Autoregressive And Moving Average Research Articles

Asymptotic inference of the ARMA model with time‐functional variance noises

Asymptotic inference of the ARMA model with time‐functional variance noises

Sustainable Public Transportation in a Volatile, Uncertain, Complex, and Ambiguous (VUCA) Age

A well-functioning public transport system is one of the foundations of the Smart city concept and sustainable cities. The COVID period offers an excellent opportunity to examine the impact of different factors, because throughout this period society was faced with both health and governmental impacts that had different effects. Public transport use in the EU member states from the turn of the millennium until the beginning of the pandemic ranged from 17–18% to 27% of total journeys. The COVID-19 virus caused a 5–7% decrease in public transport use. The present study analyses the relationship between these effects and the number of paying passengers on public transport in Debrecen. Four hypotheses were put forward, i.e., that (1) the evolution of travel tickets, (2) general passes, (3) discounted passes and (4) replacement tickets were influenced by the evolution of the active COVID-19 case rate. The data were collected from the Debrecen Transport Company (DKV) for the period 1 January 2020–12 December 2021, and the Worldometers.info database. Statistical analyses were performed using an autoregressive and moving average (ARMA) model. We found that COVID’s active case numbers did not affect sales, but some of the government measures did have an effect. The results of this research can be used to inform future decisions to maintain and improve urban transport.

PROBABILISTIC MODELS AND METHODS OF REGRESSION ANALYSIS OF VOLATILE FINANCIAL TIME SERIES

The article considers financial and economic time series in production, banking, and investment branches. Empirical research in the field of economics increasingly uses data at the individual or household level obtained from surveys. Some variables are difficult enough to measure that such problems arise even when estimating simple bivariate regressions; when panel data are used in ways that effectively distinguish much of the true change while adding to the noise. Results of analysis of real information give the reasons to suppose that the most adequate mathematic models of non-stationary financial time series are homoscedastic and heteroscedastic probabilistic models with partially unknown impact factors. We propose the auto regression and moving average (ARMA) models for analysis of homoscedastic series and auto regression and integrated moving average (ARIMA) models for analysis of heteroscedastic series. These models cover rather wide class of random processes, which are non-stationary in wide and narrow sense. Correct choice of model order allows getting the results with acceptable errors (discrepancy) using rather simple models. We showed the principal useless of tendency to non-critical enlarging of order of moving average and regression equations. Moreover, the model gets much more complicated, and the errors of extrapolation, corresponding with forecasting, grow very quickly. The article attempts a preliminary survey and analysis of time series data for the specification of a model of the interrelationship of variables. It should be recognized that the practical implementation of the above rules is not trivial. In particular, it is obvious that it is possible to obtain satisfactory estimates of the spectrum of financial and economic time series, but at the moment it is not clear how to quantitatively estimate volatility values, cooperation processes in conflict conditions, etc. Only further analysis, both theoretical and empirical, can provide answers to these questions.

Analysis and design of control systems via parameter‐based approach

Analysis and design of control systems via parameter‐based approach

Shaping energy cost management in process industries through clustering and soft sensors

With the ever-increasing growth of energy demand and costs, process monitoring of operational costs is of great importance for process industries. In this light, both financial budget management and local operational optimization supposed to be guaranteed properly. To achieve this goal, a support vector machine recursive feature elimination (SVM-RFE) method together with clustering algorithm was developed to extract features while serving as importance measurements of each input variable for the sequential prediction model construction. Then, the four variants of autoregressive and moving average (ARMA), i.e., ARMA with exogenous input (ARMAX) based on recursive least squares algorithm (RLS), ARMAX based on recursive extended least squares algorithm (RELS), nonlinear auto-regressive neural network (NARNN) and nonlinear auto-regressive neural network with exogenous input (NARXNN), were applied, respectively, to predict the costs incurred in the daily production for process industries. The methods were validated in the Benchmark Simulation Model No.2-P (BSM2-P) and a practical data set about steel industry energy consumption from an open access database (University of California, Irvine (UCI)), respectively. The nonlinear model, NARXNN, was validated to achieve better performance in terms of mean square error (MSE) and correlation coefficient (R), when used for multi-step prediction of the aforementioned datasets with strong nonlinear and coupled characteristics.

