The significant rise in the air pollution index due to black carbon (BC) can be ascribed to heavy energy dependency of developing nations on coal as their primary energy resource. For countries like India, Coal is the principal contributor to energy demand required for electricity generation and expansion of industry. Bokaro, Jharia and Raniganj are the three important coal fields located in India. The BC concentration data from these coal fields is analysed and forecasted with a suitable developed conjunction mathematical model to look for solutions to the alarming pollution levels both nationally and globally. The model so developed helps to lower the error metrices significantly while forecasting the pollution data as compared to individual soft computing model.

The incessant degradation of the environment is a major global challenge in today’s world, which is posing huge threat to the human health and environmental equilibrium. The escalating accumulation of hazardous pollutants in the air and water, and the subsequent threats to human health, are driven by complex interconnected mechanisms involving climate variability, geographical characteristics, and anthropogenic activities. Since these processes exhibit strong non-linear and dynamic behavior, it becomes very arduous to depict accurate forecasts using conventional statistical methods. Artificial Neural Networks (ANNs) have captured notable attention to overcome these challenges because of their ability to model intricate non-linear relationships in diverse environmental systems. This study demonstrates an extensive review of ANN applications across environmental and non-environmental domains. It looks forward to primarily focusing on the environmental systems, which would comprise of air quality modeling, management of water resources and predictions related to health. A critical analysis of more than 135 peer-reviewed articles from high-impact journals has been conducted to bring out the efficaciousness, shortcomings, and advancements of ANN-based modeling frameworks. The findings indicate that while individual ANN models are competent to represent the non-linear relationships, their performance is often constrained by issues such as local minima convergence, overfitting, and reduced generalizations under noisy and non-stationary conditions. The review further illustrates that when ANN models are seamlessly connected with methods such as wavelet decomposition, ARIMA, and evolutionary optimization techniques, the hybrid frameworks steadily reflect the immense strength, stability, and precision of forecasting compared to the standalone ANN models. The comparative evidence emphatically suggest that hybrid models provide a stronger benchmark for complex real world datasets, especially in the highly variable environmental systems. The study draws the conclusion that focuses on the escalating significance of hybrid intelligent systems and highlights the areas of subsequent research on model interpretability, uncertainty handling, and adaptive learning. This paper is organized into five main sections: an introduction to ANNs, their historical development, applications of ANN models in environmental studies, a detailed review of these practical implementations, and a discussion of results. By consolidating this knowledge, we can foster collaborative efforts towards developing more effective strategies for mitigating environmental pollution and safeguarding the planet for future generations.

Environmental pollution is a critical challenge that requires our attention due to its potential for irreversible damage to our planet. As urbanization and technological advancements continue, addressing the degradation of vital environmental components, including air, water, and soil, caused by hazardous waste released from industrial activities is essential. Pollutants disrupt the ecological balance and pose serious health risks to humans, animals, and birds. To combat this issue, effective tools and methodologies are necessary. For example, wavelet hybrid modelling significantly enhances our ability to predict concentrations of air and water pollutants, which can lead to informed decision-making and future improvements. Accurate predictions can be achieved effectively with wavelet hybrid models. A review of approximately 150 research papers highlights the advancements in forecasting environmental pollutants, climate variations, and groundwater levels using various wavelet hybrid models. These studies demonstrate the versatility of different wavelet hybrid models compared to traditional single models in forecasting time series data. Researchers use a range of statistical indices, including Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), Nash-Sutcliffe Efficiency (NSE), and R-squared (R²), to evaluate their effectiveness. The findings indicate that wavelet hybrid models offer a promising approach, showing greater accuracy in forecasting time series data than single models. This paper is structured into five comprehensive sections: an introduction to wavelets, their historical context, the applications of wavelet-coupled models in environmental studies, a review of these practical applications and discussions of results. By sharing this knowledge, we can collaborate on more effective strategies for mitigating environmental pollution and protecting our planet for future generations.

The analysis and prediction of stock market prices are crucial areas of research due to their complex, chaotic, and nonlinear features. As a result, making significant gains in stock market investments is a crucial task. However, expert and intelligent modeling techniques can help in achieving positive stock market returns. In this study, we use the Monte Carlo (MC) simulation method to generate multiple future values of the time series of closing prices of a particular stock of BSE using a combination of wavelet denoising and the autoregressive integrated moving average (ARIMA) model. The multiple future realizations of stock prices produced by the Monte Carlo (MC) simulation can help minimize risk and uncertainty in stock market investments. Firstly, we use wavelet analysis to detect significant noise levels in the time series at each scale in discrete wavelet decomposition, which is then eliminated by an appropriate wavelet denoising method. Next, the time series of denoised stock prices is fitted with a suitable ARIMA model, and the future values are obtained using this model. The future values of the denoised time series are simulated using MC simulation. The results of the study show that simulated forecasts obtained by MC simulation using the integrated wavelet-denoising-ARIMA model become more accurate with increasing simulation count than by applying a single ARIMA model to noisy stock price series. It has also been observed that MC simulation reduces the standard error of estimates to one half when the number of simulations is quadrupled.

