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 Annual Proceedings of the South African Statistical Association Conference
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 Congress 1, 2010
Annual Proceedings of the South African Statistical Association Conference  Congress 1, November 2010
Congress 1, November 2010

Volatility modelling using ARIMAGARCH models in a hyperinflationary economic environment : the Zimbabwean experience
Authors: C. Sigauke, D. Maposa, E. Mudimu and P. NyamugureSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 1 –14 (2010)More LessThe use of ARIMAGARCHtype models for modelling volatility in a hyperinflationaty economic environment is investigated. The robustness and resilience of GARCH type models in forecasting conditional mean and volatility of monthly stock prices of eight counters listed on the Zimbabwe Stock Exchange (ZSE) over the period 1993 to 2004 under the assumption of a skewed Student  t distribution is tested. Symmetric and asymmetric GARCH type models are used. The results suggest that the monthly returns are characterized by an ARMA(0,1) process. This means that shocks to conditional mean dissipate after one period. Empirical results show that ARMA(0,1)  TARCH(1,1) model achieves the most accurate volatility forecasts followed by the ARMA(0,1)  GARCH(1,1) model. These results are useful in financial modeling in unstable and hyperinflationary economies.

Crossvalidation selection of the smoothing parameter in nonparametric hazard rate estimation
Author Francois Van GraanSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 15 –22 (2010)More LessAn improved version of the crossvalidation bandwidth selector is proposed by using the technique of bootstrap aggregation. Simulation results show that this selector compares very favorably to a bootstrap bandwidth selector based on an asymptotic representation of the mean weighted integrated squared error for the kernelbased estimator of the hazard rate function in the presence of rightcensored samples.

A "statistical" derivation of the price of a call option
Author F. LombardSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 23 –27 (2010)More LessDetails of the final steps in the derivation of the BlackScholes call option price and the corresponding hedge ratios are rarely given in typical introductorylevel finance textbooks. Readers are often informed that "... the result follows by standard calculus...". In this paper it is shown how the missing details can be filled in by using simple statistical, as opposed to calculus, methods. Nothing more than secondyear university level statistics is required to understand the methodology.

A statistical approach to the analytic hierarchy process
Authors: Gaetan M. Kabera and Linda M. HainesSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 28 –35 (2010)More LessRanking objects compared pairwise according to a single criterion in the Analytic Hierarchy Process generally involves the use of Saaty's eigenvector method (EVM) or, less often, the logarithm least squares method (LLSM). We introduce an approach based on the logistic distribution and compare it to the EVM and the LLSM using a numerical example.

Maximum likelihood estimation in models for binary crossover studies
Authors: G.B. Matthews and N.A.S. CrowtherSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 36 –43 (2010)More LessA maximum likelihood (ML) estimation procedure is presented for the expected frequencies when modelling binary data from twoperiod crossover studies. This procedure provides a simple approach to parameter estimation in models for binary crossover experiments, and in particular for a lognonlinear model proposed by Becker & Balagtas (1993).

Evaluation of noise removal in signals by LULU operators
Authors: I.N. FabrisRotelli, K. Van Oldenmark and P.J. Van StadenSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 44 –51 (2010)More LessThe LULU smoothers are effective nonlinear smoothers for signals. We investigate their ability to remove different noise types, namely symmetrical and skewed, as well as heavy and lighttailed, thereby uncovering the true underlying signal. These smoothers prove very effective in removing noise originating from the same distribution as that noise which originally contaminated the signal.

Doptimal population designs for the simple linear random coefficients regression model
Authors: Legesse Kassa Debusho and Linda M. HainesSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 52 –59 (2010)More LessIn this paper Doptimal population designs for the simple linear random coefficients regression model with values of the explanatory variable taken from a set of equally spaced, nonrepeated time points are considered. The Doptimal designs depend on the values of the variance components and locally optimal designs are therefore considered. It is shown that, if the time points are linearly transformed, then the Doptimal population designs for both the fixed effects and the variance components do not necessarily map onto one another. This result is illustrated numerically by means of a simple example.

Performance of confidence intervals on the among group variance in the unbalanced onefactor random effects model
Authors: M. Van der Rijst, A.J. Van der Merwe and J. HugoSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 60 –67 (2010)More LessThe objective of this paper is to simultaneously compare the performance of six methods for constructing approximate confidence intervals on the amonggroup variance component in a simulation study by using their ability to maintain the stated confidence coefficient as criteria. Results suggest that the generalized confidence interval performs well in all designs considered.

