Autoregressive Moving Average Research Articles

Application of time series and multivariate statistical models for water quality assessment and pollution source apportionment in an Urban River, New Jersey, USA.

Water quality monitoring reveals changing trends in the environmental condition of aquatic systems, elucidates the prevailing factors impacting a water body, and facilitates science-backed policymaking. A 2020 hiatus in water quality data tracking in the Lower Passaic River (LPR), New Jersey, has created a 5-year information gap. To gain insight into the LPR water quality status during this lag period and ahead, water quality indices computed with 16-year historical data available for 12 physical, chemical, nutrient, and microbiological parameters were used to predict water quality between 2020 and 2025 using seasonal autoregressive moving average (ARIMA) models. Average water quality ranged from good to very poor (34 ≤ µWQI ≤ 95), with noticeable spatial and seasonal variations detected in the historical and predicted data. Pollution source tracking with the positive matrix factorization (PMF) model yielded significant R2 values (0.9 < R2 ≤ 1) for the input parameters and revealed four major LPR pollution factors, i.e., combined sewer systems, surface runoff, tide-influenced sediment resuspension, and industrial wastewater with pollution contribution rates of 23-30.2% in the upstream and downstream study areas. Significant correlation of toxic metals, nutrients, and sewage indicators suggest similarities in their sources.

Tire wear monitoring using feature fusion and CatBoost classifier

Addressing the critical issue of tire wear is essential for enhancing vehicle safety, performance, and maintenance. Worn-out tires often lead to accidents, underscoring the need for effective monitoring systems. This study is vital for several reasons: safety, as worn tires increase the risk of accidents due to reduced traction and longer braking distances; performance, as uneven tire wear affects vehicle handling and fuel efficiency; maintenance costs, as early detection can prevent more severe damage to suspension and alignment systems; and regulatory compliance, as ensuring tire integrity helps meet safety regulations imposed by transportation authorities. In response, this study systematically evaluates tire conditions at 25%, 50%, 75%, and 100% wear, with an intact tire as a reference, using vibration signals as the primary data source. The analysis employs statistical, histogram, and autoregressive–moving-average (ARMA) feature extraction techniques, followed by feature selection to identify key parameters influencing tire wear. CatBoost is used for feature classification, leveraging its adaptability and efficiency in distinguishing varying wear patterns. Additionally, the study incorporates feature fusion to combine different types of features for a more comprehensive analysis. The proposed methodology not only offers a robust framework for accurately classifying tire wear levels but also holds significant potential for real-time implementation, contributing to proactive maintenance practices, prolonged tire lifespan, and overall vehicular safety.

Prepivoted Augmented Dickey-Fuller Test with Bootstrap-Assisted Lag Length Selection

We investigate the application of prepivoting in conjunction with lag length selection to correct the size and power performance of the Augmented Dickey-Fuller test for a unit root. The bootstrap methodology used to perform the prepivoting is a residual based AR bootstrap that ensures that bootstrap replicate time series are created under the null irrespective of whether the originally observed series obeys the null hypothesis or not. Simulation studies wherein we examine the performance of our proposed method are given; we evaluate our method’s performance on ARMA(1,1) models with varying configurations for size and power performance. We also propose a novel data dependent lag selection technique that uses bootstrap data under the null to select an optimal lag length; the performance of our method is compared to existing lag length selection criteria.

A neural network-based ARMA model for fuzzy time series data

A neural network-based ARMA model for fuzzy time series data

Hybrid WARIMA-WANN algorithm for data prediction in bridge health monitoring system

Application of data-driven algorithm to model and predict the future trend of the structural health monitoring (SHM) data serves as important references for the future safety evaluation and decision-making of the bridges. An innovative hybrid WARIMA-WANN algorithm combining the Wavelet model, the autoregressive moving average (ARIMA) model and the artificial neural network (ANN) model is proposed to predict massive monitoring data in the bridge SHM system. The WPT serves as the decomposition function for the linear and nonlinear components of the hybrid model. The separated linear/nonlinear components are individually predicted with the ARIMA/ANN models and then combined to obtain the prediction values of the future data. The hybrid method is applied to predict the deflection values of a single-tower cable-stayed bridge. Multiple parameters in individual models are discussed and selected to increase the credibility of the prediction results for the example bridge. The results show that the proposed hybrid algorithm successfully captures the linear and nonlinear coupling relationships inside the SHM data from the frequency perspective of view and shows the best prediction performance when compared with the other four existing models. Different prediction steps obviously influence prediction performance due to the periodic nature of the bridge SHM data.

