Thesis (Ph.D. (Statistics)) -- University of Limpopo, 2022 / Using the ARFIMA (autoregressive and fractionally integrated moving aver age) model extended with sGARCH (standard generalised autoregressive con ditional heteroscedasticity) and ’gjrGARCH (Glosten-Jagannathan-Runkle gen eralised autoregressive conditional heteroscedascity) innovations, fractional in tegration approach and state space model, this study has empirically examined persistency of inflation dynamics of Ghana and South Africa, the only two coun tries in Sub-Saharan Africa with Inflation Targeting (IT) monetary policy. The first part of the analysis employed monthly CPI (Consumer Price Index) in flation series for the period January 1971 to October 2014 obtained from the Bank of Ghana (BoG), and for the period January 1995 to December 2014 ob tained from Statistics South Africa. The second part involves the estimation of threshold effect of inflation on economic growth using annual data obtained from the IMF (International Monetary Fund) database for the period 1981 to 2014, for both countries. Results from the study showed that structural breaks, long memory and non linearities (or regime shifts) are largely responsible for inflation persistence, hence the ever-changing nature of inflation rates of Ghana and South Africa. ARFIMA(3,0.35,1)-‘gjrGARCH(1,1) under Generalised Error Distribution (GED) and ARFIMA(3,0.50,1)-‘gjrGARCH(1,1) under Student-t Distribution (STD) mod els provided the best fit for persistence in the conditional mean (or level) of CPI for Ghana and South Africa, respectively. The results from these models pro vided evidence of time-varying conditional mean and volatility in CPI inflation rates of both countries. The two models also revealed an asymmetric effect of inflationary shocks, where negative shocks appear to have greater impact than positive shocks, in terms of persistence on the conditional mean with time varying volatility. This thesis proposes a model that combines fractional integration with non linear deterministic terms based on the Chebyshev polynomials in time for the analysis of CPI inflation rates of Ghana and South Africa. We tested for non-linear deterministic terms in the context of fractional integration and esti mated the fractional differencing parameters, d to be 1.11 and 1.32 respectively, for the Ghanaian and the South African inflation rates, but the non-linear trends were found to be statistically insignificant in the two series. New ev idence from this thesis depicts that inflation rate of Ghana is highly persistent and non-mean reverting, with an estimated fractional differencing parameter, d > 1.0, and will therefore require some policy action to steer inflation back to stability. However, the South African inflation series was found to be a cyclical process with an order of integration estimated to be d = 0.7, depicting mean reversion, with the length of the cycles approximated to last for 80 months. Finally, the thesis incorporated structural breaks, long memory, non-linearity, and some explanatory variables into a state space model and estimated the threshold effect of inflation on economic growth. The empirical results suggest that inflation below the estimated levels of 9% and 6% for Ghana and South Africa respectively, will be conducive for economic growth. The policy implications of these results for both countries are as follows. First, both series had similar properties responsible for inducing inflation persistence such as structural breaks, non-linearities, long memory and asymmetric re sponse to negatives shocks - but with varied degrees of magnitude. For both countries, the conditional mean and unobserved components such as volatility for both countries were found to be time-varying. This thesis, therefore, recom mends to the BoG and the South African Reserve Bank (SARB) - responsible for monetary policies, and the Finance Ministers of both governments - respon sible for fiscal policies, to take the above-mentioned properties into account in the formulation of their monetary policies. Second, the thesis recommends that the BoG and the SARB consolidate the IT policy, since keeping inflation below the targets set of 9% and 6%, respectively for Ghana and South Africa, will boost economic growth. Third, policymakers could also design measures (monetary and fiscal policies) such as increase in interest rates, credit control, and reduction of unnecessary expenditure, among others, to control inflation due to its adverse effects on market volatility. Even though an increase in interest rates could assist in curtailing the recent and anticipated increase in inflation rates in both countries, where targets have been missed by Ghana and South Africa, it will also be prudent to legislate monetary policies around demand-supply side since the problem of both coun tries appears to be more of a structuralist than a monetarist. It is, therefore, recommended that both countries tighten the IT monetary policy in order to re duce inflation persistence. This will eventually impact on poverty and income distribution with ramifications for economic growth and/or development. The fourth implication of these results is that governments and central banks should be mindful of the actions and decisions they take, in the sense that unguarded decisions and unnecessary alarms could raise uncertainties in the economy, which could, in turn, affect the future trajectory of inflation. Finally, the thesis recommends that governments of both countries strengthen the pri vate sector, which is the engine of growth. For small and open economies such as Ghana and South Africa, this will grow the economy through job creation and restore investor confidence. / National Research Foundation (NRF), Department of Science and Technology (DST), Telkom’s Tertiary Education Support Programme (TESP) and the NRF-DST Centre of Excellence for Mathematical and Statistical Sciences (CoE-MaSS)

