Search Results (141)

Multivariate space–time datasets are often collected at discrete, regularly monitored time intervals and are typically treated as components of time series in environmental science and other applied fields. To effectively characterize such data in geostatistical frameworks, valid and practical covariance models are essential. In this work, we propose several classes of multivariate spatio-temporal covariance matrix functions to model underlying stochastic processes whose discrete temporal margins correspond to well-known autoregressive and moving average (ARMA) models. We derive sufficient and/or necessary conditions under which these functions yield valid covariance matrices. By leveraging established methodologies from time series analysis and spatial statistics, the proposed models are straightforward to identify and fit in practice. Finally, we demonstrate the utility of these multivariate covariance functions through an application to Kansas weather data, using co-kriging for prediction and comparing the results to those obtained from traditional spatio-temporal models. Full article

Accurate precipitation forecasting remains a critical challenge due to the nonlinear and multifactorial nature of rainfall dynamics. This is particularly important in arid regions like Tamanghasset, where precipitation is the primary driver of agricultural viability and water resource management. This study evaluates the performance of several time series models for monthly rainfall prediction, including the autoregressive integrated moving average (ARIMA), Exponential Smoothing State Space Model (ETS), Seasonal and Trend decomposition using Loess with ETS (STL-ETS), Trigonometric Box–Cox transform with ARMA errors, Trend and Seasonal components (TBATS), and neural network autoregressive (NNAR) models. Historical monthly precipitation data from 1953 to 2020 were used to train and test the models, with lagged observations serving as input features. Among the approaches considered, the NNAR model exhibited superior performance, as indicated by uncorrelated residuals and enhanced forecast accuracy. This suggests that NNAR effectively captures the nonlinear temporal patterns inherent in the precipitation series. Based on the best-performing model, rainfall was projected for the year 2021, providing actionable insights for regional hydrological and agricultural planning. The results highlight the relevance of neural network-based time series models for climate forecasting in data-scarce, climate-sensitive regions. Full article

Long-span structures are highly vulnerable to wind-induced vibrations, which can pose a significant threat to their structural stability and safety. This paper introduces a novel monitoring method that combines Permanent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) technology with Auto-Regressive Moving Average (ARMA) models, providing an innovative approach to monitoring wind-induced vibrations in large-span bridges. While previous studies have focused on individual techniques, this integrated approach is largely unexplored and offers a new perspective for structural health monitoring. By collating a series of SAR images and examining phase alterations on the bridge surface, a three-tiered detection methodology is employed to identify stable points accurately. The surface deformation data are then analyzed alongside wind speed and weather data to construct a comprehensive model elucidating the relationship between the bridge and vibrations. The ARMA model is used for real-time monitoring and assessment. Experimental results demonstrate that this method offers precise, real-time monitoring of wind-resistant stability. By leveraging the spatial accuracy and long-term monitoring capability of PS-InSAR, along with the time-series forecasting strength of ARMA models, the method enables data-driven analysis of bridge vibrations. It also provides comprehensive coverage under various conditions, enhancing the safety of long-span bridges through advanced predictive analytics. Full article

Background/Objectives: The implementation of artificial intelligence-based systems for disease detection using biomedical signals is challenging due to the limited availability of training data. This paper deals with the generation of synthetic EEG signals using deep learning-based models, to be used in future research for training Parkinson’s disease detection systems. Methods: Linear models, such as AR, MA, and ARMA, are often inadequate due to the inherent non-linearity of time series. To overcome this drawback, long short-term memory (LSTM) networks are proposed to learn long-term dependencies in non-linear EEG time series and subsequently generate synthetic signals to enhance the training of detection systems. To learn the forward and backward time dependencies in the EEG signals, a Bidirectional LSTM model has been implemented. The LSTM model was trained on the UC San Diego Resting State EEG Dataset, which includes samples from two groups: individuals with Parkinson’s disease and a healthy control group. Results: To determine the optimal number of cells in the model, we evaluated the mean squared error (MSE) and cross-correlation between the original and synthetic signals. This method was also applied to select the length of the hidden state vector. The number of hidden cells was set to 14, and the length of the hidden state vector for each cell was fixed at 4. Increasing these values did not improve MSE or cross-correlation and unnecessarily increased computational complexity. The proposed model’s performance was evaluated using the mean-squared error (MSE), Pearson’s correlation coefficient, and the power spectra of the synthetic and original signals, demonstrating the suitability of the proposed method for this application. Conclusions: The proposed model was compared to Autoregressive Moving Average (ARMA) models, demonstrating superior performance. This confirms that deep learning-based models, such as LSTM, are strong alternatives to statistical models like ARMA for handling non-linear, multifrequency, and non-stationary signals. Full article

