Stationary Time Series Models Research Articles

Assessment of suspended sediment export and dynamics using in‐line turbidity sensors and time series statistical models

Assessment of suspended sediment export and dynamics using in‐line turbidity sensors and time series statistical models

Spatiotemporal variations of precipitation patterns in the middle and lower reaches of Yangtze River Basin

Context With escalating global climate change, regional flood disasters have become increasingly prevalent. Precipitation, as a primary influencing factor, has garnered significant attention. Aims This study is based on precipitation data to investigate the spatiotemporal characteristics of precipitation in the middle and lower reaches of Yangtze River Basin (MLYB), trying to explore more concise methods for precipitation forecasting. Methods Statistical methods were employed to analyse historical precipitation patterns, followed by forecasting future trends using statistical time series models. Key results Precipitation in the MLYB exhibited a decreasing trend during 1961–2010, which shifted to an increasing trend after 2011, becoming more pronounced since 2017. Precipitation patterns in the MLYB were clearly increasing in the east and decreasing in the west, with the Taihu Basin showing the greatest rise. The ARIMA model predicted a significant increase in precipitation after 2022. Conclusions In recent years, precipitation in the MLYB has significantly increased, especially in downstream areas. Although the ARIMA model offers an effective and reasonably simple method for short-term forecast, it struggles with complex terrain influences. Implications These findings provide a theoretical basis for flood prevention in the MLYB, as well as a reference for precipitation prediction simulations in data-limited regions.

Investigating Permselectivity in PVDF Mixed Matrix Membranes Using Experimental Optimization, Machine Learning Segmentation, and Statistical Forecasting.

This research examines the correlation between interfacial characteristics and membrane distillation (MD) performance of copper oxide (Cu) nanoparticle-decorated electrospun carbon nanofibers (CNFs) polyvinylidene fluoride (PVDF) mixed matrix membranes. The membranes were fabricated by a bottom-up phase inversion method to incorporate a range of concentrations of CNF and Cu + CNF particles in the polymer matrix to tune the porosity, crystallinity, and wettability of the membranes. The resultant membranes were tested for their application in desalination by comparing the water vapor transport and salt rejection rates in the presence of Cu and CNF. Our results demonstrated a 64% increase in water vapor flux and a salt rejection rate of over 99.8% with just 1 wt % loading of Cu + CNF in the PVDF matrix. This was attributed to enhanced chemical heterogeneity, porosity, hydrophobicity, and crystallinity that was confirmed by electron microscopy, tensiometry, and scattering techniques. A machine learning segmentation model was trained on electron microscopy images to obtain the spatial distribution of pores in the membrane. An Autoregressive Integrated Moving Average with Explanatory Variable (ARIMAX) statistical time series model was trained on MD experimental data obtained for various membranes to forecast the membrane performance over an extended duration.

Precision in Insurance Forecasting: Enhancing Potential with Ensemble and Combination Models based on the Adaptive Neuro-Fuzzy Inference System in the Egyptian Insurance Industry

ABSTRACT Enhancing the precision of retention ratio predictions holds profound significance for insurance industry decision-makers and those vested in advancing insurance services. Precision helps insurance companies navigate inflationary pressures and evaluate underwriting profitability, enabling reliable prognoses of future underwriting gains. As far as we know, although there have been multiple attempts to construct a predictive model for retention ratio, none of these attempts have used combining models or studied the Egyptian market. Therefore, this study contributes significantly to this developing field by providing combining models, which combined statistical time series models such as Exponential Smoothing (ES), and Autoregressive Integrated Moving Average (ARIMA), with Adaptive Neuro-Fuzzy Inference System (ANFIS). Two different types of combinations are employed with these models. Furthermore, the study introduces three ensemble models designed for the purpose of predicting the retention ratio within the Egyptian insurance market. Dataset was carefully gathered from the EFSA’s annual reports, focused on the property-liability insurance sector within the Egyptian insurance market and covers the time period from 1989 to 2021. Next, the proposed models are assessed employing well-established statistical assessment metrics, namely, Mean Absolute Error (MAE), Mean Absolute Percent Error (MAPE), R Square (R2), and Root Mean Square Error (RMSE). The results show that combining and ensemble methods improve predicted accuracy. A multi-linear regression-based ensemble model that combines ARIMA, ES, and ANFIS models outperforms both single and combined models in robustness. The article concludes that the insurance industry can greatly benefit from modern predictive methods to make sound decisions.