Differential Privacy for Class-Based Data: A Practical Gaussian Mechanism

In this paper, we present a notion of differential privacy (DP) for data that comes from different classes. Here, the class-membership is private information that needs to be protected. The proposed method is an output perturbation mechanism that adds noise to the release of query response such that the analyst is unable to infer the underlying class-label. The proposed DP method is capable of not only protecting the privacy of class-based data but also meets quality metrics of accuracy and is computationally efficient and practical. We illustrate the efficacy of the proposed method empirically while outperforming the baseline additive Gaussian noise mechanism.We also examine a real-world application and apply the proposed DP method to the autoregression and moving average (ARMA) forecasting method, protecting the privacy of the underlying data source. Case studies on the real-world advanced metering infrastructure (AMI) measurements of household power consumption validate the excellent performance of the proposed DP method while also satisfying the accuracy of forecasted power consumption measurements.

Application of GPR technology in moisture content detection of stored grain

How to detect grain moisture content storage inefficiently, non-destructively, and quickly is a critical task in the storage process of the modern grain industry. The influence of media with different moisture content on the propagation and attenuation of electromagnetic wave energy is the premise and basis for applying electromagnetic wave technology in detecting grain moisture content. To explore the applicability of electromagnetic wave technology in detecting grain moisture content, we used ground penetrating radar (GPR) technology and auto regressive and moving average (ARMA) power spectrum analysis method to detect and study the moisture content of the typical national grain depots and local grain depots. The results show that GPR technology could realize the moisture content of stored grains and solve the problems of detection distance, non-destructive, and detection dead ends. Compared with the actual test data, the correlation is above 90%, the error can be controlled within 0.5%, and the measurement accuracy is higher, within ±0.3%. The continuous distribution profile of stored grain moisture content was obtained using the ARMA method. The moisture content distribution range of the rice barn was 10-14%, showing the regularity of the moisture content distribution in the middle layer > upper-middle layer > lower-middle layer > bottom layer > grain surface layer. It indicates that the GPR technology has particular advantages in food safety detection and provides data support for real-time detection of food storage safety.

China Coastal Bulk (Coal) Freight Index Forecasting Based on an Integrated Model Combining ARMA, GM and BP Model Optimized by GA

The China Coastal Bulk Coal Freight Index (CBCFI) is the main indicator tracking the coal shipping price volatility in the Chinese market. This index indicates the variable performance of current status and trends in the coastal coal shipping sector. It is critical for the government and shipping companies to formulate timely policies and measures. After investigating the fluctuation patterns of the shipping index and the external factors in light of forecasting accuracy requirements of CBCFI, this paper proposes a nonlinear integrated forecasting model combining ARMA (Auto-Regressive and Moving Average), GM (Grey System Theory Model) and BP (Back-Propagation) Model Optimized by GA (Genetic Algorithms). This integrated model uses the predicted values of ARMA and GM as the input training samples of the neural network. Considering the shortcomings of the BP network in terms of slow convergence and the tendency to fall into local optimum, it innovatively uses a genetic algorithm to optimize the BP network, which can better exploit the prediction accuracy of the combined model. Thus, establishing the combined ARMA-GM-GABP prediction model. This work compares the short-term forecasting effects of the above three models on CBCFI. The results of the forecast fitting and error analysis show that the predicted values of the combined ARMA-GM-GABP model are fully consistent with the change trend of the actual values. The prediction accuracy has been improved to a certain extent during the observation period, which can better fit the CBCFI historical time series and can effectively solve the CBCFI forecasting problem.

A Hybrid Method for Structural Modal Parameter Identification Based on IEMD/ARMA: A Numerical Study and Experimental Model Validation

This article presents a hybrid method of structural modal parameter identification, based on improved empirical mode decomposition (EMD) and autoregressive and moving average (ARMA). Special attention is given to some implementation issues, such as the modal mixing, false modes, the judgment of the real intrinsic mode function (IMF) of classical EMD, and the difficulty of fixing the order of ARMA. To resolve the existing defects of EMD, an improved EMD (IEMD) that combines frequency band filtering and cluster analysis is proposed in this paper, where frequency band filtering divides the signal into several narrowband signals before the EMD process, and cluster analysis is used to determine the real IMFs. Euclidean distance is used to cluster the decomposition results, with no need to adjust any indexes or thresholds, and only by means of using the nearest distance to efficiently determine the real IMF. Moreover, IEMD is used as a pre-processing tool for ARMA, to resolve the difficulty of fixing its order. The capabilities of the proposed method were compared and assessed using a numerical simulation and an experimental model. The numerical simulation and experimental results showed that the improved method could resolve the modal mixing and false modal problems in the classical EMD process and could automatically identified the real IMFs, while the proposed IEMD was combined with ARMA to successfully identify the frequency and mode shape of the structure. Additionally, since each IMF is a single component signal, it is easy to determine the order of the ARMA model.

