Felix O. Mettle

A methodology for stochastic analysis of share prices as Markov chains with finite states

Price volatilities make stock investments risky, leaving investors in critical position when uncertain decision is made. To improve investor evaluation confidence on exchange markets, while not using time series methodology, we specify equity price change as a stochastic process assumed to possess Markov dependency with respective state transition probabilities matrices following the identified state pace (i.e. decrease, stable or increase). We established that identified states communicate, and that the chains are aperiodic and ergodic thus possessing limiting distributions. We developed a methodology for determining expected mean return time for stock price increases and also establish criteria for improving investment decision based on highest transition probabilities, lowest mean return time and highest limiting distributions. We further developed an R algorithm for running the methodology introduced. The established methodology is applied to selected equities from Ghana Stock Exchange weekly trading data.

A Study of the Estimation of the Gini Coefficient of Income Using Lorenz Curve

DOI: 10.9734/BJMCS/2016/24494 Editor(s): (1) Sun-Yuan Hsieh, Department of Computer Science and Information Engineering, National Cheng Kung University, Taiwan. Reviewers: (1) Johan Fellman, Swedish School of Economics and Business Administration, Finland. (2) Todd Christopher Headrick, Southern Illinois University Carbondale, USA. Complete Peer review History: http://sciencedomain.org/review-history/13807

Comparison of Least Squares Method and Bayesian with Multivariate Normal Prior in Estimating Multiple Regression Parameters

Based on an assumption of multivariate normal priors for p arameters of multivariate regression model, this study outlines an algorithm for application of traditional Bayesian method to estimate regression parameters. From a given set of data, a Jackknife sample of least squares regression coefficient estimates are obtained and used to derive estimates of the mean vecto r and covariance matrix of the assumed multivariate normal prior distribution of the regression param eters. Driven to determine whether Bayesian methods to multivariate regression parameter estimation present a stable and consistent improvement over classical regression modeling or not, the study results indi cate that the Bayesian method and Least Squares Method (LSM) produced almost the same estimates for the regression parameters and coefficient of determination (to 4.dp) with the Bayesian method having sma ller standard errors.

Extreme value modelling of Ghana stock exchange index

AbstractModelling of extreme events has always been of interest in fields such as hydrology and meteorology. However, after the recent global financial crises, appropriate models for modelling of such rare events leading to these crises have become quite essential in the finance and risk management fields. This paper models the extreme values of the Ghana stock exchange all-shares index (2000–2010) by applying the extreme value theory (EVT) to fit a model to the tails of the daily stock returns data. A conditional approach of the EVT was preferred and hence an ARMA-GARCH model was fitted to the data to correct for the effects of autocorrelation and conditional heteroscedastic terms present in the returns series, before the EVT method was applied. The Peak Over Threshold approach of the EVT, which fits a Generalized Pareto Distribution (GPD) model to excesses above a certain selected threshold, was employed. Maximum likelihood estimates of the model parameters were obtained and the model’s goodness of fit was assessed graphically using Q–Q, P–P and density plots. The findings indicate that the GPD provides an adequate fit to the data of excesses. The size of the extreme daily Ghanaian stock market movements were then computed using the value at risk and expected shortfall risk measures at some high quantiles, based on the fitted GPD model.

Large Deviation Principle for the Empirical Degree Measure of Preferential Attachment Random Graphs

We consider preferential attachment random graphs which may be obtained as follows: It starts with a single node. If a new node appears, it is linked by an edge to one or more existing node(s) with a probability proportional to function of their degree. For a class of linear preferential attachment random graphs we find a large deviation principle (LDP) forthe empirical degree measure. In the course of the prove this LDP we establish an LDP for the empirical degree and pair distribution see Theorem 2.3, of the fitness preferential attachment model of random graphs.