The current research aimed to monitor and assess the heavy metal contamination in the surface water of 53 sampling sites along the selected rivers using principal component analysis and cluster analysis. For this purpose, both physiochemical parameters such as the temperature (T), the potential of hydrogen (pH), total dissolved solids (TDS) and electroconductivity (EC), and heavy metals such as iron (Fe), chromium (Cr), nickel (Ni), cadmium (Cd), lead (Pb) and arsenic (As) are analyzed as potential water contaminants. The average values of pH, TDS, EC and T are found at 7.75, 70.89 mg/L, 139.11 µs/cm and 20.29 °C, respectively, and heavy metals including Cr, Ni, Cd, Pb, As and Fe are observed at 0.04, 0.04, 0.04, 0.03, 0.001 and 0.04 mg/L, respectively. Moreover, it is found that in both rivers hazardous metals, including Cr (100%), Cd (92.30%), Pb (100%), Ni (100%) and Fe (91%), exceed the permissible limits of the WHO.

Based on different surveys, dairy farmers are concerned about extensive use of exogenous oxytocin in buffaloes, which is being held responsible for reproductive problems including irregular oestrous cycle and delayed ovulation. For these concerns, effects of oxytocin injection on postpartum follicular dynamics, postpartum oestrous interval (PEI), oestrous length, the interval from onset of ostrus to ovulation and blood progesterone (P4) were studied in Nili-Ravi buffaloes. For this purpose, 23 animals within 1 week after calving were randomly divided into three groups: without oxytocin (CON; n = 7), 10 i.u. oxytocin (LOW; n = 8), 30 i.u. oxytocin – (HIGH; n = 8) and used to record the PEI for the study period of 154 days. At subsequent estrus, three buffaloes from each group (not served) were selected randomly to monitor two cycles for 6 weeks. Transrectal ultrasonography was performed to evaluate follicular and corpus luteum (CL) development, and blood sampling was done for progesterone (P4) analysis. These results revealed that postpartum oestrous interval (PEI) decreased significantly in oxytocin-treated groups. The number of small, medium and total follicles on the left ovary was significantly higher in the HIGH group. However, an overall number of small and total follicles on both right and left ovaries was significantly higher in CON and HIGH groups. On the other hand, there was no difference in the number of follicles on the right ovary among all treatment groups. The same was true for the size of pre-ovulatory follicles, CL, P4 concentrations and oestrous cycle length. The intervals from onset of estrus to ovulation and from standing estrus to ovulation were increased considerably in the HIGH group. It is concluded that exogenous oxytocin administration resulted in the shortening of PEI but triggered a delay in ovulation. Moreover, a higher dose of oxytocin could stimulate the growth of small, medium, and total follicles in postpartum Nili-Ravi buffaloes.

The quantitative description of meteorological drought from various geographical locations and indicators is crucial for early drought warning to avoid its negative impacts. Therefore, the current study proposes a new framework to comprehensively accumulate spatial and temporal information for meteorological drought from various stations and drought indicators (indices). The proposed framework is based on two major components such as the Monthly-based Monte Carlo Feature Selection (MMCFS,) and Monthly-based Joint Index Weights (MJIW). Besides, three commonly used SDI are jointly assessed to quantify drought for selected geographical locations. Moreover, the current study uses the monthly data from six meteorological stations in the northern region for 47 years (1971-2017) for calculating SDI values. The outcomes of the current research explicitly accumulate regional spatiotemporal information for meteorological drought. In addition, results may serve as an early warning to the effective management of water resources to avoid negative drought impacts in Pakistan.

Neighbor designs are popular to control neighbor effects. Among neighbor designs, strongly balanced neighbor designs are important to estimate treatment effects and neighbor effects independently. Minimal circular strongly balanced neighbor designs (MCSBNDs) can be obtained only for odd v (number of treatments). For v even, minimal circular nearly strongly balanced neighbor designs are used which satisfied all conditions of MCSBNDs except that the treatment labeled as (v − 1) does not appear as its own neighbor. These designs can be converted directly in some other useful classes of neighbor designs. These designs are efficient to minimize the bias due to the neighbor effects.

The experiments where response of a treatment (direct effect) is affected by the treatment(s) applied in neighboring units, neighbor designs are used to balance the neighbor effects. Being the economical, minimal neighbor designs are preferred by the experimenters. Minimal circular neighbor designs could not be constructed for almost every case of v even, where v is number of treatments. For v even, minimal circular generalized neighbor designs are preferred. In this article, algorithms are developed to obtain minimal circular generalized neighbor designs in which (a) v/2 of the unordered pairs, and (b) 3v/2 of the unordered pairs, do not appear as neighbor whereas the remaining ones appear once. These algorithms are also coded with R-language.