Demand forecasting for platelet usage: From univariate time series to multivariable models.

Platelet products are both expensive and have very short shelf lives. As usage rates for platelets are highly variable, the effective management of platelet demand and supply is very important yet challenging. The primary goal of this paper is to present an efficient forecasting model for platelet demand at Canadian Blood Services (CBS). To accomplish this goal, five different demand forecasting methods, ARIMA (Auto Regressive Integrated Moving Average), Prophet, lasso regression (least absolute shrinkage and selection operator), random forest, and LSTM (Long Short-Term Memory) networks are utilized and evaluated via a rolling window method. We use a large clinical dataset for a centralized blood distribution centre for four hospitals in Hamilton, Ontario, spanning from 2010 to 2018 and consisting of daily platelet transfusions along with information such as the product specifications, the recipients' characteristics, and the recipients' laboratory test results. This study is the first to utilize different methods from statistical time series models to data-driven regression and machine learning techniques for platelet transfusion using clinical predictors and with different amounts of data. We find that the multivariable approaches have the highest accuracy in general, however, if sufficient data are available, a simpler time series approach appears to be sufficient. We also comment on the approach to choose predictors for the multivariable models.

A review of predictive uncertainty estimation with machine learning

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive uncertainty estimation with machine learning algorithms, as well as the related metrics (consistent scoring functions and proper scoring rules) for assessing probabilistic predictions. The review covers a time period spanning from the introduction of early statistical (linear regression and time series models, based on Bayesian statistics or quantile regression) to recent machine learning algorithms (including generalized additive models for location, scale and shape, random forests, boosting and deep learning algorithms) that are more flexible by nature. The review of the progress in the field, expedites our understanding on how to develop new algorithms tailored to users’ needs, since the latest advancements are based on some fundamental concepts applied to more complex algorithms. We conclude by classifying the material and discussing challenges that are becoming a hot topic of research.

Modeling COVID-19 Disease with Deterministic and Data-Driven Models Using Daily Empirical Data in the United Kingdom

The COVID-19 pandemic has had a significant impact on countries worldwide, including the United Kingdom (UK). The UK has faced numerous challenges, but its response, including the rapid vaccination campaign, has been noteworthy. While progress has been made, the study of the pandemic is important to enable us to properly prepare for future epidemics. Collaboration, vigilance, and continued adherence to public health measures will be crucial in navigating the path to recovery and building resilience for the future. In this article, we propose an overview of the COVID-19 situation in the UK using both mathematical (a nonlinear differential equation model) and statistical (time series modeling on a moving window) models on the transmission dynamics of the COVID-19 virus from the beginning of the pandemic up until July 2022. This is achieved by integrating a hybrid model and daily empirical case and death data from the UK. We partition this dataset into before and after vaccination started in the UK to understand the influence of vaccination on disease dynamics. We used the mathematical model to present some mathematical analyses and the calculation of the basic reproduction number (R0). Following the sensitivity analysis index, we deduce that an increase in the rate of vaccination will decrease R0. Also, the model was fitted to the data from the UK to validate the mathematical model with real data, and we used the data to calculate time-varying R0. The homotopy perturbation method (HPM) was used for the numerical simulation to demonstrate the dynamics of the disease with varying parameters and the importance of vaccination. Furthermore, we used statistical modeling to validate our model by performing principal component analysis (PCA) to predict the evolution of the spread of the COVID-19 outbreak in the UK on some statistical predictor indicators from time series modeling on a 14-day moving window for detecting which of these indicators capture the dynamics of the disease spread across the epidemic curve. The results of the PCA, the index of dispersion, the fitted mathematical model, and the mathematical model simulation are all in agreement with the dynamics of the disease in the UK before and after vaccination started. Conclusively, our approach has been able to capture the dynamics of the pandemic at different phases of the disease outbreak, and the result presented will be useful to understand the evolution of the disease in the UK and future and emerging epidemics.