Nonlinear web tension control of a roll-to-roll printed electronics system

Roll-to-roll printed electronics (R2RPE) is a low-cost and high-efficiency manufacturing method for high-density circuits printed on flexible substrates. Stable web tension control is essential for excellent printing quality. However, due to many uncertainties in terms of the model errors, roll machining errors, and external disturbances, etc., it is difficult to guarantee the tension control accuracy especially for conventional control methods. For this purpose, a nonlinear model predictive control (MPC) scheme is proposed to eliminate the tension disturbance of the R2RPE system. The dynamic model of the unwind roller is firstly established, and then the factors affecting the web tension are analyzed. The nonlinear dynamic matrix control (NDMC) based on an auto-regressive and moving average (ARMA) model is introduced to eliminate the tension disturbance. To evaluate the effectiveness of the proposed control method, the tension controls using the traditional proportional-integral-derivative (PID), fuzzy PID and proposed NDMC are simulated with MATLAB for performance comparisons. Finally, an R2RPE prototype is fabricated for performance tests. The experimental results validate the effectiveness of the proposed control scheme. Keywords: Roll-to-roll printed electronics, web tension control, dynamic modeling.

Whittle parameter estimation for vector ARMA models with heavy-tailed noises

This paper studies the Whittle estimation for vector autoregressive and moving average (ARMA) models with heavy-tailed noises. It is shown that the Whittle estimator is consistent with the rate of convergence n1/αL̃(n) and its limiting distribution is a function of two stable random vectors, where L̃(n) is a slowly varying function and α∈(0,2) is the tail index of heavy-tailed vector noise. A simulation study is carried out to assess the performance of this estimator in finite samples and a real example is given. This paper includes several limiting theorems for the general heavy-tailed vector processes, which is independent of interest.

Prediksi Jumlah Penjualan Rumah di Bojongsoang ditengah Pandemi Covid-19 dengan Metode ARIMA

This study aims to determine the accuracy of the ARIMA method with the Carmer matrix in forecasting or predicting the number of house sales in the Bojongsoang area which is still experiencing a period of crisis. The data used in this study is secondary data in the form of time series data on the number of house sales. In the ARIMA method, we perform stationary data, then look for autoregressive (AR), moving average (MA), and ARMA (Autoregressive and Moving Average) values. From the available data, the number of house sales has decreased, therefore forecasting is carried out using the ARIMA (1,1,1) model for future home sales to assist property developers in estimating future development projects. the results of the forecasting carried out using the ARIMA (1,1,1) method, which shows that the prediction of the number of house sales in the Bojongsoang area in the June - December period experienced a stable number of house sales

Autoregressive and moving average models for zero‐inflated count time series

Zero inflation is a common nuisance while monitoring disease progression over time. This article proposes a new observation‐driven model for zero‐inflated and over‐dispersed count time series. The counts given from the past history of the process and available information on covariates are assumed to be distributed as a mixture of a Poisson distribution and a distribution degenerated at zero, with a time‐dependent mixing probability, . Since, count data usually suffers from overdispersion, a Gamma distribution is used to model the excess variation, resulting in a zero‐inflated negative binomial regression model with mean parameter . Linear predictors with autoregressive and moving average (ARMA) type terms, covariates, seasonality and trend are fitted to and through canonical link generalized linear models. Estimation is done using maximum likelihood aided by iterative algorithms, such as Newton‐Raphson (NR) and Expectation and Maximization. Theoretical results on the consistency and asymptotic normality of the estimators are given. The proposed model is illustrated using in‐depth simulation studies and two disease datasets.

