, ΔTE = 0.5 ms, TEmax = 6.1 ms) acquisitions. For GRE acquisitions, the multispectral ARMA and NLSQ models produced higher slopes (0.032-0.035) compared with the monoexponential model and published in vivo R2 *-HIC calibrations (0.025-0.028). However, for UTE acquisition for shorter echo spacing (≤0.5 ms) and longer maximum echo time, TEmax (≥6 ms), the multispectral and monoexponential signal models produced similar R2 *-HIC slopes (1.5 T, 0.028-0.032; 3 T, 0.014-0.016) and precision values (coefficient of variation < 25%) across the full clinical spectrum of HICs at both 1.5 T and 3 T. The phantom analysis also showed that all signal models demonstrated a significant improvement in R2 * estimation for UTE acquisition compared with GRE, confirming our simulation findings. Future work should investigate the performance of multispectral fat-water models by simulating liver models in coexisting conditions of iron overload and steatosis for accurate R2 * and fat quantification.

Modelling and forecasting dairy milk production: Evidence from Autoregressive Moving Average (ARMA) models

Dairy sector is one of the fastest growing sectors in the world with little global contributions from African countries and from Nigeria in particular. This study modelled and forecast diary milk production in Iwo and its environs using different variants of Autoregressive Moving Average (ARMA) models. Data used in this study comprised the daily milk production in Iwo and environs between 26th May, 2021 and 31st May, 2022 as obtained from Bowen University milk collection centre in Iwo, Nigeria. Sstationary was examined using the ADF test and p-value of. 0020 indicating the data is stationary at level (p<.05). Preliminary result indicates that milk production in the study area was as it peak in June, 2021 with 295 litres and the least value was obtained in September, 2021 with average of 63.95 litres in 2021 and 64.93 litres in 2022 respectively. There was no significant difference in litres of milk produced between these two years (p>.05). Four ARMA models, ARMA(1,1), ARMA(1,2), ARMA(2,1) and ARMA(2,2) were identified as tentative models with BIC values of 7.528, 7.550, 7.549 and 7.570 respectively. The four tentative models satisfied model diagnostic checking (p>0.05) and ARMA (1,1) gave the lowest value of Root Mean Square Error. Hence, ARMA(1,1) was adjudged as the best forecasting model among the competing models. Result of 30 days forecast shows that there will be a consistent steady increase in milk production within a range of 38 litres to 55 litres per day.

Autoregressive Moving Average Model-Free Predictive Current Control for PMSM Drives

To eliminate the influence of the parameter mismatches and obtain high model quality, a model-free predictive current control (MF-PCC) strategy based on the autoregressive moving average (ARMA) structure is proposed in this paper and applied to the permanent magnet synchronous motor (PMSM) speed control system. Since the ARMA model group which is a family of mathematical models containing AR, MA and ARMA structures considers operating states within several sampling periods to achieve better model accuracy, the plant is online designed as this type, and its coefficients are estimated according to the sampled data by the normalized least-mean-square (NLMS) algorithm with adaptive normalized step length to achieve improved model quality with reduced calculation burden. Compared with the ultra-local MF-PCC strategy, advantages of better stator current quality and robustness are demonstrated by the experimental results, as well as the reduced calculation burden compared with the recursive least square (RLS) algorithm used to estimate the coefficients.

VAM: An End-to-End Simulator for Time Series Regression and Temporal Link Prediction in Social Media Networks

We present a machine-learning-driven end-to-end simulator, called the <i>Volume-Audience-Match</i> (VAM) simulator. VAM&#x2019;s purpose is to simulate future phenomena related to various topics of discussion in social media networks. We focus our attention on the social media platform, Twitter, due to its abundant use in today&#x2019;s world. VAM was applied to do time series forecasting to predict the future: 1) number of total activities; 2) number of active old users; and 3) number of newly active users over the span of 24 hours from the start time of prediction. VAM then used these macroscopic volume predictions (VPs) to perform user link predictions. A user&#x2013;user edge was assigned to each of the activities in the 24 future time steps. We report that VAM outperformed multiple baseline models in the time series task, which were the auto-regressive integrated moving average (ARIMA), auto regressive moving average (ARMA), auto regressive (AR), moving average (MA), Persistence Baseline, and state-of-the-art tNodeEmbed models. Furthermore, we show that VAM outperformed the Persistence Baseline and tNodeEmbed models used for the user-assignment tasks. Finally, it is also shown that using Reddit activity data improves prediction accuracy.