Comparison of prediction results of Dendrolimus punctatus larvae peak occurrence based on eight prediction models

AbstractIn order to clarify the prediction accuracy of eight models for predicting the peak occurrence of the first generation larvae of Dendrolimus punctatus and provide basis for the pest control, a catastrophe prediction model was established based on the peak occurrence of the first generation larvae of Dendrolimus punctatus in Qianshan City, Anhui Province from 1983 to 2016, and compared with other seven prediction models. Comparing the forecasting results in 2015 and 2016 with actual value and taking 1 head/plant as the error standard, the errors of multiple regression models with six factors as independent variables, namely, peak occurrence of pupae in overwintering generation, peak occurrence of eggs in the first generation, cumulative population in overwintering generation, peak occurrence of adults in overwintering generation, rainfall in early April and parasitic rate of Trichogrammatid in the first generation eggs of Dendrolimus punctatus, were 0.21 heads/plant and 0.23 heads/plant with accuracy rate of 100%. The errors of stepwise regression model with the same six factors were 0.23 head/plant and 0.29 head/plant. The prediction accuracy of artificial BP neural network model, Markov chain model, contingency table model, stationary time series model, and fuzzy comprehensive evaluation model was 100%, but variance period extrapolation model had an accuracy rate of 88%. The accuracy of catastrophe prediction model was related to the selection of catastrophe threshold. Comprehensive comparison of the above eight models, multiple regression, stepwise regression, artificial BP neural network, Markov chain model, stationary time series model, and catastrophe prediction model were more accurate.

A statistical approach to analyze and forecast the dynamics of active fire in the Brazilian legal Amazon

Anthropic fires are hugely responsible for the deforestation of the Brazilian legal Amazon region, one of the world’s most important ecosystems. In this way, policies must be implemented to reduce such a phenomenon. Preventive policies must be manifold, but historical time series analysis and active fire behavior predictions might subside part of the actions. Following this track, the present study aims to understand the spatiotemporal dynamics of active fire, using historical data of active fire comprising all states in the Brazilian legal Amazon region from January 2000 to December 2022. We used information from the National Institute for Space Research to fit appropriate statistical models for counting time series and forecast the monthly behavior of active fire until May 2023. The results showed that approximately 73% of active fires were registered in Pará, Mato Grosso, and Rondônia states, mainly between 2000 and 2010. In Pará, the forecast obtained reflects the phenomenon’s seasonality, with a higher concentration between August and November. In summary, the adopted methodology provided results that facilitated an understanding of the dynamics of active fire in the Brazilian legal Amazon region and can be considered a relevant tool to help authorities formulate public policies for arson prevention.

Exploring the dynamics of monkeypox transmission with data-driven methods and a deterministic model.

Mpox (formerly monkeypox) is an infectious disease that spreads mostly through direct contact with infected animals or people's blood, bodily fluids, or cutaneous or mucosal lesions. In light of the global outbreak that occurred in 2022-2023, in this paper, we analyzed global Mpox univariate time series data and provided a comprehensive analysis of disease outbreaks across the world, including the USA with Brazil and three continents: North America, South America, and Europe. The novelty of this study is that it delved into the Mpox time series data by implementing the data-driven methods and a mathematical model concurrently-an aspect not typically addressed in the existing literature. The study is also important because implementing these models concurrently improved our predictions' reliability for infectious diseases. We proposed a traditional compartmental model and also implemented deep learning models (1D- convolutional neural network (CNN), long-short term memory (LSTM), bidirectional LSTM (BiLSTM), hybrid CNN-LSTM, and CNN-BiLSTM) as well as statistical time series models: autoregressive integrated moving average (ARIMA) and exponential smoothing on the Mpox data. We also employed the least squares method fitting to estimate the essential epidemiological parameters in the proposed deterministic model. The primary finding of the deterministic model is that vaccination rates can flatten the curve of infected dynamics and influence the basic reproduction number. Through the numerical simulations, we determined that increased vaccination among the susceptible human population is crucial to control disease transmission. Moreover, in case of an outbreak, our model showed the potential for epidemic control by adjusting the key epidemiological parameters, namely the baseline contact rate and the proportion of contacts within the human population. Next, we analyzed data-driven models that contribute to a comprehensive understanding of disease dynamics in different locations. Additionally, we trained models to provide short-term (eight-week) predictions across various geographical locations, and all eight models produced reliable results. This study utilized a comprehensive framework to investigate univariate time series data to understand the dynamics of Mpox transmission. The prediction showed that Mpox is in its die-out situation as of July 29, 2023. Moreover, the deterministic model showed the importance of the Mpox vaccination in mitigating the Mpox transmission and highlighted the significance of effectively adjusting key epidemiological parameters during outbreaks, particularly the contact rate in high-risk groups.