Characterizing nonlinear, nonstationary, and heterogeneous hydrologic behavior using ensemble rainfall–runoff analysis (ERRA): proof of concept

Abstract. A classical approach to understanding hydrological behavior is the unit hydrograph and its many variants, but these often assume linearity (runoff response is proportional to effective precipitation), stationarity (runoff response to a given unit of rainfall is identical, regardless of when it falls), and spatial homogeneity (runoff response depends only on spatially averaged precipitation). In the real world, by contrast, runoff response is typically nonlinear, nonstationary, and spatially heterogeneous. Quantifying this nonlinearity, nonstationarity, and spatial heterogeneity is essential to unraveling the mechanisms and subsurface properties controlling hydrological behavior. Here, I present proof-of-concept demonstrations illustrating how nonlinear, nonstationary, and spatially heterogeneous rainfall–runoff behavior can be quantified, directly from data, using ensemble rainfall–runoff analysis (ERRA), a data-driven, model-independent method for quantifying rainfall–runoff relationships across a spectrum of time lags. I show how ERRA uses nonlinear deconvolution to quantify how catchments' runoff responses vary with precipitation intensity and to estimate their precipitation-weighted runoff response distributions. I further illustrate how ERRA combines nonlinear deconvolution with de-mixing techniques to reveal how runoff response depends jointly on precipitation intensity and nonstationary ambient conditions, including antecedent wetness and vapor pressure deficit. I demonstrate how ERRA's de-mixing techniques can be used to quantify spatially heterogeneous runoff responses in different parts of a catchment, even if those subcatchments are not separately gauged. I also illustrate how ERRA's broken-stick deconvolution capabilities can be used to quantify multiscale runoff responses that combine hydrograph peaks lasting for hours and recessions lasting for weeks, well beyond the average spacing between storms. ERRA can unscramble these multiple effects on runoff response even if they are overprinted on each other through time and even if they are corrupted by autoregressive moving average (ARMA) noise. Results from this approach may be informative for catchment characterization, process understanding, and model–data comparisons; they may also lead to a better understanding of storage dynamics and landscape-scale connectivity. An R script is provided to perform the necessary calculations, including uncertainty analysis.

Robust estimation for Threshold Autoregressive Moving-Average models

Threshold autoregressive moving-average (TARMA) models extend the popular TAR model and are among the few parametric time series specifications to include a moving average in a non-linear setting. The state dependent reactions to shocks is particularly appealing in Economics and Finance. However, no theory is currently available when the data present heavy tails or anomalous observations. Here we provide the first theoretical framework for robust M-estimation for TARMA models and study its practical relevance. Under mild conditions, we show that the robust estimator for the threshold parameter is super-consistent, while the estimators for autoregressive and moving-average parameters are strongly consistent and asymptotically normal. The Monte Carlo study shows that the M-estimator is superior, in terms of both bias and variance, to the least squares estimator, which can be heavily affected by outliers. The findings suggest that robust M-estimation should be generally preferred to the least squares method. We apply our methodology to a set of commodity price time series; the robust TARMA fit presents smaller standard errors and superior forecasting accuracy. The results support the hypothesis of a two-regime non-linearity characterised by slow expansions and fast contractions.

Forecasting the Volatility of Tuna Fish Prices in North Sumatra using the ARCH Method in the Period January - April 2024

Tuna (Euthynnus affinis) is one of the most important fisheries commodities in Indonesia with significant economic value, especially in its contribution to fisheries export revenue. However, the price of tuna experiences significant fluctuations that can affect local and national economic stability. This study analyzes the daily price fluctuations of tuna in the North Sumatra market from January 1, 2024 to April 29, 2024 using a time series analysis approach. Daily price data were collected and analyzed to identify existing price patterns and volatility. The Autoregressive Conditional Heteroskedasticity (ARCH) model was selected to address the heteroscedasticity in the data, which suggests that the volatility of tuna prices can be well predicted based on past price behavior. The analysis steps include identifying the optimal ARCH model using the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF), as well as testing parameter significance and normality assumptions to validate the model fit. The results show that the ARMA (1,0,0) model is the optimal one to model the price volatility of yellow tuna with the MAPE obtained of 2.382. compared to the ARMA-ARCH method with the MAPE value obtained of 2,747. Because it still contains heteroskedasticity effects, even though the results are good, the prediction results do not closely match the original data. The model is effective in improving price forecasting accuracy, which is important to support decision-making in risk management and economic planning in the fisheries sector. The findings contribute to understanding the dynamics of the yellowtail market and optimizing strategies for fisheries management.