A multi-criterion optimization of mechanical properties and sustainability performance in friction stir welding of 6061-T6 AA

Nowadays, the transportation industry is curious about fabricating lightweight vehicles under a sustainable manufacturing process to minimize fuel consumption costs and environmental footprints. Assessing the sustainability performance metrics of the friction stir welding (FSW) process reduces the sawing costs and environmental impacts. However, the evaluation and assessment of the sustainability performance metrics integrated with the mechanical properties of the weld joint have not been sufficiently studied. Thus, this study investigates the multi-criterion process parameter optimization of friction stir welding (FSW) to attain an optimum parameter to enhance the mechanical properties of the weld joint and decrease energy consumption and carbon dioxide emission. Experimentations are conducted using a vertical CNC milling machine on a 5 mm 6061-T6 AA material with a butt joint orientation. Tool rotational speed, traverse speed, and tool profile were used as processing parameters. Response of the study, such as transient temperature and energy consumption, was measured during the joining process, whereas hardness, tensile strength, and CO2 emission were examined post-processing. The multi-criterion optimization was done using the Taguchi-based grey relational analysis method. In addition, the transient temperature was predicted by an auto-regressive moving average (ARIMA) and Ansys simulation. The finding showed that higher rotational and minimum welding speeds had imparted a sound weld. Besides, the analysis of variance results showed that welding speed has a significant parameter at a 95% confidence interval. The proposed ARIMA model's result showed that the transient temperature prediction accuracy reached 99.922%, and the error percentage between the FEA simulation and experimental work reached 2.067%.

Real-time Monitoring Algorithm of Muscle State Based on sEMG Signal

Muscle fatigue can occur when we do too much physical activity in a short period of time, or if we have not been exercising regularly. For patients who need rehabilitation training, muscle fatigue has certain safety risks. Therefore, real-time monitoring of muscle fatigue is very necessary and meaningful. At present, there are few studies on the assessment of muscle status, and most of the methods are limited to the detection of fatigue threshold, lagging behind the occurrence of fatigue. This paper analyzes the change law of the fatigue process model and summarizes it, and designs it into a real-time evaluation algorithm of muscle state. First, the autoregressive moving average (ARMA) model is constructed utilizing surface electromyography (sEMG) and joint motion angle data. Next, the parameters are identified and monitored in real-time. Finally, hierarchical clustering is employed to categorize levels of fatigue. The algorithm is capable of capturing changes in fatigue-induced correlations between sEMG and the corresponding joint motion angles during dynamic movements, enabling accurate classification of muscle fatigue states. Experimental results have demonstrated the effectiveness of the algorithm, which has significant implications for real-time evaluation of human muscle state and the design of control systems in human-computer interaction.

Hourly Network Anomaly Detection on HTTP Using Exponential Random Graph Models and Autoregressive Moving Average

Network anomaly detection solutions can analyze a network’s data volume by protocol over time and can detect many kinds of cyberattacks such as exfiltration. We use exponential random graph models (ERGMs) in order to flatten hourly network topological characteristics into a time series, and Autoregressive Moving Average (ARMA) to analyze that time series and to detect potential attacks. In particular, we extend our previous method in not only demonstrating detection over hourly data but also through labeling of nodes and over the HTTP protocol. We demonstrate the effectiveness of our method using real-world data for creating exfiltration scenarios. We highlight how our method has the potential to provide a useful description of what is happening in the network structure and how this can assist cybersecurity analysts in making better decisions in conjunction with existing intrusion detection systems. Finally, we describe some strengths of our method, its accuracy based on the right selection of parameters, as well as its low computational requirements.