Modelling 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.

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.Electronic supplementary materialThe online version of this article (doi:10.1186/2193-1801-3-657) contains supplementary material, which is available to authorized users.

Face recognition has gained prominence among the various biometric-based methods (such as fingerprint and iris) due to its noninvasive characteristics. Modern face recognition modules/algorithms have been successful in many application areas (access control, entertainment/leisure, security system based on biometric data, and user-friendly human-machine interfaces). In spite of these achievements, the performance of current face recognition algorithms/modules is still inhibited by varying environmental constraints such as occlusions, expressions, varying poses, illumination, and ageing. This study assessed the performance of Principal Component Analysis with singular value decomposition using Fast Fourier Transform (FFT-PCA/SVD) for preprocessing the face recognition algorithm on left and right reconstructed face images. The study found that average recognition rates for the FFT-PCA/SVD algorithm were 95% and 90% when the left and right reconstructed face images are used as test images, respectively. The result of the paired sample t-test revealed that the average recognition distances for the left and right reconstructed face images are not significantly different when FFT-PCA/SVD is used for recognition. FFT-PCA/SVD is recommended as a viable algorithm for recognition of left and right reconstructed face images.

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Experiments have shown that, even one to three day old babies are able to distinguish between known faces (Chiara, Viola, Macchi, Cassia, & Leo, 2006). So how hard could it be for a computer? It has been established that face recognition is a dedicated process in the brain (Marqueś, 2010). Thus the idea of imitating this skill inherent in human beings by machines can be very rewarding though the idea of developing an intelligent and self-learning system may require supply of sufficient information to the machine. This study proposes multivariate statistical evaluation of the recognition performance of Principal Component Analysis and Singular Value Decomposition (PCA/SVD) and a Whitened Principal Component Analysis and Singular Value Decomposition algorithms (Whitened PCA/SVD) under varying environmental constraints. The Repeated Measures Design, Paired Comparison test, Box's M test and Profile Analysis were used for performance evaluation of the algorithms on the merit of efficiency and consistency in recognizing face images with variable facial expressions. The study results showed that, PCA/SVD is consistent and computationally efficient when compared to Whitened PCA/SVD.