Milton Abdul Thorlie’s research while affiliated with Dalian University of Technology and other places

The present penalized quantile variable selection methods are only applicable to finite number of predictors or do not have oracle property associated with estimator. This technique is considered as an alternative to ordinary least squares regression in case of the outliers and the heavy-tailed errors existing in linear models. The variable selection through quantile regression with diverging number of parameters is investigated in this paper. The convergence rate of estimator with smoothly clipped absolute deviation penalty function is also studied. Moreover, the oracle property with proper selection of tuning parameter for quantile regression under certain regularity conditions is also established. In addition, the rank correlation screening method is used to accommodate ultra-high dimensional data settings. Monte Carlo simulations demonstrate finite performance of the proposed estimator. The results of real data reveal that this approach provides substantially more information as compared with ordinary least squares, conventional quantile regression, and quantile lasso.

This article examines volatility models for modeling and forecasting the Standard & Poor 500 (S&P 500) daily stock index returns, including the autoregressive moving average, the Taylor and Schwert generalized autoregressive conditional heteroscedasticity (GARCH), the Glosten, Jagannathan and Runkle GARCH and asymmetric power ARCH (APARCH) with the following conditional distributions: normal, Student’s t and skewed Student’s t-distributions. In addition, we undertake unit root (augmented Dickey–Fuller and Phillip–Perron) tests, co-integration test and error correction model. We study the stationary APARCH (p) model with parameters, and the uniform convergence, strong consistency and asymptotic normality are prove under simple ordered restriction. In fitting these models to S&P 500 daily stock index return data over the period 1 January 2002 to 31 December 2012, we found that the APARCH model using a skewed Student’s t-distribution is the most effective and successful for modeling and forecasting the daily stock index returns series. The results of this study would be of great value to policy makers and investors in managing risk in stock markets trading.

The quantile regression technique is considered as an alternative to the classical ordinary least squares (OLS) regression in case of outliers and heavy tailed errors existing in linear models. In this work, the consistency, asymptotic normality, and oracle property are established for sparse quantile regression with a diverging number of parameters. The rate of convergence of the combined penalized estimator is also established. Furthermore, the rank correlation screening (RCS) method is applied to deal with an ultrahigh dimensional data. The simulation studies, the analysis of hedonic housing prices and the demand for clean air dataset are conducted to illustrate the finite sample performance of the proposed method.

This article examines the accuracy and forecasting performance of volatility models for the Leones/USA dollars exchange rate return, including the ARMA, Generalized Autoregressive Conditional Heteroscedasticity (GARCH), and Asymmetric GARCH models with normal and non-normal (student's t and skewed Student t) distributions. In fitting these models to the monthly exchange rate returns data over the period January 2004 to December 2013, we found that, the Asymmetric (GARCH) and GARCH model better fits under the non-normal distribution than the normal distribution and improve the overall estimation for measuring conditional variance. The GJR-GARCH model using the skewed Student t-distribution is most successful and better forecast the Sierra Leone exchange rate volatility. Finally, the study suggests that the given models are suitable for modeling the exchange rate volatility of Sierra Leone and the Asymmetric GARCH models shows asymmetric in exchange rate returns, resulting to the presence of leverage effect. Given the implication of exchange rate volatility, the study would be of great value to policy makers, investors and researchers at home and abroad in promoting development of the capital market and foreign exchange market stability in emerging economies.