Unveiling the Significance of Individual Level Predictions: A Comparative Analysis of GRU and LSTM Models for Enhanced Digital Behavior Prediction

The widespread use of technology has led to a transformation of human behaviors and habits into the digital space; and generating extensive data plays a crucial role when coupled with forecasting techniques in guiding marketing decision-makers and shaping strategic choices. Traditional methods like autoregressive moving average (ARMA) can-not be used at predicting individual behaviors because we can-not create models for each individual and buy till you die (BTYD) models have limitations in capturing the trends accurately. Recognizing the paramount importance of individual-level predictions, this study proposes a deep learning framework, specifically uses gated recurrent unit (GRU), for enhanced behavior analysis. This article discusses the performance of GRU and long short-term memory (LSTM) models in this framework for forecasting future individual behaviors and presenting a comparative analysis against benchmark BTYD models. GRU and LSTM yielded the best results in capturing the trends, with GRU demonstrating a slightly superior performance compared to LSTM. However, there is still significant room for improvement at the individual level. The findings not only demonstrate the performance of GRU and LSTM models but also provide valuable insights into the potential of new techniques or approaches for understanding and predicting individual behaviors.

The impact of new VAT enforcement on financial performance: Evidence from Saudi Arabia non-financial listed companies using the event study and ARMA model

This paper examines the influence of the new 15 % Value Added Tax (VAT) enforcement on non-financial listed companies in Saudi Arabia. By comparing financial data from 2019, before the VAT implementation and the COVID-19 pandemic, with data from 2020, during both the VAT increase and the pandemic, the research aims to uncover the consequences of this tax policy change. Utilizing charts, tables, and an event study analysis approach with the Autoregressive Moving Average (ARMA) model, we investigated key financial indicators such as Shareholders' Equity (SE), Total Income (TI), Total Revenues (TR), Net Income (NI), Total Expenses (TE), Other Changes in Operating Activity (COA), and Cash at the End of the Period (CEP). The findings reveal significant financial impacts, highlighting companies' challenges due to the increased tax burden. Shareholders' Equity dropped from an average of 11.55 million to 4.57 million, and Total Income and Total Revenues decreased from approximately 1.73 million to 316,234 and from 1.95 million to 331,605, respectively. Net Income sharply declined from 406,109 to 74,624, and Total Expenses decreased from about 1.18 million to 223,495. Other Changes in Operating Activity shifted from a negative mean of −168,936 to a positive 523,520, and Cash at the End of the Period fell from 1.99 million to 666,663. These results suggest that the VAT increase has significantly strained companies' financial performance, emphasizing the need to consider such tax reforms carefully, particularly in developing countries. The study concludes that while the VAT increase aims to enhance government revenues, it imposes substantial financial strain on companies, potentially leading to long-term economic repercussions. Policymakers should consider these implications and implement practical measures to optimize the VAT system and support business resilience in the face of such reforms.

Calibration of Arctic ice core bromine enrichment records for past sea ice reconstructions

Bromine in ice cores has been proposed as a qualitative sea ice proxy to produce sea ice reconstructions for the polar regions. Here we report the first statistical validation of this proxy with satellite sea ice observations by combining bromine enrichment (with respect to seawater, Brenr) records from three Greenlandic ice cores (SIGMA-A, NU and RECAP) with satellite sea ice imagery, over three decades. We find that during the 1984–2016 satellite-era, ice core Brenr values are significantly correlated with first-year sea ice formed in the Baffin Bay and Labrador Sea supporting that the gas-phase bromine enrichment processes, preferentially occurring over the sea ice surface, are the main driver for the Brenr signal in ice cores. Moreover, in assessing Brenr's capability to record historical sea ice variability, we compare 20th-century Arctic Sea ice historical and proxy records with our reconstructions, based on an autoregressive–moving-average (ARMA) model, finding overall good agreement. While further enhancements are warranted, including site-specific calibrations and a comprehensive investigation into bromine transport-related concerns, this study presents a new method to quantitatively reconstruct past seasonal sea ice variability through bromine enrichment in ice cores.

