Theses and Dissertations (Mathematical Sciences)
http://hdl.handle.net/10500/3017
Wed, 10 Feb 2016 06:48:59 GMT2016-02-10T06:48:59ZForecasting annual tax revenue of the South African taxes using time series Holt-Winters and ARIMA/SARIMA Models
http://hdl.handle.net/10500/19903
Forecasting annual tax revenue of the South African taxes using time series Holt-Winters and ARIMA/SARIMA Models
Makananisa, Mangalani P.
This study uses aspects of time series methodology to model and forecast major taxes such as Personal Income Tax (PIT), Corporate Income Tax (CIT), Value Added Tax (VAT) and Total Tax Revenue(TTAXR) in the South African Revenue Service (SARS).
The monthly data used for modeling tax revenues of the major taxes was drawn from January 1995 to March 2010 (in sample data) for PIT, VAT and TTAXR. Due to higher volatility and emerging negative values, the CIT monthly data was converted to quarterly data from the rst quarter of 1995 to the rst quarter of 2010. The competing ARIMA/SARIMA and Holt-Winters models were derived, and the resulting model of this study was used to forecast PIT, CIT, VAT and TTAXR for SARS fiscal years 2010/11, 2011/12 and 2012/13. The results show that both the SARIMA and Holt-Winters models perform well in modeling and forecasting PIT and VAT, however the Holt-Winters model outperformed the SARIMA model in modeling and forecasting the more volatile CIT and TTAXR. It is recommended that these methods are used in forecasting future payments, as they are precise about forecasting tax revenues, with minimal errors and fewer model revisions being necessary.
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10500/199032015-10-01T00:00:00ZPricing outside barrier options when the monitoring of the barrier starts at a hitting time
http://hdl.handle.net/10500/19730
Pricing outside barrier options when the monitoring of the barrier starts at a hitting time
Mofokeng, Jacob Moletsane
This dissertation studies the pricing of Outside barrier call options, when their activation starts at a
hitting time. The pricing of Outside barrier options when their activation starts at time zero, and the
pricing of standard barrier options when their activation starts at a hitting time of a pre speci ed
barrier level, have been studied previously (see [21], [24]).
The new work that this dissertation will do is to price Outside barrier call options, where they will be
activated when the triggering asset crosses or hits a pre speci ed barrier level, and also the pricing of
Outside barrier call options where they will be activated when the triggering asset crosses or hits a
sequence of two pre specifed barrier levels. Closed form solutions are derived using Girsanov's theorem
and the re
ection principle. Existing results are derived from the new results, and properties of the new
results are illustrated numerically and discussed.
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10500/197302015-02-01T00:00:00ZCanonical correlation analysis of aggravated robbery and poverty in Limpopo Province
http://hdl.handle.net/10500/19629
Canonical correlation analysis of aggravated robbery and poverty in Limpopo Province
Rwizi, Tandanai
The study was aimed at exploring the relationship between poverty and aggravated
robbery in Limpopo Province. Sampled secondary data of aggravated robbery of-
fenders, obtained from the South African Police (SAPS), Polokwane, was used in the
analysis. From empirical researches on poverty and crime, there are some deductions
that vulnerability to crime is increased by poverty. Poverty set was categorised by
gender, employment status, marital status, race, age and educational attainment.
Variables for aggravated robbery were house robbery, bank robbery, street/common
robbery, carjacking, truck hijacking, cash-in-transit and business robbery. Canonical
correlation analysis was used to make some inferences about the relationship of these
two sets. The results revealed a signi cant positive correlation of 0.219(p-value =
0.025) between poverty and aggravated robbery at ve per cent signi cance level. Of
the thirteen variables entered into the poverty-aggravated model, ve emerged as sta-
tistically signi cant. These were gender, marital status, employment status, common robbery and business robbery.