This paper proposes a new approach for the generalization of Poisson regression for count time series data typically sampled at different frequencies to improve the forecasting accuracy of dengue cases in Pakistan. Mixed data sampling (MIDAS) was introduced in the context of Poisson regression because it enables us to model and forecast dengue events more accurately. Different polynomial weights selected from the literature are applied in the MIDAS and U-MIDAS settings, and different forecast combinations are used to improve the forecasting accuracy of dengue event counts. For the 2006–2017 period, the proposed model correctly forecasts significantly more dengue cases than does the standard Poisson regression model for all forecasting horizons. Furthermore, Google Trends data can be a usefuladdition to traditional numeric data for forecasting dengue cases.

This thesis consists of four research articles. The first two articles assess the effectiveness of various shrinkage estimation methods within mixed data sampling (MIDAS) regression models and find that our proposed methods have superior performance compared to existing models. The third article extends MIDAS models to encompass count data, and the fourth article evaluates the performance of a specific proposed shrinkage method in forecasting stock price volatility.

In the first article, which focuses on MIDAS regression in a nonparametric way, two-parameter nonparametric shrinkage estimation methods are developed to estimate the MIDAS regression parameters. The proposed methodology is compared with one-parameter nonparametric and parametric MIDAS regression, both theoretically via simulation and practically in terms of forecasting U.S. inflation rates. The proposed two-parameter estimator outperforms the one-parameter estimator and other comparative methods, both theoretically and empirically.

In the second article, the two-dimensional panel data regression model is extended to a multidimensional context for mixed-frequency data. We use the least absolute shrinkage and selection operator (LASSO), sparse group (sg)-LASSO, and elastic net unrestricted MIDAS (U-MIDAS) for estimation. The theoretical properties of the extended models are evaluated using Monte Carlo simulations. The proposed model is empirically applied to now cast three-dimensional home ownership vacancy rates across states, metropolitan statistical areas (MSAs), and time in the U.S. Finally, we compare the predictive performance of this extended model with the traditional three-dimensional panel data regression model. The extended model demonstrates superior performance over traditional multidimensional methods, both theoretically and empirically.

The third article introduces a generalized Poisson regression model for count time series data, applied within a MIDAS framework. The new MIDAS Poisson regression model (MIDAS-PRM) is used to forecast the monthly dengue counts from high-frequency environmental parameters and Google Trends data.

Forecasts are generated using a rolling window forecast scheme and forecast combinations. We conclude that the proposed MIDAS-PRM significantly enhances predictive performance compared to the standard time series PRM and other benchmark time series models.

The fourth article proposes two-parameter ridge shrinkage estimation methods to estimate the realized volatility (RV) of the heterogeneous autoregressive (HAR) model. The proposed estimator, which is notable for its orthogonality properties, is employed to forecast the RV of stock prices. The proposed estimator is evaluated through simulations and empirical applications, demonstrating superior performance both theoretically and empirically compared to traditional methods.

We expanded the use of structured machine learning in regression for nowcasting by utilizing multidimensional panel data. Our primary goal was to predict home ownership vacancy rates across various states and metropolitan statistical areas, especially when key economic data are sampled at mixed frequencies. We successfully employed our proposed extended multidimensional machine learning panel data model to forecast the three-dimensional home ownership vacancy rate in the United States. The results suggest that our extended multidimensional time series regression model is very useful for nowcasting/forecasting home ownership vacancy rates and for performing better than does the traditional time series regression model. Our results are general, and our extended multidimensional time series regression model can be applied to any multidimensional macroeconomic problem.

The heterogeneous autoregressive (HAR) model, applied to the realized volatility (RV) of financial time series, is specifically designed to capture both the persistent memory and the time-varying dynamically evolving nature of volatility clustering characteristics in financial time-series data. Typically, HAR models establish a linear relationship linking the current and past RVs using ordinary least squares (OLS) for estimation. However, this methodology might exhibit reduced reliability when RV data encounter abrupt and enduring shocks. To address this issue, we introduce a two-parameter shrinkage estimator for the HAR-RV model, incorporating two additional variables for sudden shocks to capture the broader spectrum of market behavior and conditions. This estimator effectively mitigates overparameterization issues and exhibits superior properties in scenarios involving sudden market changes and underlying trends. This enhancement not only improves the model’s goodness of fit but also improves the accuracy of out-of-sample forecasts. We apply our estimator to forecast financial time series, with the empirical results demonstrating superior forecasting performance in terms of improved out-of-sample R² values, corroborating our theoretical insights andsimulation studies.

