Forecasting of AQI (PM2.5) for the three most polluted cities in India during COVID-19 by hybrid Daubechies discrete wavelet decomposition and autoregressive (Db-DWD-ARIMA) model.

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 (PM2.5) 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.

Autoregressive models in environmental forecasting time series: a theoretical and application review.

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.

Prediction of COVID-19 pervasiveness in six major affected states of India and two-stage variation with temperature.

Coronavirus disease knocked in Wuhan city of China in December 2019 which spread quickly across the world and infected millions of people within a short span of time. COVID-19 is a fast-spreading contagious disease which is caused by SARS-CoV-2 (severe acute respiratory syndrome-coronavirus-2). Accurate time series forecasting modeling is the need of the hour to monitor and control the universality of COVID-19 effectively, which will help to take preventive measures to break the ongoing chain of infection. India is the second highly populated country in the world and in summer the temperature rises up to 50°, nowadays in many states have more than 40° temperatures. The present study deals with the development of the autoregressive integrated moving average (ARIMA) model to predict the trend of the number of COVID-19 infected people in most affected states of India and the effect of a rise in temperature on COVID-19 cases. Cumulative data of COVID-19 confirmed cases are taken for study which consists of 77 sample points ranging from 1st March 2020 to 16th May 2020 from six states of India namely Delhi (Capital of India), Madya Pradesh, Maharashtra, Punjab, Rajasthan, and Uttar Pradesh. The developed ARIMA model is further used to make 1-month ahead out of sample predictions for COVID-19. The performance of ARIMA models is estimated by comparing measures of errors for these six states which will help in understanding future trends of COVID-19 outbreak. Temperature rise shows slightly negatively correlated with the rise in daily cases. This study is noble to analyse the variation of COVID-19 cases with respect to temperature and make aware of the state governments and take precautionary measures to flatten the growth curve of confirmed cases of COVID-19 infections in other states of India, nearby countries as well.

Correction to: Statistical, time series and fractal analysis of full stretch of river Yamuna (India) for water quality management.

As corresponding author, while going through higher research in this area, it is found that the formula for Hurst exponent given in equation (13) on page no. 401 is wrongly written.

Study of ARIMA and least square support vector machine (LS-SVM) models for the prediction of SARS-CoV-2 confirmed cases in the most affected countries.

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.

Development of new hybrid model of discrete wavelet decomposition and autoregressive integrated moving average (ARIMA) models in application to one month forecast the casualties cases of COVID-19.

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.

Statistical variability comparison in MODIS and AERONET derived aerosol optical depth over Indo-Gangetic Plains using time series modeling.

A lot of studies in the literature of Aerosol Optical Depth (AOD) done by using Moderate Resolution Imaging Spectroradiometer (MODIS) derived data, but the accuracy of satellite data in comparison to ground data derived from ARrosol Robotic NETwork (AERONET) has been always questionable. So to overcome from this situation, comparative study of a comprehensive ground based and satellite data for the period of 2001-2012 is modeled. The time series model is used for the accurate prediction of AOD and statistical variability is compared to assess the performance of the model in both cases. Root mean square error (RMSE), mean absolute percentage error (MAPE), stationary R-squared, R-squared, maximum absolute percentage error (MAPE), normalized Bayesian information criterion (NBIC) and Ljung-Box methods are used to check the applicability and validity of the developed ARIMA models revealing significant precision in the model performance. It was found that, it is possible to predict the AOD by statistical modeling using time series obtained from past data of MODIS and AERONET as input data. Moreover, the result shows that MODIS data can be formed from AERONET data by adding 0.251627 ± 0.133589 and vice-versa by subtracting. From the forecast available for AODs for the next four years (2013-2017) by using the developed ARIMA model, it is concluded that the forecasted ground AOD has increased trend.

Time series model prediction and trend variability of aerosol optical depth over coal mines in India.

A study of the assessment and management of air quality was carried out at 11 coal mines in India. Long-term observations (about 13 years, March 2000-December 2012) and modeling of aerosol loading over coal mines in India are analyzed in the present study. In this respect, the Box-Jenkins popular autoregressive integrated moving average (ARIMA) model was applied to simulate the monthly mean Terra Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD550 nm) over 11 sites in the coal mines region. The ARIMA model was found as the most suitable model with least normalized Bayesian information criterion (BIC) and root mean square error and high value of R (2). Estimation was done with the Ljung-Box test. Finally, a forecast for a 3-year period from January 2013 to December 2015 was calculated which showed that the model forecasted values are following the observed trend quite well over all mining areas in India. The average values of AOD for the next 3 years (2013-2015) at all sites are found to be 0.575 ± 0.13 (Raniganj), 0.452 ± 0.12 (Jharia), 0.339 ± 0.13 (Bokaro), 0.280 ± 0.09 (Bishrampur), 0.353 ± 0.13 (Korba), 0.308 ± 0.08 (Talcher), 0.370 ± 0.11 (Wardha), 0.35 ± 0.10 (Adilabad), 0.325 ± 0.09 (Warangal), 0.467 ± 0.09 (Godavari Valley), and 0.236 ± 0.07 (Cuddapah), respectively. In addition, long-term lowest monthly mean AOD550 values are observed over Bishrampur followed by Cuddapah, Talcher, Warangal, Adilabad, Korba, Wardha, Godavari Valley, Jharia, and Raniganj. Raniganj and Jharia exhibit the highest AOD values due to opencast mines and extensive mining activities as well as a large number of coal fires. Similarly, the highest AOD values are observed during the monsoon season among all four seasons over all the mining sites. Raniganj exhibits the highest AOD value at all seasons and at all sites. In contrast, the lowest seasonal AOD values are observed during the post-monsoon season over Raniganj, Talcher, Wardha, Adilabad, Warangal, and Godavari Valley. Similarly, over Jharia, Bokaro, Bishrampur, Korba, and Cuddapah, the lowest AOD values are found in the winter season. Increasing trends in AOD550 have been observed over Raniganj, Bokaro, Bishrampur, Korba, Talcher, and Wardha as well as over Adilabad and Godavari Valley, which is in agreement with previous works. Negative or decreasing AOD trend is found only over Jharia, Warangal, and Cuddapah without being statistically significant. Seasonal trends in AODs have also been studied in the present paper.

Statistical, time series, and fractal analysis of full stretch of river Yamuna (India) for water quality management.

River water is a major resource of drinking water on earth. Management of river water is highly needed for surviving. Yamuna is the main river of India, and monthly variation of water quality of river Yamuna, using statistical methods have been compared at different sites for each water parameters. Regression, correlation coefficient, autoregressive integrated moving average (ARIMA), box-Jenkins, residual autocorrelation function (ACF), residual partial autocorrelation function (PACF), lag, fractal, Hurst exponent, and predictability index have been estimated to analyze trend and prediction of water quality. Predictive model is useful at 95% confidence limits and all water parameters reveal platykurtic curve. Brownian motion (true random walk) behavior exists at different sites for BOD, AMM, and total Kjeldahl nitrogen (TKN). Quality of Yamuna River water at Hathnikund is good, declines at Nizamuddin, Mazawali, Agra D/S, and regains good quality again at Juhikha. For all sites, almost all parameters except potential of hydrogen (pH), water temperature (WT) crosses the prescribed limits of World Health Organization (WHO)/United States Environmental Protection Agency (EPA).