The use of parametric cost estimating and risk management techniques to improve project cost estimates during feasibility studies

**Authors:**Molefi, Khotso Daniel**Date:**2013-11-25**Subjects:**Risk management , Cost estimates , Project management - Cost control , Work breakdown structure , Parameter estimation**Type:**Thesis**Identifier:**uj:7803 , http://hdl.handle.net/10210/8698**Description:**M.Ing. (Engineering Management) , “A robust set of estimates puts a project on a firm footing from day 1, allowing the project manager to apply the right level of resources at the appropriate time. If the plan has been based on poor estimates, problems will occur during the execution of the project …” This statement places great importance on the ability to estimate costs as accurately as practicable early during a project life cycle. Many techniques have been proposed with the aim of aiding with the production of early cost estimates,which have acceptable accuracies necessary for Feasibility Study purposes. One such technique is Parametric Cost Estimating for developing Parametric Cost Models used in producing these conceptual estimates.At the heart of Parametric Cost Estimating Technique, is a fundamental statistical technique commonly known as Linear Regression Analysis.The problem that the research addresses is that of the general misconception found to prevail within project houses that some engineering systems are too complex to model using the Parametric Cost Estimating Technique. The objectives of this research are to investigate and demonstrate the effectiveness of this technique in predicting the costs of a system for Feasibility Study purposes. The objectives were achieved by conducting a secondary literature review of case studies of similar Parametric Cost Models that were developed by others for engineering systems of varying complexities. A second method used in achieving the objectives included formulating a case study in which a Parametric Cost Model was developed to illustrate the concept and to prove that the accuracies produced by the model meet the requirements for Feasibility Studies.The research was limited to initial project costs required for Feasibility Studies,ignoring the effects of qualitative factors,focusing only on the acquisition costs and not the total life cycle costs of the system.The case study was developed for a passenger motor vehicle as the system of interest because sufficient cost data in the form of vehicle retail price and performance specifications is publicly available in car magazines making it possible to build a meaningful Parametric Cost Model. The Parametric Cost Model was developed using Microsoft Excel 2007 and had a Mean Absolute Error Rate of 10.9% and the range of accuracy obtained, -20% to 10% with 67% confidence level and -30% to 30% with 95% confidence level, conforming to a Class 4 estimate which meets the accuracy requirements for a Feasibility Study.**Full Text:**

**Authors:**Molefi, Khotso Daniel**Date:**2013-11-25**Subjects:**Risk management , Cost estimates , Project management - Cost control , Work breakdown structure , Parameter estimation**Type:**Thesis**Identifier:**uj:7803 , http://hdl.handle.net/10210/8698**Description:**M.Ing. (Engineering Management) , “A robust set of estimates puts a project on a firm footing from day 1, allowing the project manager to apply the right level of resources at the appropriate time. If the plan has been based on poor estimates, problems will occur during the execution of the project …” This statement places great importance on the ability to estimate costs as accurately as practicable early during a project life cycle. Many techniques have been proposed with the aim of aiding with the production of early cost estimates,which have acceptable accuracies necessary for Feasibility Study purposes. One such technique is Parametric Cost Estimating for developing Parametric Cost Models used in producing these conceptual estimates.At the heart of Parametric Cost Estimating Technique, is a fundamental statistical technique commonly known as Linear Regression Analysis.The problem that the research addresses is that of the general misconception found to prevail within project houses that some engineering systems are too complex to model using the Parametric Cost Estimating Technique. The objectives of this research are to investigate and demonstrate the effectiveness of this technique in predicting the costs of a system for Feasibility Study purposes. The objectives were achieved by conducting a secondary literature review of case studies of similar Parametric Cost Models that were developed by others for engineering systems of varying complexities. A second method used in achieving the objectives included formulating a case study in which a Parametric Cost Model was developed to illustrate the concept and to prove that the accuracies produced by the model meet the requirements for Feasibility Studies.The research was limited to initial project costs required for Feasibility Studies,ignoring the effects of qualitative factors,focusing only on the acquisition costs and not the total life cycle costs of the system.The case study was developed for a passenger motor vehicle as the system of interest because sufficient cost data in the form of vehicle retail price and performance specifications is publicly available in car magazines making it possible to build a meaningful Parametric Cost Model. The Parametric Cost Model was developed using Microsoft Excel 2007 and had a Mean Absolute Error Rate of 10.9% and the range of accuracy obtained, -20% to 10% with 67% confidence level and -30% to 30% with 95% confidence level, conforming to a Class 4 estimate which meets the accuracy requirements for a Feasibility Study.**Full Text:**

Estimation and testing in location-scale families of distributions

**Authors:**Potgieter, Cornelis Jacobus**Date:**2011-10-11T08:08:30Z**Subjects:**Parameter estimation , Statistical hypothesis testing , Distribution (Probability theory)**Type:**Thesis**Identifier:**uj:7244 , http://hdl.handle.net/10210/3898**Description:**D.Phil. , We consider two problems relating to location-scale families of distributions. Firstly, we consider methods of parameter estimation when two samples come from the same type of distribution, but possibly differ in terms of location and spread. Although there are methods of estimation that are asymptotically efficient, our interest is in fi nding methods which also have good small-sample properties. Secondly, we consider tests for the hypothesis that two samples come from the same location-scale family. Both these problems are addressed using methods based on empirical distribution functions and empirical characteristic functions.**Full Text:**