Testing for coefficient distortion due to outliers with an application to the economic impacts of climate change

Outlying observations can bias regression estimates, requiring the use of outlier-robust estimators. Comparing robust estimates to those obtained using ordinary least squares (OLS) is a common robustness check, however, such comparisons have been mostly informal due to the lack of available tests. Here we introduce a formal test for coefficient distortion due to outliers in regression models. Our proposed test is based on the difference between OLS and robust estimates obtained using a class of Huber-skip M-type estimators (such as Impulse Indicator Saturation or Robustified Least Squares). We show that our distortion test has an asymptotic chi-squared distribution by establishing the asymptotics of the corresponding Huber-skip M-estimators using an empirical process Central Limit Theorem recently developed in the literature. The test is valid for cross-sectional, as well as panel, and stationary or deterministically-trending time series models. To improve finite sample performance and to alleviate concerns on distributional assumptions, we explore several bootstrap testing schemes. We apply our outlier distortion test to estimates of the macro-economic impacts of climate change allowing for adaptation.

Active sensing ultrasonic guided wave-based damage diagnosis via stochastic stationary time-series models

In the context of acousto-ultrasonic guided wave-based structural health monitoring, a statistical damage detection and identification (collectively referred to as damage diagnosis) framework for metallic and composite materials is proposed. Stochastic stationary time-series autoregressive (AR) models are used to model the ultrasonic wave propagation between piezoelectric actuator-sensor pairs on structural components and enable the damage diagnosis process via the use of the AR estimated parameters and corresponding covariance matrices. The proposed method exploits guided wave signals including the reflection parts, and thus the extraction of the S0 and/or A0 modes is not necessary, while the statistical properties and variation of estimated model parameters with respect to damage intersecting and non-intersecting wave propagation paths are presented and assessed. To investigate the method’s performance and robustness, two variations are proposed based on the singular value decomposition and principal component analysis. The obtained modified AR parameter vectors are then used to estimate appropriate statistical characteristic quantities used to enable the damage detection and identification tasks. The diagnosis is based on properly defined statistical hypotheses decision-making schemes and predetermined type I error probabilities. The performance and applicability of the method are explored experimentally via a series of tests on aluminum and composite coupons under various damage scenarios for damage intersecting and non-intersecting paths. The results of the present study demonstrated the effectiveness and robustness of the proposed modeling and diagnostic framework for guided wave-based damage diagnosis that can be implemented in a potentially automated way.

Analysing the geographical impact on short-term solar irradiance forecasting using univariate and multivariate time series models

ABSTRACT Sustainable development is significantly hampered by air pollution brought on by greenhouse gas emissions. One of the primary contributors to air pollution is coal, which is used in thermal power plants. Substituting power plants from combustible sources to renewable energy sources can reduce air pollution to an extent. Solar energy is one of the most readily accessible renewable energy sources. High Global Horizontal Irradiance (GHI) is advantageous for deploying solar power plants, allowing maximum electricity production. However, the spatiotemporal factors affecting GHI are not analyzed, which can improve the forecasting accuracy. The proposed work analyzes the geographical impact of solar irradiation using statistical time-series models called ARIMA (Auto Regression Integrated Moving Average) and VAR (Vector Auto Regression) using four datasets from two different locations in India. The statistical time-series models can analyze the impact of the features and can show how the effect improves the performance of the multivariate model compared to the univariate model. The study aims to find the influence of the geographical factors of Global Horizontal Irradiance (GHI) based on the location chosen to build a solar power plant. The effectiveness of the univariate and multivariate models in forecasting solar irradiance is also discussed. The RMSE (root mean square error) analysis shows that the multivariate model VAR outperforms the univariate model in predicting solar irradiance. There is a 1–25% variance in the RMSE values between the ARIMA and VAR models at different locations and a 1–19% variance in MAE (Mean Absolute Error) value, while a 94–98% variance in MAPE (mean absolute percentage error) value. A deep analysis of factors that affect the precision of global horizontal irradiance (GHI) and the causal impact of variables is also analyzed using different variable impact tests. This variable selection is achieved by a feature selection algorithm called Maximum Relevance Minimum Redundancy (MRMR).

Discrete Wavelet Transform and Ensemble Tree Algorithms for Air Pollutant Modeling: A Case Study

Air pollution is one of the greatest environmental problems of our time on a global and local scale. Elevated and even low but constant levels of harmful emissions in the air in urbanized areas pose serious risks to the health of the population. This paper develops a new approach for statistical modeling of time series of air pollutants, depending on meteorological factors. A new framework based on discrete wavelet transform (DWT) is proposed for decomposing pollutant's time series as a sum of components that represent trend, seasonality, and other specific characteristics. A key element in the applied DWT is an adaptive scheme for selecting the threshold value to control the reverse DWT's accuracy for achieving better prediction of the time series values. The resulting components are modeled with cutting-edge predictive ensemble tree algorithms, including bagging, boosting, and stacking techniques. This approach is tested with real data measured with a mobile automated station in the Plovdiv region, Bulgaria. All models are evaluated, analyzed, and cross-validated. The models are applied for short-term pollution forecasts.