Machine Learning provides certain algorithms which provide software data with much accuracy in predicting outcomes without absolutely stating them. Basic fundamental of artificial intelligence and machine learning is to setup models and use algorithms which accept user data input and utilize statistical data to forecast output, and update the output as new data becomes available. Today, stores and hypermarkets monitor the sales data of each product to forecast future customer demand and improve inventory management. The objective of this research paper is to create a sales forecasting model for the popular supermarket big Mart. We have proposed a forecasting model using XG boost regressor technology to forecast the sales of big firms just like big mart, and we came to know that the model performs well with existing models resulting in better performance.

The preset paper discusses the COVID-19 pandemic in India and the development of a data-driven model to predict COVID-19 confirmed cases, casualties, and recoveries in the country. The Coronavirus Disease 2019 (COVID-19) was first identified in December 2019 in the Hubei Province of the People's Republic of China. It quickly spread to 220 countries worldwide and had a significant impact. In India, the second wave of COVID-19 hit in April 2021, resulting in over 40 million reported cases and three lakh casualties. India ranked second in COVID-19 infections globally, after the United States of America. To better understand the dynamics of the COVID-19 pandemic in India, a data-driven WANFIS (Wavelet Adaptive Neuro-Fuzzy Inference System) model was developed. This model uses discrete wavelet decomposition to extract information from input data and predict the escalation of confirmed cases, casualties, and recoveries in India. The WANFIS model's effectiveness was compared to other models like the artificial neural network (ANN) model and individual ANFIS model, and it proved to be more robust in predicting COVID-19 transmission. The proposed WANFIS model has the potential to effectively forecast the transmission of infectious diseases, enabling government and health officials to anticipate and prepare for emergencies more effectively.

Air pollution has emerged as a significant environmental challenge at the global level, and India is majorly affected by it. Numerous emission sources, such as automobiles, industries, fuel-burning for household and commercial activities, and dust due to construction activities, are responsible for air pollution. The lockdown in India which was clamped for controlling the spread of virulent disease also brought down the level of pollutants in air significantly. The proposed approach deals with the application of the hybrid model of Daubechies discrete wavelet decomposition (Db-DWD) and the autoregressive integrated moving average (ARIMA) model for modeling and forecasting the chaotic data of air quality index (PM 2.5 ) from the three most polluted cities (Agra, New Delhi, and Varanasi) in India for pre and within lockdown periods. The estimated outputs of the component series are then reconstructed to obtain the final forecast of the AQI data. The statistical evaluation compares the performance of the simple ARIMA model and the joint Db-DWD-ARIMA model. Also, the coupled model has been applied for forecasting efficacy with Daubechies mother wavelet of orders 5, 8, 10, and 12. The hybrid model reduced forecasting errors and improved accuracy significantly. Secondly, the forecasting efficiencies in this hybrid model have enhanced with the increase in wavelet order. This study will help to assess and take appropriate steps to control air pollution levels and to monitor the growing air pollutants, which will be significant for our existence.

Though globalization, industrialization, and urbanization have escalated the economic growth of nations, these activities have played foul on the environment. Better understanding of ill effects of these activities on environment and human health and taking appropriate control measures in advance are the need of the hour. Time series analysis can be a great tool in this direction. ARIMA model is the most popular accepted time series model. It has numerous applications in various domains due its high mathematical precision, flexible nature, and greater reliable results. ARIMA and environment are highly correlated. Though there are many research papers on application of ARIMA in various fields including environment, there is no substantial work that reviews the building stages of ARIMA. In this regard, the present work attempts to present three different stages through which ARIMA was evolved. More than 100 papers are reviewed in this study to discuss the application part based on pure ARIMA and its hybrid modeling with special focus in the field of environment/health/air quality. Forecasting in this field can be a great contributor to governments and public at large in taking all the required precautionary steps in advance. After such a massive review of ARIMA and hybrid modeling involving ARIMA in the fields including or excluding environment/health/atmosphere, it can be concluded that the combined models are more robust and have higher ability to capture all the patterns of the series uniformly. Thus, combining several models or using hybrid model has emerged as a routinized custom.