**Authors:**Potgieter, Cornelis Jacobus**Date:**2011-10-11T08:08:30Z**Subjects:**Parameter estimation , Statistical hypothesis testing , Distribution (Probability theory)**Type:**Thesis**Identifier:**uj:7244 , http://hdl.handle.net/10210/3898**Description:**D.Phil. , We consider two problems relating to location-scale families of distributions. Firstly, we consider methods of parameter estimation when two samples come from the same type of distribution, but possibly differ in terms of location and spread. Although there are methods of estimation that are asymptotically efficient, our interest is in fi nding methods which also have good small-sample properties. Secondly, we consider tests for the hypothesis that two samples come from the same location-scale family. Both these problems are addressed using methods based on empirical distribution functions and empirical characteristic functions.**Full Text:**

On the modeling of asset returns and calibration of European option pricing models

- Robbertse, Johannes Lodewickes

**Authors:**Robbertse, Johannes Lodewickes**Date:**2008-07-07T09:11:28Z**Subjects:**Options (Finance) , Distribution (Probability theory) , Gaussian distribution , Levy processes , Parameter estimation , Goodness-of-fit tests , Prices , Mathematical models**Type:**Thesis**Identifier:**uj:10194 , http://hdl.handle.net/10210/756**Description:**Prof. F. Lombard**Full Text:**

**Authors:**Robbertse, Johannes Lodewickes**Date:**2008-07-07T09:11:28Z**Subjects:**Options (Finance) , Distribution (Probability theory) , Gaussian distribution , Levy processes , Parameter estimation , Goodness-of-fit tests , Prices , Mathematical models**Type:**Thesis**Identifier:**uj:10194 , http://hdl.handle.net/10210/756**Description:**Prof. F. Lombard**Full Text:**

Estimation of parameters and tests for parameter changes in fractional Gaussian noise

- Robbertse, Johannes Lodewickes

**Authors:**Robbertse, Johannes Lodewickes**Date:**2013-07-29**Subjects:**Gaussian processes , Random noise theory , Parameter estimation**Type:**Thesis**Identifier:**uj:7705 , http://hdl.handle.net/10210/8570**Description:**D.Phil. (Mathematical Statistics) , Fractional Brownian motion and its increment process, fractional Gaussian noise, are syn- onymous with the concept of long range dependence. A strictly stationary time series is said to exhibit long range dependence or long memory if its autocorrelations decrease to zero as a power of the lag, but their sum over all lags is not absolutely convergent. This phenomenon has been observed in numerous scientific areas such as hydrology, ethernet traffic data, stock returns and exchange rates, to name just a few. The extent of long memory dependence is characterized by the value of the so called Hurst exponent or Hurst coefficient H. Approximate normality and unbiasedness of the maximum likelihood estimate of H hold reasonably well for sample sizes as small as 20 if the mean and scale parameters are known. We show in a Monte Carlo study that if the latter two parameters are unknown, the bias and variance of the maximum likelihood estimate of H both increase substantially. We also show that the bias can be reduced by using a jackknife or parametric bootstrap proce- dure. However, in very large samples, maximum likelihood estimation becomes problematic because of the large dimension of the covariance matrix that must be inverted. We consider an approach for estimating the Hurst exponent by taking first order differ- ences of fractional Gaussian noise. We find that this differenced process has short memory and that, consequently, we may assume approximate independence between the estimates of the Hurst exponents in disjoint blocks of data. We split the data into a number of con- tiguous blocks, each containing a relatively small number of observations. Computation of the likelihood function in a block then presents no computational problem. We form a pseudo likelihood function consisting of the product of the likelihood functions in each of the blocks and provide a formula for the standard error of the resulting estimator of H. This formula is shown in a Monte Carlo study to provide a good approximation to the true standard error. Application of the methodology is illustrated in two data sets. The long memory property of a time series is primarily characterized by H. In general, such series are exceptionally long, therefore it is natural to enquire whether or not H remains constant over the full extent of the time series. We propose a number of tests for the hypothesis that H remains constant, against an alternative of a change in one or more values of H. Formulas are given to enable calculation of asymptotic p-values. We also propose a permutational procedure for evaluating exact p-values. The proposed tests are applied to three sets of data.**Full Text:**