Model selection for time series with nonlinear trend

A two-step model selection procedure is proposed for autoregressive and moving-average (ARMA) model class. It is an adaptive least absolute shrinkage and selection operator (adLASSO) type model selection method that simultaneously chooses both the orders and significant lagged variables when the autoregressive and moving-average (ARMA) time series is contaminated with a nonlinear trend. The adLASSO is applied not to the observations, but to the detrended residuals. The proposed two-step adLASSO model selection procedure under some conditions can identify the true model with probability approaching one as the sample size increases, and the asymptotic properties of estimators are not affected by the replacement of observations with detrended residuals. The simulation studies show that the proposed method performs well with sample size as small as 50. The application of the method is illustrated by the annual varve thickness data collected from a location in Massachusetts.

Scenario-Based Two-Stage Stochastic Scheduling of Microgrid Considered as the Responsible Load

This article presents a novel linear programming (LP) based two-stage stochastic approach for microgrids (MGs) under uncertainties. In this regard, the day-ahead programming of dispatchable resources in MG was modeled, considering the uncertainties in demand loads, and upstream network electricity price. Moreover, the inherent stochastic nature of wind and solar resources as well as the environmental aspects were modeled to find a realistic solution. Also, real-time pricing (RTP), demand response (DR) program considering the energy storage system (ESS) as a DR option was implemented on an MG as a smart customer. The extensive form of the two-stage stochastic recourse model was properly implemented for dispatchable and non-dispatchable resources. Furthermore, scenario generation and reduction procedures were realized with autoregressive and moving average (ARMA) model-based time-series (TS), and backward reduction (BR) method by the Kantorovich distance (KD), respectively. The simulations on a grid-connected MG, including micro-turbine (MT), fuel-cell (FC), wind-turbine (WT), photovoltaic module (PV), and ESS were reported in operational cases based on one month of real recorded data for wind speed, solar irradiance, demand load, and upstream network electricity price. The results for the next day in real-time confirmed the accuracy of the developed optimization methodology.

Recursive linear models optimized by bioinspired metaheuristics to streamflow time series prediction

AbstractTime series forecasting problems are often addressed using linear techniques, especially the autoregressive (AR) models, due to their simplicity combined with good performances. It is possible to generalize a linear predictor by allowing infinite impulse response (IIR) through the addition of feedback loops, as occurs in the autoregressive and moving average (ARMA) models and IIR filters. However, the calculation of the free coefficients of these structures is more complex, as the optimization problem has no closed‐form solution. This work conducts an extensive investigation on the use of linear models to predict monthly seasonal streamflow series associated with Brazilian hydroelectric plants. The main goal is to reach the best achievable performance with linear approaches. We propose the application of recursive models, estimating their parameters with the aid of bioinspired metaheuristics: particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), and two immune‐inspired algorithms, the CLONALG, and the artificial immune network for optimization (Opt‐aiNet). The AR model is also considered. The results to multistep ahead forecasting indicated that the insertion of feedback loops increased the performances, with ARMA being the best predictor. The DE, PSO, and GA led to the minimum values of mean‐squared error during the tests, while DE yielded the smallest dispersion.

Stochastic optimization of integrated energy system considering network dynamic characteristics and psychological preference

To improve the flexibility of integrated energy system (IES) and promote the clean energy accommodation, an IES stochastic optimization model considering the network dynamic characteristics and psychological preference is proposed. Firstly, the uncertainty and spatial-temporal correlation between multiple wind farms are dealt by the auto-regressive and moving average (ARMA) time series and Cholesky decomposition, and then typical scenarios are constructed by the scenario method. Secondly, considering the dynamic characteristics of heat and gas networks such as heat network delay, thermal inertia of buildings and gas linepack, the IES model which coordinates the supply side, transmission side and demand side is proposed. Finally, based on the mean-variance Markowitz theory and endowment effect in behavioral psychology, the influence of human psychological preference (such as risk concern and loss aversion) on the IES is reflected. A 52-node electricity-gas-heat IES is used to verify the proposed model. The simulation results reveal that the network dynamic characteristics and demand response (DR) can effectively improve the IES flexibility and wind power accommodation. Meanwhile, the psychological preference and wind power spatial-temporal correlation also have significant influence on the IES optimization.