Порівняння потужності критеріїв наявності тренду в часових рядах

The subject of research is methods, mathematical models, and methods of continuous analysis of a multidimensional set of output variables and state variables of power and energy installations built on the basis of gas turbine engines, which in general constitute time series. The purpose of this work is to establish the power of trend and randomness criteria by statistical modeling of time series with a linear trend and the use of known trend and randomness statistics to establish their empirical distributions and operational characteristics for comparing trend criteria by their power. The tasks faced by the developers were to determine the empirical distributions of known parametric and non-parametric trend statistics when applying the linear trend model in superposition with a random component, and set the level of errors of the first kind (false solution), with a given level of errors of the second kind (false anxiety). The methods that were used to achieve the established goal of the research: general methods of trend analysis, methods of applied statistics, and methods of conducting computer experiments. The results of the research provide a rationale for the approach to establishing the power of known criteria of trend and randomness. The limitation of the known methods of applied statistics is that it is theoretically only possible to refute the hypothesis regarding the randomness of the initial data at a certain level of significance, which determines the level of errors of the second kind (false alarms). Establishing the level of errors of the first kind (wrong decision) poses significant difficulties, because in the presence of a trend, the time series can no longer be stationary. But it is the statistical level of such errors that actually determines the strength of the criteria for the presence of a trend in the time series. The resolution of this contradiction is proposed by means of statistical modeling of time series with a linear trend and the use of well-known trend and randomness statistics to establish their empirical distributions and operational characteristics and to compare trend criteria according to their power. Statistical modeling was performed for a number of trend and randomness statistics, namely: the most common parametric statistics: correlation criterion and its modifications, Fisher's criterion, and Student's criterion; and non-parametric Wald-Wolfowitz criteria; Bartles; as well as the inversion criterion. According to the results of statistical modeling, it was established that the Student's criterion is the most powerful of the parametric criteria, and the inversion criterion is the most powerful of the non-parametric criteria. It is understood that such conclusions are valid when the assumptions regarding the initial statistical model of data generation in the form of a superposition of a linear trend and a random component as a sample from the general population of independent and normally distributed random variables and the corresponding algorithm for processing time series counts for the formation of decisive statistics are fulfilled. The scientific novelty of the obtained results lies in the fact that for the first time, the issue of comparing the power of parametric and non-parametric criteria of trend and randomness with respect to the applied model of data generation in the form of a linear trend in superposition with a random component was considered. The practical significance of the obtained results lies in the fact that the research results make it possible to choose an appropriate criterion based on its power for solving applied tasks of monitoring the technical condition of power and energy installations built on the basis of gas turbine engines.

Comparative analysis of deep learning and classical time series methods to forecast natural gas demand during COVID-19 pandemic

ABSTRACT The lockdown measures implemented to contain the COVID-19 pandemic have had a considerable effect on the consumption of natural gas, which is closely linked to the economic growth of countries. Accurately forecasting natural gas demand is critical for making informed decisions in unprecedented and unexpected situations. This study aims to compare artificial learning-based algorithms and classical statistical time series models in predicting natural gas demand during the pandemic, using Turkey as a case study. Common time series prediction methods, including Autoregressive Integrated Moving Average (ARIMA), Nonlinear Autoregression Neural Network (NARNN), Support Vector Regression (SVR), and Long Short-Term Memory (LSTM), were utilized for this purpose. The impact of the pandemic on natural gas demand was analyzed by including 2-year natural gas consumption data since its onset. Root mean square error (RMSE), correlation coefficient (R), and mean absolute error (MAE) criteria were used as performance evaluation metrics to select the best model. The results confirmed that the deep-learning-based LSTM model provided better prediction accuracy than time-series benchmark models, with the lowest RMSE (9.442) and the highest R (0.997) values in the test dataset. Furthermore, the results were validated by statistical analysis using the Diebold-Mariano and Nemenyi tests.