**Authors:**Robbertse, Johannes Lodewickes**Date:**2013-07-29**Subjects:**Gaussian processes , Random noise theory , Parameter estimation**Type:**Thesis**Identifier:**uj:7705 , http://hdl.handle.net/10210/8570**Description:**D.Phil. (Mathematical Statistics) , Fractional Brownian motion and its increment process, fractional Gaussian noise, are syn- onymous with the concept of long range dependence. A strictly stationary time series is said to exhibit long range dependence or long memory if its autocorrelations decrease to zero as a power of the lag, but their sum over all lags is not absolutely convergent. This phenomenon has been observed in numerous scientific areas such as hydrology, ethernet traffic data, stock returns and exchange rates, to name just a few. The extent of long memory dependence is characterized by the value of the so called Hurst exponent or Hurst coefficient H. Approximate normality and unbiasedness of the maximum likelihood estimate of H hold reasonably well for sample sizes as small as 20 if the mean and scale parameters are known. We show in a Monte Carlo study that if the latter two parameters are unknown, the bias and variance of the maximum likelihood estimate of H both increase substantially. We also show that the bias can be reduced by using a jackknife or parametric bootstrap proce- dure. However, in very large samples, maximum likelihood estimation becomes problematic because of the large dimension of the covariance matrix that must be inverted. We consider an approach for estimating the Hurst exponent by taking first order differ- ences of fractional Gaussian noise. We find that this differenced process has short memory and that, consequently, we may assume approximate independence between the estimates of the Hurst exponents in disjoint blocks of data. We split the data into a number of con- tiguous blocks, each containing a relatively small number of observations. Computation of the likelihood function in a block then presents no computational problem. We form a pseudo likelihood function consisting of the product of the likelihood functions in each of the blocks and provide a formula for the standard error of the resulting estimator of H. This formula is shown in a Monte Carlo study to provide a good approximation to the true standard error. Application of the methodology is illustrated in two data sets. The long memory property of a time series is primarily characterized by H. In general, such series are exceptionally long, therefore it is natural to enquire whether or not H remains constant over the full extent of the time series. We propose a number of tests for the hypothesis that H remains constant, against an alternative of a change in one or more values of H. Formulas are given to enable calculation of asymptotic p-values. We also propose a permutational procedure for evaluating exact p-values. The proposed tests are applied to three sets of data.**Full Text:**

Estimation of discretely sampled continuous diffusion processes with application to short-term interest rate models

**Authors:**Van Appel, Vaughan**Date:**2014-10-13**Subjects:**Estimation theory , Parameter estimation , Stochastic differential equations , Interest rates - Mathematical models , Monte Carlo method , Jackknife (Statistics) , Jump processes**Type:**Thesis**Identifier:**uj:12582 , http://hdl.handle.net/10210/12372**Description:**M.Sc. (Mathematical Statistics) , Stochastic Differential Equations (SDE’s) are commonly found in most of the modern finance used today. In this dissertation we use SDE’s to model a random phenomenon known as the short-term interest rate where the explanatory power of a particular short-term interest rate model is largely dependent on the description of the SDE to the real data. The challenge we face is that in most cases the transition density functions of these models are unknown and therefore, we need to find reliable and accurate alternative estimation techniques. In this dissertation, we discuss estimating techniques for discretely sampled continuous diffusion processes that do not require the true transition density function to be known. Moreover, the reader is introduced to the following techniques: (i) continuous time maximum likelihood estimation; (ii) discrete time maximum likelihood estimation; and (iii) estimating functions. We show through a Monte Carlo simulation study that the parameter estimates obtained from these techniques provide a good approximation to the estimates obtained from the true transition density. We also show that the bias in the mean reversion parameter can be reduced by implementing the jackknife bias reduction technique. Furthermore, the data analysis carried out on South-African interest rate data indicate strongly that single factor models do not explain the variability in the short-term interest rate. This may indicate the possibility of distinct jumps in the South-African interest rate market. Therefore, we leave the reader with the notion of incorporating jumps into a SDE framework.**Full Text:**

**Authors:**Van Appel, Vaughan**Date:**2014-10-13**Subjects:**Estimation theory , Parameter estimation , Stochastic differential equations , Interest rates - Mathematical models , Monte Carlo method , Jackknife (Statistics) , Jump processes**Type:**Thesis**Identifier:**uj:12582 , http://hdl.handle.net/10210/12372**Description:**M.Sc. (Mathematical Statistics) , Stochastic Differential Equations (SDE’s) are commonly found in most of the modern finance used today. In this dissertation we use SDE’s to model a random phenomenon known as the short-term interest rate where the explanatory power of a particular short-term interest rate model is largely dependent on the description of the SDE to the real data. The challenge we face is that in most cases the transition density functions of these models are unknown and therefore, we need to find reliable and accurate alternative estimation techniques. In this dissertation, we discuss estimating techniques for discretely sampled continuous diffusion processes that do not require the true transition density function to be known. Moreover, the reader is introduced to the following techniques: (i) continuous time maximum likelihood estimation; (ii) discrete time maximum likelihood estimation; and (iii) estimating functions. We show through a Monte Carlo simulation study that the parameter estimates obtained from these techniques provide a good approximation to the estimates obtained from the true transition density. We also show that the bias in the mean reversion parameter can be reduced by implementing the jackknife bias reduction technique. Furthermore, the data analysis carried out on South-African interest rate data indicate strongly that single factor models do not explain the variability in the short-term interest rate. This may indicate the possibility of distinct jumps in the South-African interest rate market. Therefore, we leave the reader with the notion of incorporating jumps into a SDE framework.**Full Text:**

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