Instead of applying the commonly used parametric Almon or Beta lag distribution of MIDAS, Breitung and Roling (J Forecast 34:588–603, 2015) suggested a nonparametric smoothed least-squares shrinkage estimator (henceforth SLS1) for estimating mixed-frequency models. This SLS1 approach ensures a flexible smooth trending lag distribution. However, even if the biasing parameter in SLS1 solves the overparameterization problem, the cost is a decreased goodness-of-fit. Therefore, we suggest a modification of this shrinkage regression into a two-parameter smoothed least-squares estimator (SLS2). This estimator solves the overparameterization problem, and it has superior properties since it ensures that the orthogonality assumption between residuals and the predicted dependent variable holds, which leads to an increased goodness-of-fit. Our theoretical comparisons, supported by simulations, demonstrate that the increase in goodness-of-fit of the proposed two-parameter estimator also leads to a decrease in the mean square error of SLS2, compared to that of SLS1 . Empirical results, where the inflation rate is forecasted based on the oil returns, demonstrate that our proposed SLS2 estimator for mixed-frequency models provides better estimates in terms of decreased MSE and improved R2, which in turn leads to better forecasts.

In this article, we propose Liu-type shrinkage estimators for the zero-inflated Poisson regression (ZIPR) model in the presence of multicollinearity. Our new approach is a remedy to the problem of inflated variances for the ML estimation technique—which is a standard approach to estimate these types of count data models. When the data are in the form of non-negative integers with a surplus of zeros it induces overdispersion in the dependent variable. Considerable multicollinearity is frequently observed, but usually disregarded, for these types of data sets. Based on a Monte Carlo study we illustrate that our proposed estimators exhibit better MSE and MAE than the usual ML estimator and some other Liu estimators in the presence of multicollinearity. To demonstrate the advantages and the empirical relevance of our improved estimators, maternal death data are analyzed and the results illustrate similar benefits as is demonstrated in our simulation study.

Agricultural production is greatly influenced by environmental parameters such as temperature, rainfall, humidity, and wind speed. The accurate information about environmental parameters plays a vital and useful role when making policies for the agriculture sector as well as for other sectors. Pakistan meteorological department observed these environmental parameters at more than 90 stations. The allocation of these monitoring stations is not made systematically correct. This leads to inaccurate predictions for unobserved locations. The study aims to propose a monitoring network by which these prediction errors of the environmental parameters can be minimized. The well-known prediction techniques named, model-based ordinary kriging and model-based universal kriging (UK) with the known Matheron variogram model are used for prediction purposes. We investigate the monitoring network of Pakistan for rainfall and focus on both the optimal deletion/addition of monitoring stations from/to this network. The two stochastic search algorithms, spatial simulated annealing, and genetic algorithm are used for optimization purposes. Furthermore, the minimization of the Average Kriging Variance (AKV) is taken as the interpolation accuracy measure. The spatial simulated annealing exhibits a lower AKV as compared to the Genetic algorithm when adding/removing the optimal/redundant locations from the monitoring network.

Livestock plays a vital role in Pakistan’s economy. Buffalo is the primary source of milk and meat, which is a basic need for human health. So, there is a need to forecast the buffalo population of Pakistan. The main objective of the current study is to determine an appropriate empirical model for forecasting buffalo population of Pakistan to assess its future trend up to the year 2030. We apply different Autoregressive Integrated Moving Average (ARIMA) models on the buffalo population-based on fifty-years’ time-series dataset. Different model selection criteria are used to test the reliability of the ARIMA models. Based on these criteria, we perceive that ARIMA (1, 0, 0) is a more suitable model. Moreover, we also test the fitted model assumptions, such as normality and independence, to find out more accurate forecasted values. This study revealed that the buffalo population expected to increase 30% up to the year 2030 under the assumption that there is no irregular trend can be encountered during forecasted years.

This article introduces some Liu parameters in the linear regression model based on the work of Shukur, Månsson, and Sjölander. These methods of estimating the Liu parameter d increase the efficiency of Liu estimator. The comparison of proposed Liu parameters and available methods has done using Monte Carlo simulation and a real data set where the mean squared error, mean absolute error and interval estimation are considered as performance criterions. The simulation study shows that under certain conditions the proposed Liu parameters perform quite well as compared to the ordinary least squares estimator and other existing Liu parameters. 