This paper proposes an enhanced vibration-based damage detection index leveraging autoregressive moving average (ARMA) time-series modeling. The method relies on the fact that material deterioration alters the vibration features of the structure. Thus, the proposed method employs an innovative usage of the ARMA time-series modeling to capture subtle shifts in the vibration response. Specifically, first, a reference ARMA model is fitted on the acceleration response of the undamaged structure. Next, a damage index (DI) is built from the goodness of fit between predicted responses from the reference ARMA model and the actual measured damaged-state acceleration data. Experimental validation was conducted on a steel beam subjected to a controlled accelerated corrosion (up to 40% thickness loss), simulating real-world degradation. Accelerations due to quick-release tests were collected using two accelerometers, along with thickness measurements providing ground-truth damage progression. Results demonstrate that the proposed method can provide sufficient sensitivity in detecting early-stage corrosion progression. This finding highlights the proposed usage of ARMA model’s potential for early structural damage detection, offering significant advantages for safety and maintenance strategies in civil engineering applications. Full article

There is now a vast body of literature on ARMA and VARMA models with time-dependent or time-varying coefficients. A large part of it is based on local stationary processes using time rescaling and assumptions of regularity with respect to time. A recent paper has presented an alternative asymptotic theory for the parameter estimators based on several distinct assumptions that seem difficult to verify at first look, especially for time-dependent VARMA or tdVARMA models. The purpose of the present paper is to detail several examples that illustrate the verification of the assumptions in that theory. These assumptions bear on the moments of the errors, the existence of the information matrix, but also how the coefficients of the pure moving average representation of the derivatives of the residuals (with respect to the parameters and evaluated at their true value) behave. We will do that analytically for two bivariate first-order models, an autoregressive model, and a moving average model, before sketching a generalization to higher-order models. We also show simulation results for these two models illustrating the analytical results. As a consequence, not only the assumptions can be checked but the simulations show how well the small sample behavior of the estimators agrees with the theory. Full article

Financial assets often exhibit explosive price surges followed by abrupt collapses, alongside persistent volatility clustering. Motivated by these features, we introduce a mixed causal–noncausal invertible–noninvertible autoregressive moving average generalized autoregressive conditional heteroskedasticity (MARMA–GARCH) model. Unlike standard ARMA processes, our model admits roots inside the unit disk, capturing bubble-like episodes and speculative feedback, while the GARCH component explains time-varying volatility. We propose two estimation approaches: (i) Whittle-based frequency-domain methods, which are asymptotically equivalent to Gaussian likelihood under stationarity and finite variance, and (ii) time-domain maximum likelihood, which proves to be more robust to heavy tails and skewness—common in financial returns. To identify causal vs. noncausal structures, we develop a higher-order diagnostics procedure using spectral densities and residual-based tests. Simulation results reveal that overlooking noncausality biases GARCH parameters, downplaying short-run volatility reactions to news ($\alpha$) while overstating volatility persistence ($\beta$). Our empirical application to Bitcoin and Ethereum enhances these insights: we find significant noncausal dynamics in the mean, paired with pronounced GARCH effects in the variance. Imposing a purely causal ARMA specification leads to systematically misspecified volatility estimates, potentially underestimating market risks. Our results emphasize the importance of relaxing the usual causality and invertibility assumption for assets prone to extreme price movements, ultimately improving risk metrics and expanding our understanding of financial market dynamics. Full article

