Farhat Iqbal

Pollution Status of Pakistan: A Retrospective Review on Heavy Metal Contamination of Water, Soil, and Vegetables

Trace heavy metals, such as arsenic, cadmium, lead, chromium, nickel, and mercury, are important environmental pollutants, particularly in areas with high anthropogenic pressure. In addition to these metals, copper, manganese, iron, and zinc are also important trace micronutrients. The presence of trace heavy metals in the atmosphere, soil, and water can cause serious problems to all organisms, and the ubiquitous bioavailability of these heavy metal can result in bioaccumulation in the food chain which especially can be highly dangerous to human health. This study reviews the heavy metal contamination in several areas of Pakistan over the past few years, particularly to assess the heavy metal contamination in water (ground water, surface water, and waste water), soil, sediments, particulate matter, and vegetables. The listed contaminations affect the drinking water quality, ecological environment, and food chain. Moreover, the toxicity induced by contaminated water, soil, and vegetables poses serious threat to human health.

Diagnostic Checking for GARCH-Type Models

The asymptotic distributions of squared and absolute residual autocorrelations for GARCH model estimated by M-estimators are derived. Two diagnostic tests are developed which can be used to check the adequacy of GARCH model fitted by using M-estimators. Simulation results show that the empirical sizes of both tests are close to the nominal size in most of the cases. The power of test based on absolute residual autocorrelation is found better than test based on squared residual autocorrelations. Our results reveal that there are estimators that can fit GARCH-type models better than the commonly used quasi-maximum likelihood estimator under non normal errors. An application to real data set is also presented.

Robust Estimation for the Orthogonal GARCH Model

In this paper, we propose a class of robust M‐estimators for the orthogonal generalized autoregressive conditional heteroscedastic (GARCH) model. The method involves the estimation of only univariate GARCH models and hence easy to estimate and does not put additional constraints on the model. The forecasting performance of the class of robust estimators in predicting correlation and value‐at‐risk using various evaluation measures are investigated. We found empirical evidences of the better predictive potential of estimators such as least absolute deviation and B‐estimator over the widely used quasi‐maximum likelihood estimator when the error distribution is heavy‐tailed and asymmetric. Applications to real data sets are also presented.

A Weighted Linear Estimator of Multivariate ARCH Parameters

A weighted linear estimator (WLE) of the parameters of multivariate ARCH models is proposed. The accuracy of WLE in estimating the parameters of multivariate ARCH models is compared with the widely used quasi-maximum likelihood estimator (QMLE) through simulations. Application to real data sets are also presented and forecasts of variance-covariance matrix and value-at-risk (VaR) are obtained. The weighted resampling methods are used to approximate the sampling distribution of the proposed estimator. Our study indicates that the forecasting performance of WLE is not inferior and one-day ahead risk estimates are also found better than the QMLE.