Drought is one of the disastrous natural hazards with complex seasonal and spatial patterns. Understanding the spatial patterns of drought and predicting the likelihood of inter-seasonal drought persistence can provide substantial operational guidelines for water resource management and agricultural production. This study examines drought persistence by identifying the spatial patterns of seasonal drought frequency and inter-seasonal drought persistence in the northeastern region of Pakistan. The Standardized Precipitation Index (SPI) with a three-month time scale is used to examine meteorological drought. Furthermore, Bayesian logistic regression is used to calculate the probability and odds ratios of drought occurrence in the current season, given the previous season's SPI values. For instance, at Balakot station, for the summer-to-autumn season, the value of the odds ratio is significant (6.78). It shows that one unit increase in SPI of the summer season will cause a 5.78 times to increase in odds of autumn drought occurrence. The average drought frequency varies from 37.3 to 89.1%, whereas the average inter-seasonal drought persistence varies from 21.9 to 91.7% in the study region. Results indicate that some areas in the study region, like Kakul and Garhi Dupatta, are more prone to drought and vulnerable to inter-seasonal drought persistence. Furthermore, the Bayesian logistic regression results reveal a negative relationship between spring drought occurrence and winter SPI, demonstrating that the overall study region is more prone to winter-to-spring drought persistence and less vulnerable to summer-to-autumn drought persistence. Overall study has concluded that the region's seasonal drought forecast is challenging due to uncertain drought persistence patterns. However, the Bayesian logistic regression model provides more accurate and precise regional seasonal drought forecasts. The outcome of the present study provides scientific evidence to develop early warning systems and manage seasonal crops in Pakistan.

The actual impact of landslides in Pakistan is highly underestimated and has not been addressed to its full extent. This study focuses on the impact which landslides had in the last 17 years, with focus on mortality, gender of deceased, main triggers (landslides and fatal landslides), and regional identification of the hotspots in Pakistan. Our study identified 1089 landslides (including rockfalls, rockslides, mudslides, mudflows, debris flows) out of which 180 landslides were fatal and claimed lives of 1072 people. We found that rain (rainfall and heavy rainfall)-related landslides were the deadliest over the entire study period. The main trigger of landslides in Pakistan is heavy rainfall which comprises over 50% of the triggers for the landslide, and combined with normal rainfall, this rate climbs to over 63%. The second main reason for landslide occurrence is spontaneous (due to rock instability, erosion, climate change, and other geological elements) with landslides accounting for 22.3% of all the landslides. Landslides caused by rain-related events amounted to 41.67% of the fatalities, whereas spontaneous landslides caused 29.44% of the deaths and the human induced events accounted for 25.5% of the fatalities. The fatal landslides accounted for 19.53% deaths of the children. Our study also found that more than 48% of the deadly landslides occurred between the months of January to April, whereas the least fatal landslides occurred in the month of June which accounted for only 3% of all the fatal landslides in Pakistan.

The coronavirus pandemic (COVID-19) has impacted the usual global movement patterns, atmospheric pollutants, and climatic parameters. The current study sought to assess the impact of the COVID-19 lockdown on urban mobility, atmospheric pollutants, and Pakistan’s climate. For the air pollution assessment, total column ozone (O3), sulphur dioxide (SO2), and tropospheric column nitrogen dioxide (NO2) data from the Ozone Monitoring Instrument (OMI), aerosol optical depth (AOD) data from the Multi-angle Imaging Spectroradiometer (MISR), and dust column mass density (PM2.5) data from the MERRA-2 satellite were used. Furthermore, these datasets are linked to climatic parameters (temperature, precipitation, wind speed). The Kruskal–Wallis H test (KWt) is used to compare medians among k groups (k > 2), and the Wilcoxon signed-rank sum test (WRST) is for analyzing the differences between the medians of two datasets. To make the analysis more effective, and to justify that the variations in air quality parameters are due to the COVID-19 pandemic, a Generalized Linear Model (GLM) was used. The findings revealed that the limitations on human mobility have lowered emissions, which has improved the air quality in Pakistan. The results of the study showed that the climatic parameters (precipitation, Tmax, Tmin, and Tmean) have a positive correlation and wind speed has a negative correlation with NO2 and AOD. This study found a significant decrease in air pollutants (NO2, SO2, O3, AOD) of 30–40% in Pakistan during the strict lockdown period. In this duration, the highest drop of about 28% in NO2 concentrations has been found in Karachi. Total column O3 did not show any reduction during the strict lockdown, but a minor decline was depicted as 0.38% in Lahore and 0.55% in Islamabad during the loosening lockdown. During strict lockdown, AOD was reduced up to 23% in Islamabad and 14.46% in Lahore. The results of KWt and WRST evident that all the mobility indices are significant (p < 0.05) in nature. The GLM justified that restraining human activities during the lockdown has decreased anthropogenic emissions and, as a result, improved air quality, particularly in metropolitan areas.