Comparison of ARIMA and Exponential Smoothing Models in Prediction of Stock Prices

Stock prices tend to show trends or seasonality or have random walk movements. Time series statistical models developed over time aid prediction of stock prices to assist informed decision-making for investors. These models provide quantitative information to financial specialists at the time of placing their buy–sell orders. The paper compares the movement of two univariate time series using two forecasting models—exponential smoothing and autoregressive integrated moving average (ARIMA) (p; d; q). We predict stock prices of selected 15 companies across three sectors (banking, pharmaceuticals, and Information technology) from NIFTY 50 data for the period April 01, 2016 to March 31, 2021. All these 15 companies are representative constituents of the three sectors within the Nifty 50 index. Performances of models were assessed through forecasting error measures such as root mean square error and mean absolute percentage error. Performances of both models were identical for nine stocks. Prediction based on ARIMA was more accurate for six stocks, whereas exponential smoothing model was a better indicator of stock prices in the case of one stock. However, the differences in error measures of the both the models are marginal, and parsimony principle may drive the choice of model.

Continuous-time locally stationary time series models

AbstractWe adapt the classical definition of locally stationary processes in discrete time (see e.g. Dahlhaus, ‘Locally stationary processes’, in Time Series Analysis: Methods and Applications (2012)) to the continuous-time setting and obtain equivalent representations in the time and frequency domains. From this, a unique time-varying spectral density is derived using the Wigner–Ville spectrum. As an example, we investigate time-varying Lévy-driven state space processes, including the class of time-varying Lévy-driven CARMA processes. First, the connection between these two classes of processes is examined. Considering a sequence of time-varying Lévy-driven state space processes, we then give sufficient conditions on the coefficient functions that ensure local stationarity with respect to the given definition.

Ensemble Hindcasting of Coastal Wave Heights

Long records of wave parameters are central to the estimation of coastal flooding risk and the causes of coastal erosion. This paper leverages the predictive power of wave height history and correlations with wind speed and direction to build statistical models for time series of wave heights to develop a method to fill data-gaps and extend the record length of coastal wave observations. A threshold regression model is built where the threshold parameter, based on lagged wind speed, explains the nonlinear associations, and the lagged predictors in the model are based on a well-established empirical wind-wave relationship. The predictive model is completed by addressing the residual conditional heteroscedasticity using a GARCH model. This comprehensive model is trained on time series data from 2005 to 2013, using wave height and wind data both observed from a buoy in Long Island Sound. Subsequently, replacing wind data with observations from a nearby coastal station provides a similar level of predictive accuracy. This approach can be used to hindcast wave heights for past decades given only wind information at a coastal station. These hindcasts are used as a representative of the unobserved past to carry out extreme value analysis by fitting Generalized Pareto (GP) distribution in a peaks over threshold (POT) framework. By analyzing longer periods of data, we can obtain reliable return value estimates to help design better coastal protection structures.

Climate Change: Linear and Nonlinear Causality Analysis

The goal of this study is to detect linear and nonlinear causal pathways toward climate change as measured by changes in global mean surface temperature and global mean sea level over time using a data-based approach in contrast to the traditional physics-based models. Monthly data on potential climate change causal factors, including greenhouse gas concentrations, sunspot numbers, humidity, ice sheets mass, and sea ice coverage, from January 2003 to December 2021, have been utilized in the analysis. We first applied the vector autoregressive model (VAR) and Granger causality test to gauge the linear Granger causal relationships among climate factors. We then adopted the vector error correction model (VECM) as well as the autoregressive distributed lag model (ARDL) to quantify the linear long-run equilibrium and the linear short-term dynamics. Cointegration analysis has also been adopted to examine the dual directional Granger causalities. Furthermore, in this work, we have presented a novel pipeline based on the artificial neural network (ANN) and the VAR and ARDL models to detect nonlinear causal relationships embedded in the data. The results in this study indicate that the global sea level rise is affected by changes in ice sheet mass (both linearly and nonlinearly), global mean temperature (nonlinearly), and the extent of sea ice coverage (nonlinearly and weakly); whereas the global mean temperature is affected by the global surface mean specific humidity (both linearly and nonlinearly), greenhouse gas concentration as measured by the global warming potential (both linearly and nonlinearly) and the sunspot number (only nonlinearly and weakly). Furthermore, the nonlinear neural network models tend to fit the data closer than the linear models as expected due to the increased parameter dimension of the neural network models. Given that the information criteria are not generally applicable to the comparison of neural network models and statistical time series models, our next step is to examine the robustness and compare the forecast accuracy of these two models using the soon-available 2022 monthly data.