Most of the stock market data are high-frequency data showing nonlinearity, asymmetry, and chaotic behavior due to sharp variations in prices over time. Volatility explains these sudden variations in prices over time and is related to conditional variances that reveal some important facts about stock market returns. So, volatility modeling is required to investigate these significant facts of stock market returns. Autoregressive conditional heteroskedastic (ARCH) models are powerful tools for modeling and estimating conditional variances and volatility in stock market prices. The present study deals with volatility prediction of stock market returns using different variants of Generalized Autoregressive Conditional Heteroskedastic (GARCH) models such as Exponential Autoregressive conditional heteroskedastic (EGARCH) and Glosten-Jagannathan-Runkle (GJR) models with Gaussian distribution and Student's t-distribution. The input data for the study consist of stock market data of the daily and weekly returns of the BSE 100 S&P stock index series from 2009 to 2019. After modeling the daily and weekly returns with GARCH, EGARCH, and GJR models, the volatility of price returns is forecasted for the out-of-sample period. The performance of the proposed models has been evaluated by error statistics that compare the values of original volatility with the predicted values. The results reveal that the out-of-sample volatility forecast with the EGARCH model tends to generate more accurate results with Student's t-distribution when compared to GARCH and GJR models.

Fresh air is imminent for life and to thrive on this planet. However, this vital component of life is ill-effected by fast-paced industrialization, urbanization, automobiles, factories, and coal-based thermal power generation as over the years these have jeopardized the air quality index. Due to hazardous impact of black carbon on the environment as well as human health, researchers have turned their attention towards its study. The artificial neural network and econometric ARIMA model are used to predict black carbon emissions from three major coal mines located at Bokaro, Jharia, and Raniganj in India. A comparative analysis of these two techniques over three different forecasting horizons is carried out for investigating short-term or long-term efficiencies of both the models. The three coal mines have large emissions of particulate matter ( $$P{M}_{2.5}$$ ) that contribute significantly to pollution levels. A multilayer perceptron feedforward artificial neural network with Bayesian regularization-backpropagation neural network (BR-BPNN) algorithm is employed. The efficiency of neural network models is evaluated by mean absolute deviation (MAD), root mean square error (RMSE), and coefficient of determination (R2) values. For all the forecasting horizons and in all the accuracy measures, the BR-BPNN outperformed the traditional econometric ARIMA model in predicting the black carbon concentration values with a considerable reduction in errors ranging from 60 to 70% for all the sites. In addition, the performance of an ARIMA model is found to be dependent on the length of the forecasting horizon. However, no such evidence is found for ANN model in forecasting black carbon concentration data.

Air is the basis for the existence of life on Earth; but in the present age of modernization the degrading quality of air year by year, due to the growth of Industrialization, urbanization, automobiles, coal-fired thermal power plants, and various other factories is the matter of real concern. To predict the future growth of air pollutants numerous prediction models have been developed by researchers. Time-series ARIMA model although quite useful for forecasting but fails to handle non-stationary problems. Among all the existing forecasting models, wavelets along with the Machine learning models have proved to be very successful and have been widely used in various fields like mathematical modeling, signal recognition, image recognition, classification, function approximation, data processing, filtering, clustering, compression, robotics, and decision making. It is also used in the field of mathematical forecasting for developing efficient prediction models. This paper aims to develop a wavelet-ANFIS conjugation model and a wavelet-ARIMA coupled model along with the time-series ARIMA model for the prediction of black carbon concentration over the Raniganj, Jharia, and Bokaro coal mines of India, by considering a long term data obtained by NASA (http://nasa.gov/) and compare the results obtained by these models for determining the best prediction model. The validity of the results is tested with the help of error measures like RMSE, MSE, MAPE, MAE, and relative error. Results over the three sample sites conclude that the Wavelet-ANFIS conjugation approach outperforms the wavelet-ARIMA coupled approach and the simple time-series ARIMA model.