Fully modified least absolute devotions and fully modified M in estimating regression model with non-stationary explanatory variable and auto correlated random errors

The research is concerned with the adoption of two robust estimation methods: The fully modified least absolute devotions method (FM-LAD) and the fully modified M method (FM-M), in estimating the parameters of regression model with non-stationary explanatory variable and autocorrelated random errors which can be modeled according to one of the mixed models, autoregressive and moving average (ARMA). The research aims to make a comparison between these two methods based on the results of their estimation using simulation experiments prepared for this purpose. The results of the simulation experiment showed the advantage of the fully modified M method over the second method depending on the trade-off criterion mean squared error (MSE).

A three-stage framework for smoky vehicle detection in traffic surveillance videos

The smoky vehicle exhaust pollutes the air and endangers human health. Existing methods detecting smoky vehicles in traffic surveillance videos are with high false alarm rates due to the diversity of smoke characteristics and continuous interferences of common vehicles. To solve this issue, this paper presents a three-stage framework for smoky vehicle detection. In the first stage, a Robust Pixel Based Adaptive Segmenter (R-PBAS) algorithm, which adapts to cameras shaking, is proposed to extract moving objects. The Cumulative Color Histogram (CCH) is adopted to extract smoke-colored blocks from moving objects. In the second stage, three groups of features, including Non-Redundant Robust Local Binary Pattern (NR-RLBP), Weighted Co-occurrence Histograms of Oriented Gradients (W-CoHOG), and Motion Boundary Histograms (MBH) are proposed to extract texture, gradient, and motion information from smoke-colored blocks, respectively. In the third stage, we fuse smoke blocks to obtain Region of Interest (ROI) and extract frequency domain features based on Discrete Wavelet Transform (DWT). To further improve robustness, the Auto-Regressive and Moving Average (ARMA) Model and Hidden Markov Model (HMM) are adopted to model ROIs in consecutive frames. Extensive experiments show that our method performs better than existing methods.

Bridging Terrestrial Water Storage Anomaly During GRACE/GRACE-FO Gap Using SSA Method: A Case Study in China.

The terrestrial water storage anomaly (TWSA) gap between the Gravity Recovery and Climate Experiment (GRACE) and its follow-on mission (GRACE-FO) is now a significant issue for scientific research in high-resolution time-variable gravity fields. This paper proposes the use of singular spectrum analysis (SSA) to predict the TWSA derived from GRACE. We designed a case study in six regions in China (North China Plain (NCP), Southwest China (SWC), Three-River Headwaters Region (TRHR), Tianshan Mountains Region (TSMR), Heihe River Basin (HRB), and Lishui and Wenzhou area (LSWZ)) using GRACE RL06 data from January 2003 to August 2016 for inversion, which were compared with Center for Space Research (CSR), Helmholtz-Centre Potsdam-German Research Centre for Geosciences (GFZ), Jet Propulsion Laboratory (JPL)’s Mascon (Mass Concentration) RL05, and JPL’s Mascon RL06. We evaluated the accuracy of SSA prediction on different temporal scales based on the correlation coefficient (R), Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE), which were compared with that of an auto-regressive and moving average (ARMA) model. The TWSA from September 2016 to May 2019 were predicted using SSA, which was verified using Mascon RL06, the Global Land Data Assimilation System model, and GRACE-FO results. The results show that: (1) TWSA derived from GRACE agreed well with Mascon in most regions, with the highest consistency with Mascon RL06 and (2) prediction accuracy of GRACE in TRHR and SWC was higher. SSA reconstruction improved R, NSE, and RMSE compared with those of ARMA. The R values for predicting TWS in the six regions using the SSA method were 0.34–0.98, which was better than those for ARMA (0.26–0.97), and the RMSE values were 0.03–5.55 cm, which were better than the 2.29–5.11 cm RMSE for ARMA as a whole. (3) The SSA method produced better predictions for obvious periodic and trending characteristics in the TWSA in most regions, whereas the detailed signal could not be effectively predicted. (4) The predicted TWSA from September 2016 to May 2019 were basically consistent with Global Land Data Assimilation System (GLDAS) results, and the predicted TWSA during June 2018 to May 2019 agreed well with GRACE-FO results. The research method in this paper provides a reference for bridging the gap in the TWSA between GRACE and GRACE-FO.