Modelling nutrient concentration to determine the environmental factors influencing grass quality
Authors: N. DudeniTlhone, P. Debba, A. Ramoelo, M.A. Cho and R. MathieuSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 68 –74 (2010)More LessThis paper uses the spatial and the least squares (Analysis of CovarianceANCOVA) regression methods to evaluate the important environmental factors in estimating quality grass for grazing (based on the nitrogen (N) content in grass). The environmental variables such as those based on climate (temperature and precipitation), landuse, geology, slope, aspect and altitude were specifically evaluated in these models. Spatial regression accounted for higher variability (61%) when compared to the 41% variability explained by the ANCOVA model. The models indicate that some environmental variables are useful in assessing N variability. This provides an opportunity for the design of an intergraded system to incorporate both the environmental and remote sensing variables in the estimation and mapping of nitrogen content in grazing grass across the Kruger National Park (KNP) and the surrounding areas.

Meaningful batting averages in cricket
Source: Annual Proceedings of the South African Statistical Association Conference 2010, pp 75 –82 (2010)More LessIn this paper we analyze and compare four different methods, designed to deal with the problem of an inflated batting average due to the presence of a high proportion of notout innings. Batting records from the 2010 IPL are used to illustrate the properties and shortcomings of each method.

Comparison between statistical and optimization methods in accessing unmixing of spectrally similar materials
Authors: Pravesh Debba, James Maina and Elias WillemseSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 83 –90 (2010)More LessThis paper reports on the results from ordinary least squares and ridge regression as statistical methods, and is compared to numerical optimization methods such as the stochastic method for global optimization, simulated annealing, particle swarm optimization and limited memory BroydenFletcherGoldfardSharon bound optimization method. We used each of the above mentioned methods in estimating the abundances of spectrally similar ironbearing oxide/hydroxide/sulfate minerals in complex synthetic mixtures simulated from hyperspectral data. In evaluating the various methods, spectral mixtures were generated with varying linear proportions of individual spectra from the United States Geological Survey (USGS) spectral library. We conclude that ridge regression, simulated annealing and particle swarm optimization outperforms ordinary least squares method and the stochastic method for global optimization algorithms in estimating the partial abundance of each endmember. This result was independent of the error from either a uniform or gaussian distribution. For large remote sensing scenes, typically with millions of pixels and with many endmembers, we recommend using ridge regression.

Mapping the Nyear design rainfall  a case study for the Western Cape
Authors: S. Khuluse, M. Dowdeswell, S. Khuluse, P. Debba and A. SteinSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 91 –100 (2010)More LessFlooding is often associated with heavy rainfall. Hence quantifying the probability associated with heavy rainfall events is useful in hydrology for design flood estimation and mapping. Rainfall varies over time and space, therefore it is anticipated that at high levels the process will also vary over time and space. The objective of this study is to regionally quantify the average size of a 24hour winter rainfall event associated with a 2% chance of being exceeded for an area in the Western Cape, South Africa. The point process approach to extreme value theory is employed to quantify the 50year winter rainfall return level estimate from daily rainfall data from fifteen stations in the Western Cape. Ordinary kriging is used to estimate the 50year winter rainfall return level surface over the study area. We compare the result to those obtained when the universal kriging approach is undertaken. We present a technique used to obtain spatial correlation models used in kriging, where the return level estimates are extended spatiotemporally, to circumvent inaccurate specification of the model and its parameters as a result of the spatial sparseness of the sample.

Maximum likelihood estimation for fractional Gaussian noise
Authors: J.L. Robbertse and F. LombardSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 101 –107 (2010)More LessApproximate normality and unbiasedness of the maximum likelihood estimate (MLE) of the long memory parameter H for a fractional Brownian motion holds reasonably well for sample sizes as small as 20 if the mean and variance are known. However, if the mean and variance are unknown and must also be estimated, the bias and variance of the MLE of H increases. We show that the bias can be reduced by applying a jackknife procedure, and we extend our estimation method to long memory estimation in large samples.

Empirical likelihood for nonparametric models under linear process errors
Author Yongsong QinSource: Annual Proceedings of the South African Statistical Association Conference 2010, pp 108 –113 (2010)More LessIn this paper, we study the construction of confidence intervals for a nonparametric regression function under linear process errors by using the blockwise technique. It is shown that the blockwise empirical likelihood (EL) ratio statistic is asymptotically χ^{2} distributed. The result is used to obtain EL based confidence intervals for the nonparametric regression function.