Browsing by Author "Karangwa, Innocent"

Now showing 1 - 3 of 3
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    Comparing South African financial markets behaviour to the geometric Brownian Motion Process
    (University of the Western Cape, 2008) Karangwa, Innocent; Visser, Chris; Dept. of Statistics
    This study examines the behaviour of the South African financial markets with regards to the Geometric Brownian motion process. It uses the daily, weekly, and monthly stock returns time series of some major securities trading in the South African financial market, more specifically the US dollar/Euro, JSE ALSI Total Returns Index, South African All Bond Index, Anglo American Corporation, Standard Bank, Sasol, US dollar Gold Price , Brent spot oil price, and South African white maize near future. The assumptions underlying the Geometric Brownian motion in finance, namely the stationarity, the normality and the independence of stock returns, are tested using both graphical (histograms and normal plots) and statistical test (Kolmogorov-Simirnov test, Box-Ljung statistic and Augmented Dickey-Fuller test) methods to check whether or not the Brownian motion as a model for South African financial markets holds. The Hurst exponent or independence index is also applied to support the results from the previous test. Theoretically, the independent or Geometric Brownian motion time series should be characterised by the Hurst exponent of ½. A value of a Hurst exponent different from that would indicate the presence of long memory or fractional Brownian motion in a time series. The study shows that at least one assumption is violated when the Geometric Brownian motion process is examined assumption by assumption. It also reveals the presence of both long memory and random walk or Geometric Brownian motion in the South African financial markets returns when the Hurst index analysis is used and finds that the Currency market is the most efficient of the South African financial markets. The study concludes that although some assumptions underlying the rocess are violated, the Brownian motion as a model in South African financial markets can not be rejected. It can be accepted in some instances if some parameters such as the Hurst exponent are added.
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    Imputation techniques for non-ordered categorical missing data
    (University of the Western Cape, 2016) Karangwa, Innocent; Kotze, Danelle; Blignaut, Renette
    Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of missing data may lead to bias in the estimates and incorrect inferences. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to impute or fills in missing data. The former assumes a normal distribution of the variables in the imputation model, but can also handle missing data whose distributions are not normal. The latter fills in missing values taking into account the distributional form of the variables to be imputed. The aim of this study was to determine the performance of these methods when data are missing at random (MAR) or completely at random (MCAR) on unordered or nominal categorical variables treated as predictors or response variables in the regression models. Both dichotomous and polytomous variables were considered in the analysis. The baseline data used was the 2007 Demographic and Health Survey (DHS) from the Democratic Republic of Congo. The analysis model of interest was the logistic regression model of the woman’s contraceptive method use status on her marital status, controlling or not for other covariates (continuous, nominal and ordinal). Based on the data set with missing values, data sets with missing at random and missing completely at random observations on either the covariates or response variables measured on nominal scale were first simulated, and then used for imputation purposes. Under MVNI method, unordered categorical variables were first dichotomised, and then K − 1 (where K is the number of levels of the categorical variable of interest) dichotomised variables were included in the imputation model, leaving the other category as a reference. These variables were imputed as continuous variables using a linear regression model. Imputation with MICE considered the distributional form of each variable to be imputed. That is, imputations were drawn using binary and multinomial logistic regressions for dichotomous and polytomous variables respectively. The performance of these methods was evaluated in terms of bias and standard errors in regression coefficients that were estimated to determine the association between the woman’s contraceptive methods use status and her marital status, controlling or not for other types of variables. The analysis was done assuming that the sample was not weighted fi then the sample weight was taken into account to assess whether the sample design would affect the performance of the multiple imputation methods of interest, namely MVNI and MICE. As expected, the results showed that for all the models, MVNI and MICE produced less biased smaller standard errors than the case deletion (CD) method, which discards items with missing values from the analysis. Moreover, it was found that when data were missing (MCAR or MAR) on the nominal variables that were treated as predictors in the regression model, MVNI reduced bias in the regression coefficients and standard errors compared to MICE, for both unweighted and weighted data sets. On the other hand, the results indicated that MICE outperforms MVNI when data were missing on the response variables, either the binary or polytomous. Furthermore, it was noted that the sample design (sample weights), the rates of missingness and the missing data mechanisms (MCAR or MAR) did not affect the behaviour of the multiple imputation methods that were considered in this study. Thus, based on these results, it can be concluded that when missing values are present on the outcome variables measured on a nominal scale in regression models, the distributional form of the variable with missing values should be taken into account. When these variables are used as predictors (with missing observations), the parametric imputation approach (MVNI) would be a better option than MICE.
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    Multiple imputation of unordered categorical missing data: A comparison of the multivariate normal imputation and multiple imputation by chained equations
    (Brazilian Statistical Association, 2016) Karangwa, Innocent; Kotze, Danelle; Blignaut, Renette
    . Missing data are common in survey data sets. Enrolled subjects do not often have data recorded for all variables of interest. The inappropriate handling of them may negatively affect the inferences drawn. Therefore, special attention is needed when analysing incomplete data. The multivariate normal imputation (MVNI) and the multiple imputation by chained equations (MICE) have emerged as the best techniques to deal with missing data. The former assumes a normal distribution of the variables in the imputation model and the latter fills in missing values taking into account the distributional form of the variables to be imputed. This study examines the performance of these methods when data are missing at random on unordered categorical variables treated as predictors in the regression models. First, a survey data set with no missing values is used to generate a data set with missing at random observations on unordered categorical variables.