Fri, 01 May 2015 00:00:00 GMThttp://hdl.handle.net/10500/196292015-05-01T00:00:00ZStatistical modelling of return on capital employed of individual units
http://hdl.handle.net/10500/19627
Statistical modelling of return on capital employed of individual units
Burombo, Emmanuel Chamunorwa
Return on Capital Employed (ROCE) is a popular financial instrument and communication tool for the appraisal of companies. Often, companies management and other practitioners use untested rules and behavioural approach when investigating the key determinants of ROCE, instead of the scientific statistical paradigm. The aim of this dissertation was to identify and quantify key determinants of ROCE of individual companies listed on the Johannesburg Stock Exchange (JSE), by comparing classical multiple linear regression, principal components regression, generalized least squares regression, and robust maximum likelihood regression approaches in order to improve companies decision making. Performance indicators used to arrive at the best approach were coefficient of determination ( ), adjusted ( , and Mean Square Residual (MSE). Since the ROCE variable had positive and negative values two separate analyses were done.
The classical multiple linear regression models were constructed using stepwise directed search for dependent variable log ROCE for the two data sets. Assumptions were satisfied and problem of multicollinearity was addressed. For the positive ROCE data set, the classical multiple linear regression model had a of 0.928, an of 0.927, a MSE of 0.013, and the lead key determinant was Return on Equity (ROE),with positive elasticity, followed by Debt to Equity (D/E) and Capital Employed (CE), both with negative elasticities. The model showed good validation performance. For the negative ROCE data set, the classical multiple linear regression model had a of 0.666, an of 0.652, a MSE of 0.149, and the lead key determinant was Assets per Capital Employed (APCE) with positive effect, followed by Return on Assets (ROA) and Market Capitalization (MC), both with negative effects. The model showed poor validation performance. The results indicated more and less precision than those found by previous studies. This suggested that the key determinants are also important sources of variability in ROCE of individual companies that management need to work with.
To handle the problem of multicollinearity in the data, principal components were selected using Kaiser-Guttman criterion. The principal components regression model was constructed using dependent variable log ROCE for the two data sets. Assumptions were satisfied. For the positive ROCE data set, the principal components regression model had a of 0.929, an of 0.929, a MSE of 0.069, and the lead key determinant was PC4 (log ROA, log ROE, log Operating Profit Margin (OPM)) and followed by PC2 (log Earnings Yield (EY), log Price to Earnings (P/E)), both with positive effects. The model resulted in a satisfactory validation performance. For the negative ROCE data set, the principal components regression model had a of 0.544, an of 0.532, a MSE of 0.167, and the lead key determinant was PC3 (ROA, EY, APCE) and followed by PC1 (MC, CE), both with negative effects. The model indicated an accurate validation performance. The results showed that the use of principal components as independent variables did not improve classical multiple linear regression model prediction in our data. This implied that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with.
Generalized least square regression was used to assess heteroscedasticity and dependences in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the weighted generalized least squares regression model had a of 0.920, an of 0.919, a MSE of 0.044, and the lead key determinant was ROE with positive effect, followed by D/E with negative effect, Dividend Yield (DY) with positive effect and lastly CE with negative effect. The model indicated an accurate validation performance. For the negative ROCE data set, the weighted generalized least squares regression model had a of 0.559, an of 0.548, a MSE of 57.125, and the lead key determinant was APCE and followed by ROA, both with positive effects.The model showed a weak validation performance. The results suggested that the key determinants are less important sources of variability in ROCE of individual companies that management need to work with. Robust maximum likelihood regression was employed to handle the problem of contamination in the data. It was constructed using stepwise directed search for dependent variable ROCE for the two data sets. For the positive ROCE data set, the robust maximum likelihood regression model had a of 0.998, an of 0.997, a MSE of 6.739, and the lead key determinant was ROE with positive effect, followed by DY and lastly D/E, both with negative effects. The model showed a strong validation performance. For the negative ROCE data set, the robust maximum likelihood regression model had a of 0.990, an of 0.984, a MSE of 98.883, and the lead key determinant was APCE with positive effect and followed by ROA with negative effect. The model also showed a strong validation performance. The results reflected that the key determinants are major sources of variability in ROCE of individual companies that management need to work with.
Overall, the findings showed that the use of robust maximum likelihood regression provided more precise results compared to those obtained using the three competing approaches, because it is more consistent, sufficient and efficient; has a higher breakdown point and no conditions. Companies management can establish and control proper marketing strategies using the key determinants, and results of these strategies can see an improvement in ROCE.
Wed, 01 Oct 2014 00:00:00 GMThttp://hdl.handle.net/10500/196272014-10-01T00:00:00Z