In South Africa various financial institutions and independent vendors have developed residential property valuation models to estimate the current value of historically traded properties. A natural extension to these models has been to develop historical property price indices. In this dissertation, three of the four approaches to developing property price indices will be examined. Through back–testing and other statistical methods, the most accurate and robust approach will be determined. The four major approaches available are the mean valuation per suburb, the median valuation per suburb, the repeat sales approach and hedonic regression. The mean valuation per suburb approach can be biased because of outliers in property prices. However, outliers in property prices will not influence the median valuation per suburb approach, but in cases where property values in a suburb have a skewed distribution, the valuation amount could be distorted. Neither of the above mentioned shortcomings influences the repeat sales or the hedonic regression approach. To follow the hedonic regression approach, the characteristics of the property need to be known. In South Africa, however, the available property data lacks detailed characteristics of traded properties. This dissertation will therefore focus on the first three methods. The repeat sales approach measures the growth in property prices by applying a generalized linear model to properties that have traded more than once. This approach is only possible if there is a representative amount of repeat sales able to fit a model. The focus of this project will be on the repeat sales approach, but all three the approaches discussed will be analysed to prove that the repeat sales approach is the most accurate in developing a property price index for properties in South Africa. / Thesis (M.Sc. (Risk Analysis))--North-West University, Potchefstroom Campus, 2011.

In South Africa various financial institutions and independent vendors have developed residential property valuation models to estimate the current value of historically traded properties. A natural extension to these models has been to develop historical property price indices. In this dissertation, three of the four approaches to developing property price indices will be examined. Through back–testing and other statistical methods, the most accurate and robust approach will be determined. The four major approaches available are the mean valuation per suburb, the median valuation per suburb, the repeat sales approach and hedonic regression. The mean valuation per suburb approach can be biased because of outliers in property prices. However, outliers in property prices will not influence the median valuation per suburb approach, but in cases where property values in a suburb have a skewed distribution, the valuation amount could be distorted. Neither of the above mentioned shortcomings influences the repeat sales or the hedonic regression approach. To follow the hedonic regression approach, the characteristics of the property need to be known. In South Africa, however, the available property data lacks detailed characteristics of traded properties. This dissertation will therefore focus on the first three methods. The repeat sales approach measures the growth in property prices by applying a generalized linear model to properties that have traded more than once. This approach is only possible if there is a representative amount of repeat sales able to fit a model. The focus of this project will be on the repeat sales approach, but all three the approaches discussed will be analysed to prove that the repeat sales approach is the most accurate in developing a property price index for properties in South Africa. / Thesis (M.Sc. (Risk Analysis))--North-West University, Potchefstroom Campus, 2011.

Diese Arbeit stellt Modelle und Methoden vor, die für robuste Statistiken und ihre Anwendungen in verschiedenen Bereichen entwickelt wurden. Kapitel 2 stellt einen neuartigen Partitionierungs-Clustering-Algorithmus vor, der auf Expectiles basiert. Der Algorithmus bildet Cluster, die sich an das Endverhalten der Clusterverteilungen anpassen und sie dadurch robuster machen. Das Kapitel stellt feste Tau-Clustering- und adaptive Tau-Clustering-Schemata und ihre Anwendungen im Kryptowährungsmarkt und in der Bildsegmentierung vor. In Kapitel 3 wird ein faktorerweitertes dynamisches Modell vorgeschlagen, um das Tail-Verhalten hochdimensionaler Zeitreihen zu analysieren. Dieses Modell extrahiert latente Faktoren, die durch Extremereignisse verursacht werden, und untersucht ihre Wechselwirkung mit makroökonomischen Variablen mithilfe des VAR-Modells. Diese Methodik ermöglicht Impuls-Antwort-Analysen, Out-of-Sample-Vorhersagen und die Untersuchung von Netzwerkeffekten. Die empirische Studie stellt den signifikanten Einfluss von durch finanzielle Extremereignisse bedingten Faktoren auf makroökonomische Variablen während verschiedener Wirtschaftsperioden dar. Kapitel 4 ist eine Pilotanalyse zu Non Fungible Tokens (NFTs), insbesondere CryptoPunks. Der Autor untersucht die Clusterbildung zwischen digitalen Assets mithilfe verschiedener Visualisierungstechniken. Die durch CNN- und UMAP-Regression identifizierten Cluster werden mit Preisen und Merkmalen von CryptoPunks in Verbindung gebracht. Kapitel 5 stellt die Konstruktion eines Preisindex namens Digital Art Index (DAI) für den NFT-Kunstmarkt vor. Der Index wird mithilfe hedonischer Regression in Kombination mit robusten Schätzern für die Top-10-Liquid-NFT-Kunstsammlungen erstellt. Es schlägt innovative Verfahren vor, nämlich Huberisierung und DCS-t-Filterung, um abweichende Preisbeobachtungen zu verarbeiten und einen robusten Index zu erstellen. Darüber hinaus werden Preisdeterminanten des NFT-Marktes analysiert. / This thesis provides models and methodologies developed on robust statistics and their applications in various domains. Chapter 2 presents a novel partitioning clustering algorithm based on expectiles. The algorithm forms clusters that adapt to the tail behavior of the cluster distributions, making them more robust. The chapter introduces fixed tau-clustering and adaptive tau-clustering schemes and their applications in crypto-currency market and image segmentation. In Chapter 3 a factor augmented dynamic model is proposed to analyse tail behavior of high-dimensional time series. This model extracts latent factors driven by tail events and examines their interaction with macroeconomic variables using VAR model. This methodology enables impulse-response analysis, out-of-sample predictions, and the study of network effects. The empirical study presents significant impact of financial tail event driven factors on macroeconomic variables during different economic periods. Chapter 4 is a pilot analysis on Non Fungible Tokens (NFTs) specifically CryptoPunks. The author investigates clustering among digital assets using various visualization techniques. The clusters identified through regression CNN and UMAP are associated with prices and traits of CryptoPunks. Chapter 5 introduces the construction of a price index called the Digital Art Index (DAI) for the NFT art market. The index is created using hedonic regression combined with robust estimators on the top 10 liquid NFT art collections. It proposes innovative procedures, namely Huberization and DCS-t filtering, to handle outlying price observations and create a robust index. Furthermore, it analyzes price determinants of the NFT market.