The forward kinematics of the Stewart platform is crucial for precise control and reliable operation in six-degree-of-freedom motion. However, there are some shortcomings in practical applications, such as calculation precision, computational efficiency, the capacity to resolve singular Jacobian matrix and real-time predictive performance. To overcome those deficiencies, this work proposes a hybrid strategy for forward kinematics in the Stewart platform based on dual quaternion neural network and ARMA time series prediction. This method initially employs a dual-quaternion-based back-propagation neural network (DQ-BPNN). The DQ-BPNN is partitioned into real and dual parts, composed of parameters such as driving-rod lengths, maximum and minimum lengths, to extract more features. In DQ-BPNN, a residual network (ResNet) is employed, endowing DQ-BPNN with the capacity to capture deeper-level system characteristics and enabling DQ-BPNN to achieve a better fitting effect. Furthermore, the combined modified multi-step-size factor Newton downhill method and the Newton–Raphson method (C-MSFND-NR) are employed. This combination not only enhances computational efficiency and ensures global convergence, but also endows the method with the capability to resolve a singular matrix. Finally, a traversal method is adopted to determine the order of the autoregressive moving average (ARMA) model according to the Bayesian information criterion (BIC). This approach efficiently balances computational efficiency and fitting accuracy during real-time motion. The simulations and experiments demonstrate that, compared with BPNN, the R² value in DQ-BPNN increases by 0.1%. Meanwhile, the MAE, MAPE, RMSE, and MSE values in DQ-BPNN decrease by 8.89%, 21.85%, 6.90%, and 3.3%, respectively. Compared with five Newtonian methods, the average computing time of C-MSFND-NR decreases by 59.82%, 83.81%, 15.09%, 79.82%, and 78.77%. Compared with the linear method, the prediction accuracy of the ARMA method increases by 14.63%, 14.63%, 14.63%, 14.46%, 16.67%, and 13.41%, respectively. Full article

As climate change has become of eminent importance in the last two decades, so has interest in industry-wide carbon emissions and policies promoting a low-carbon economy. Investors and policymakers could improve their decision-making by producing accurate forecasts of relevant green finance market indices: carbon efficiency, clean energy, and sustainability. The purpose of this paper is to compare the performance of single-step univariate forecasts produced by a set of selected statistical and regression-tree-based predictive models, using large datasets of over 2500 daily records of green market indices gathered in a ten-year timespan. The statistical models include simple exponential smoothing, Holt’s method, the ETS version of the exponential model, linear regression, weighted moving average, and autoregressive moving average (ARMA). In addition, the decision tree-based machine learning (ML) methods include the standard regression trees and two ensemble methods, namely the random forests and extreme gradient boosting (XGBoost). The forecasting results show that (i) exponential smoothing models achieve the best performance, and (ii) ensemble methods, namely XGBoost and random forests, perform better than the standard regression trees. The findings of this study will be valuable to both policymakers and investors. Policymakers can leverage these predictive models to design balanced policy interventions that support environmentally sustainable businesses while fostering continued economic growth. In parallel, investors and traders will benefit from an ease of adaptability to rapid market changes thanks to the computationally cost-effective model attributes found in this study to generate profits. Full article

This study examined the impact of location differentials (LDs) on soybean futures trading in South Africa. This study uses a systematic approach, employing the Autoregressive Moving Average (ARMA) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models to analyze relationships between soybean futures prices and LDs. The results suggest that LDs have caused price stabilization for most of the contract months, while the variability and occasional extremes in the spot price increased. Post-LD analysis showed that the volatility was lower, with a normalization of price structures, but, still, regional disparities were driven by transport costs and logistical issues. LDs also affected silo utilization, and the rates of re-delivery differed among regions, reflecting local market dynamics and operational efficiencies. This, in essence, suggests that LDs act to enhance the predictability of markets and price harmonization; LDs also equally require concerted interventions in regional disparities and optimization of market performances. Future studies need to determine the impact that LDs, over a long period, have on market efficiency, regional trade, and general economy-wide indicators like farmers’ incomes and rural development. Full article