Modelling and forecasting mobile money customer transaction volumes in rural and semi-urban Malawi: An autoregressive integrated moving average spatial decomposition

Mobile money technologies in Malawi have revolutionised banking and monetary transactions across geographical barriers. Prospects of profit have drawn mobile money agents to invest in the business but find it is more profitable when substantial customers subscribe to the cash-in and cash-out facilities of mobile money. Despite the initial success, several challenges have emerged, including regulatory hurdles, network reliability issues, and the need for increased financial literacy among users. The volumes of transactions in the rural areas are observably lower compared to urban areas. This study uses Bvumbwe township in Malawi to model and forecast the discrepancy of mobile money transactions in rural and semi-urban Malawi. The study uses ARIMA modelling to understand the temporal manifestation of mobile money subscription in these localities. Using ARMA (1,1) models decomposed for the semi-urban and rural area, the study finds that the semi-urban area has a disproportionately higher and lasting volume of mobile money transactions compared to the rural area. The study also finds that mobile money transactions are more susceptible to long-lasting effects of external shocks in the rural area compared to the urban area. Intuitively, the day-to-day relationship in the transactions is also stronger in the rural area. These findings highlight the need for tailored policy interventions to enhance mobile money adoption and utilization in different geographical contexts.

Effect of electricity policy uncertainty and carbon emission prices on electricity demand in China based on mixed-frequency data models

This paper first constructs the electricity policy uncertainty (EPU) in China with textual methods and analyses the effect of the EPU and carbon emission prices (CEPs) on the total electricity demand. This paper also forecasts the demand for electricity in China with three mixed-frequency data models. The results show that the EPU index efficiently captures the uncertainty of China's electricity policy. The effects of EPU and CEPs on electricity demand are significant, and incorporating them into the forecasting model will improve the accuracy and timeliness. Moreover, compared with the ARMA model and LSTM neural networks, mixed-frequency data models perform better in electricity demand forecasting.

Two improved generalized extended stochastic gradient algorithms for CARARMA systems

The paper innovatively proposes two improved generalized extended stochastic gradient (GESG) algorithms for the controlled autoregressive autoregressive moving average (CARARMA) system with autoregressive moving average (ARMA) model noise. Firstly, we propose a latest estimation based weighted generalized extended stochastic gradient (LE-WGESG) algorithm, which introduces multiple momentary corrections in the traditional parameter estimation process. By carefully adjusting the weighting coefficients of the correction quantities at different moments, the algorithm has a rapid and greater efficient convergence property. More importantly, utilizing the theory of moving data window, this paper also proposes a multi-innovation based latest estimated weighted generalized extended stochastic gradient (MI-LE-WGESG) algorithm, which can better capture the interactions among multiple correction terms and further improve the predictive ability of the model.

Research on Temperature Prediction based on BP Neural Network Approach

Weather changes have an important impact on human production and life as well as socio-economic activities. In recent years, people have also gradually paid attention to the study of weather, especially the study of temperature, and it is of great practical significance to find an accurate temperature prediction model. At the same time, the use of machine learning methods to construct a temperature model can predict temperature changes more accurately and quickly, and provide a more reliable basis for weather forecasting. Therefore, in response to the unsatisfactory accuracy of temperature prediction by traditional prediction models, this paper uses the time series of daily average temperature of Hangzhou City, China, from 2013 to 2022 as the sample data, and combines the traditional ARMA model with the BP neural network model, which enables the BP neural network model to better fit and predict the temperature changes. The study shows that the prediction accuracy of the BP neural network model is significantly improved compared with the ARMA model.

Unveiling change-point detection with ARMA-GARCH models

This paper delves into the asymptotic theory of a Cumulative Sum (CUSUM)-type test designed for detecting change points in the variance of AutoRegressive Moving-Average models, incorporating Generalized Autoregressive Conditional Heteroscedasticity innovations. We demonstrate that, under the null hypothesis (no change), the CUSUM test statistic converges to the supremum of a standard Brownian bridge. Using a Monte Carlo simulation, we highlight the strong performance of our proposed test when compared to the methods by Song and Kang. Furthermore, we provide a real-world data analysis to showcase the practical application of our test.