Fast spreading coronavirus disease 2019 (COVID-19), originated in the Wuhan city, China in December 2019, is a contagious disease caused by Severe Acute Respiratory Syndrome-Coronavirus-2 (SARS-CoV-2). Within a short period, COVID-19 infections spread over large geographical area affecting millions of people and declared a pandemic by the World Health Organization (WHO). The fast and quick spread of the virus across the globe resulted in thousands of casualties. COVID-19 prevalence in India was reported in the late of January 2020 and the number of infections increased sharply by the end of March. In such a troublesome situation, time series analysis proves very much helpful in monitoring and assessing the growth curve of COVID-19 infections. In the present study, autoregressive integrated moving average (ARIMA) models are developed for the time series data of cumulative confirmed, recovered and causalities cases of COVID-19 in India. The data set under study is broken up into two subsets, modelling and testing data sets. After analysing the input data for stationarity using autocorrelation function (ACF) and partial correlation function (PACF) plots, different ARIMA models are estimated for confirmed, recovered and causalities' cases of COVID-19 in India for modelling phase. ARIMA Model outputs are then compared with observed values of confirmed, recovered and casualties' cases for the testing phase using error analysis. It has been found that ARIMA $$\left( {0,2,3} \right)$$ , ARIMA $$\left( {0,2,5} \right)$$ and ARIMA $$\left( {1,2,1} \right)$$ models are appropriate with the lowest mean absolute percentage error (MAPE) values for the data of confirmed cases, recovered cases and casualties' cases respectively. Finally, the developed ARIMA models are used to forecast one-month ahead values of confirmed, recovered and casualties' cases of COVID-19 in India. The predictions indicate rise in confirmed COVID-19 cases and speedy recoveries as well, whereas the casualties continue to show a constant trend in future. Based on these future trends of COVID-19 outbreak, governments and policymakers can take preventive measures to break the ongoing chain of COVID-19 infections and make necessary arrangements in the wake of an emergency.

This chapter aimed to survey some significant contributions in the field of artificial neural networks to solve the prediction problems related to finance and economics, environment, hydrology and agriculture preferably. A detailed methodology of artificial neural networks with historical background has been discussed here. The results of the survey reveal that artificial neural networks give more accurate forecasts than traditional and baseline regression, ARMA and ARIMA models, etc. The major contribution of this chapter is to provide the basic terminology of ANN architecture and methodology useful for different forecasting problems, and survey the available sources of different type of data to define a new problem in this field for future research.

Everywhere around the globe, the hot topic of discussion today is the ongoing and fast-spreading coronavirus disease (COVID-19), which is caused by the severe acute respiratory syndrome coronavirus 2 (SARS-COV-2). Earlier detected in Wuhan, Hubei province, in China in December 2019, the deadly virus engulfed China and some neighboring countries, which claimed thousands of lives in February 2020. The proposed hybrid methodology involves the application of discreet wavelet decomposition to the dataset of deaths due to COVID-19, which splits the input data into component series and then applying an appropriate econometric model to each of the component series for making predictions of death cases in future. ARIMA models are well known econometric forecasting models capable of generating accurate forecasts when applied on wavelet decomposed time series. The input dataset consists of daily death cases from most affected five countries by COVID-19, which is given to the hybrid model for validation and to make one month ahead prediction of death cases. These predictions are compared with that obtained from an ARIMA model to estimate the performance of prediction. The predictions indicate a sharp rise in death cases despite various precautionary measures taken by governments of these countries.

Water is the most important substance for life on earth and every living being need freshwater to survive. Besides various sources of water, river water is all-important source of freshwater. Due to rapid urbanization, industrialization, religious and social practices on the banks of rivers, the river water gets polluted and it is one of the major issues in India. So, the need of hour is to keep a continuous check on the quality of river water parameters. Various researchers have developed accurate prediction models to estimate the future quality of river water with least forecasting errors. Autoregressive time series models have been developed to generate linear forecast only and most of them are unable to handle nonlinear problems. To handle such nonlinear problems, artificial neural network (ANN) and adaptive neuro-fuzzy interface system are found to be most efficient tool for accurate prediction. Besides these methods, wavelet decomposition tool for analyzing nonlinear situations has been used to generate forecast values close enough to observed values. The biochemical oxygen (BOD) of river Yamuna at sample site of Nizamuddin (Delhi) is predicted using the past monthly averaged data. Statistical analysis provides basis to understand the nature of wavelet domain constitutive series. The prediction results obtained using neuro-fuzzy-wavelet coupled model generates more accurate outcomes as compared to neuro-fuzzy, ANN and regression models.

Discussions about the recently identified deadly coronavirus disease (COVID-19) which originated in Wuhan, China in December 2019 are common around the globe now. This is an infectious and even life-threatening disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It has rapidly spread to other countries from its originating place infecting millions of people globally. To understand future phenomena, strong mathematical models are required with the least prediction errors. In the present study, autoregressive integrated moving average (ARIMA) and least square support vector machine (LS-SVM) models are applied to the data consisting of daily confirmed cases of SARS-CoV-2 in the most affected five countries of the world for modeling and predicting one-month confirmed cases of this disease. To validate these models, the prediction results were tested by comparing it with testing data. The results revealed better accuracy of the LS-SVM model over the ARIMA model and also suggested a rapid rise of SARS-CoV-2 confirmed cases in all the countries under study. This analysis would help governments to take necessary actions in advance associated with the preparation of isolation wards, availability of medicines and medical staff, a decision on lockdown, training of volunteers, and economic plans.