The identification of the orders of time series models plays a crucial role in their accurate specification and forecasting. The Autocorrelation Function (ACF) is commonly used to identify the order q of Moving Average (MA(q)) models, as it theoretically vanishes for lags beyond q. This property is widely used in model selection, assuming the sample ACF follows an asymptotic normal distribution for robustness. However, our examination of the sum of the sample ACF reveals inconsistencies with these theoretical properties, highlighting a deviation from normality in the sample ACF for MA(q) processes. As a natural extension of the ACF, the Extended Autocorrelation Function (EACF) provides additional insights by facilitating the simultaneous identification of both autoregressive and moving average components. Using simulations, we evaluate the performance of q-order identification in MA(q) models, which is based on the properties of ACF. Similarly, for ARMA($p,q$) models, we assess the ($p,q$)-order identification relying on EACF. Our findings indicate that both methods are effective for sufficiently long time series but may incorrectly favor an ARMA($p,q-1$) model when the $a_q$ coefficient approaches zero. Additionally, if the cumulative sums of ACF (SACF) behave consistently and the Ljung–Box test validates the proposed model, it can serve as a strong candidate. The proposed models should then be compared based on their predictive performance. We illustrate our methodology with an application to wind speed data and sea surface temperature anomalies, providing practical insights into the relevance of our findings. Full article

The rates of continuous evolution plays a crucial role in understanding the pace at which species evolve. Various statistical models have been developed to estimate the rates of continuous trait evolution for a group of related species evolving along a phylogenetic tree. Existing models often assume the independence of the rate parameters; however, this assumption may not account for scenarios where the rate of continuous trait evolution correlates with its evolutionary history. We propose using the autoregressive–moving-average (ARMA) model for modeling the rate of continuous trait evolution along the tree, hypothesizing that rates between two successive generations (ancestor–descendant) are time-dependent and correlated along the tree. We denote PhyRateARMA$(p,q)$ as a phylogenetic rate-of-continuous-trait-evolution ARMA(p,q) model in our framework. Our algorithm begins by utilizing the tree and trait data to estimate the rates on each branch, followed by implementing the ARMA process to infer the relationships between successive rates. We apply our innovation to analyze the primate body mass dataset and plant genome size dataset and test for the autoregressive effect of the rates of continuous evolution along the tree. Full article

In this work, we introduce an extension of the so-called beta autoregressive moving average ($\beta$ARMA) models. $\beta$ARMA models consider a linear dynamic structure for the conditional mean of a beta distributed variable. The conditional mean is connected to the linear predictor via a suitable link function. We propose modeling the relationship between the conditional mean and the linear predictor by means of the asymmetric Aranda-Ordaz parametric link function. The link function contains a parameter estimated along with the other parameters via partial maximum likelihood. We derive the partial score vector and Fisher’s information matrix and consider hypothesis testing, diagnostic analysis, and forecasting for the proposed model. The finite sample performance of the partial maximum likelihood estimation is studied through a Monte Carlo simulation study. An application to the proportion of stocked hydroelectric energy in the south of Brazil is presented. Full article

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. Full article

Accurate water quality prediction is the basis for good water environment management and sustainable use of water resources. As an important time series forecasting model, the Autoregressive Moving Average Model (ARMA) plays a crucial role in environmental management and sustainability research. This study addresses the factors that affect the ARMA model’s forecast accuracy and goodness of fit. The research results show that the sample size used for model parameters estimation is the main influencing factor for the goodness of fit of an ARMA model, and the prediction time is the main factor affecting the prediction error of the model. Constructing a stable and reliable ARMA model requires a certain number of samples for the estimation of model parameters. However, using an excessive number of samples will not further improve the ARMA model’s goodness of fit but rather increase the workload and difficulty of data collection. The ARMA model is not suitable for long-term forecasting because the prediction error of ARMA models increases with the increase of prediction time, and when the prediction time exceeds a certain limit, the fitted values of an ARMA model will almost no longer change with the time, which means the model has lost its significance of prediction. For time series with periodic components, introducing periodic adjustment factors into the ARMA model can reduce the prediction error. These findings enable environmental managers and researchers to apply the ARMA model more rationally, hence developing more precise pollution control and sustainable development plans. Full article