Prevalence and association with environmental factors and establishment of prediction model of atopic dermatitis in pet dogs in China.

Canine atopic dermatitis (CAD) is a common skin disease in dogs. Various pathogenic factors contribute to CAD, with dust mites, environmental pathogens, and other substances being predominant. This research involved comprehensive statistical analysis and prediction of CAD in China, using data from 14 cities. A distributed lag nonlinear model (DLNM) was developed to evaluate the impact of environmental factors on CAD incidence. Additionally, a seasonal auto-regressive moving average (ARIMA) model was used to forecast the monthly number of CAD cases. The findings indicated that CAD mainly occurs during June, July, August, and September in China. There was a positive correlation found between CAD incidence and temperature and humidity, while a negative correlation was observed with CO, PM2.5, and other pollutants.

Research on Pricing and Dynamic Replenishment Planning Strategies for Perishable Vegetables Based on the RF-GWO Model

This paper addresses the challenges of automated pricing and replenishment strategies for perishable products with time-varying deterioration rates, aiming to assist wholesalers and retailers in optimizing their production, transportation, and sales processes to meet market demand while minimizing inventory backlog and losses. The study utilizes an improved convolutional neural network–long short-term memory (CNN-LSTM) hybrid model, autoregressive moving average (ARIMA) model, and random forest–grey wolf optimization (RF-GWO) algorithm. Using fresh vegetables as an example, the cost relationship is analyzed through linear regression, sales volume is predicted using the LSTM recurrent neural network, and pricing is forecasted with a time series analysis. The RF-GWO algorithm is then employed to solve the profit maximization problem, identifying the optimal replenishment quantity, type, and most effective pricing strategy, which involves dynamically adjusting prices based on predicted sales and market conditions. The experimental results indicate a 5.4% reduction in inventory losses and a 6.15% increase in sales profits, confirming the model’s effectiveness. The proposed mathematical model offers a novel approach to automated pricing and replenishment in managing perishable goods, providing valuable insights for dynamic inventory control and profit optimization.

Non‐causal and non‐invertible ARMA models: Identification, estimation and application in equity portfolios

The mixed causal‐non‐causal invertible‐non‐invertible autoregressive moving‐average (MARMA) models have the advantage of incorporating roots inside the unit circle, thus adjusting the dynamics of financial returns that depend on future expectations. This article introduces new techniques for estimating, identifying and simulating MARMA models. Although the estimation of the parameters is done using second‐order moments, the identification relies on the existence of high‐order dynamics, captured in the high‐order spectral densities and the correlation of the squared residuals. A comprehensive Monte Carlo study demonstrated the robust performance of our estimation and identification methods. We propose an empirical application to 24 portfolios from emerging markets based on the factors: size, book‐to‐market, profitability, investment and momentum. All portfolios exhibited forward‐looking behavior, showing significant non‐causal and non‐invertible dynamics. Moreover, we found the residuals to be uncorrelated and independent, with no trace of conditional volatility.

Prediction of air compressor faults with feature fusion and machine learning

Air compressors are critical for many industries, but early detection of faults is crucial for keeping them running smoothly and minimizing maintenance costs. This contribution investigates the use of predictive machine learning models and feature fusion to diagnose faults in single-acting, single-stage reciprocating air compressors. Vibration signals acquired under healthy and different faulty conditions (inlet valve fluttering, outlet valve fluttering, inlet-outlet valve fluttering, and check valve fault) serve as the study’s input data. Diverse features including statistical attributes, histogram data, and auto-regressive moving average (ARMA) coefficients are extracted from the vibration signals. To identify the most relevant features, the J48 decision tree algorithm is employed. Five lazy classifiers viz. k-nearest neighbor (kNN), K-star, local kNN, locally weighted learning (LWL), and random subspace ensemble K-nearest neighbors (RseslibKnn) are then used for fault classification, each applied to the individual feature sets. The classifiers achieve commendable accuracy, ranging from 85.33% (K-star and local kNN) to 96.00% (RseslibKnn) for individual features. However, the true innovation lies in feature fusion. Combining the three feature types, statistical, histogram, and ARMA, significantly improves accuracy. When local kNN is used with fused features, the model achieves a remarkable 100% classification accuracy, demonstrating the effectiveness of this approach for reliable fault diagnosis in air compressors.