Bewertungen von Immobilien sollen den Marktwert einschätzen und sind notwendig für Kauf-, Verkaufs- und Bauentscheidungen, für die Kreditvergabe und für die Besteuerung. Trotz dieser eindeutigen Aufgabenstellung existierten unterschiedliche Verfahren, mit welchen Marktwerte ermittelt werden können. Ein Bewertungsverfahren soll einerseits mit ökonomischer Theorie vereinbar sein und andererseits Bewertungen generieren, die beobachtete Transaktionspreise gut vorhersagen. Die Dissertation analysiert die drei wichtigsten Bewertungsansätze Sachwert-, Vergleichswert- und Ertragswertverfahren, zeigt das jeweils zugrundeliegende Marktmodell und evaluiert die kodifizierten Verfahren nach der Wertermittlungsverordnung (WertV) anhand von beobachteten Transaktionen. Darüber hinaus gibt die Dissertation einen Überblick zu Immobilienpreisindizes und zu hedonischen Methoden. Für die ökonometrischen Analysen wurden umfangreiche Daten zum Berliner Immobilienmarkt verwendet. / Appraisals should assess the market value of properties and are necessary for buying, selling or building decisions, for lending and for taxation. Despite this unambiguous task different techniques exist for ascertaining market values. An valuation approach should be in accordance with economic theory and should generate appraisals, which are reliable estimates for transaction prices. This dissertation analyzes the three most important valuation approaches, i.e. cost, sales comparison, and income approach, shows the underlying market models and evaluates the valuation techniques that are codified in the German Regulation on Valuation (WertV). For the latter evaluations, appraisals are compared with observed transaction prices. In addition, the dissertation gives an overview on real estate price indices and on the hedonic approach. Extensive data on Berlin's real estate market are used for the econometric analysis.

Heterogeneous data with different characteristics are ubiquitous in the modern digital world. For example, the observations collected from a process may change on its mean or variance. In numerous applications, data are often of mixed types including both discrete and continuous variables. Heterogeneity also commonly arises in data when underlying models vary across different segments. Besides, the underlying pattern of data may change in different dimensions, such as in time and space. The diversity of heterogeneous data structures makes statistical modeling and analysis challenging. Detection of change-points in heterogeneous data has attracted great attention from a variety of application areas, such as quality control in manufacturing, protest event detection in social science, purchase likelihood prediction in business analytics, and organ state change in the biomedical engineering. However, due to the extraordinary diversity of the heterogeneous data structures and complexity of the underlying dynamic patterns, the change-detection and analysis of such data is quite challenging. This dissertation aims to develop novel statistical modeling methodologies to analyze four types of heterogeneous data and to find change-points efficiently. The proposed approaches have been applied to solve real-world problems and can be potentially applied to a broad range of areas. / Ph. D. / Heterogeneous data with different characteristics are ubiquitous in the modern digital world. Detection of change-points in heterogeneous data has attracted great attention from a variety of application areas, such as quality control in manufacturing, protest event detection in social science, purchase likelihood prediction in business analytics, and organ state change in the biomedical engineering. However, due to the extraordinary diversity of the heterogeneous data structures and complexity of the underlying dynamic patterns, the change-detection and analysis of such data is quite challenging. This dissertation focuses on modeling and analysis of data with heterogeneous structures. Particularly, four types of heterogeneous data are analyzed and different techniques are proposed in order to nd change-points efficiently. The proposed approaches have been applied to solve real-world problems and can be potentially applied to a broad range of areas.

State-space modelling is a powerful tool to study ecological systems. The direct inclusion of uncertainty, unification of models and data, and ability to model unobserved, hidden states increases our knowledge about the environment and provides new ecological insights. I extend the state-space framework to create multi-species models, showing that the ability to model ecosystem interactions is limited only by data availability. State-space models are fit using both Bayesian and Frequentist methods, making them independent of a statistical school of thought. Bayesian approaches can have the advantage in their ability to account for missing data and fit hierarchical structures and models with many parameters to limited data; often the case in ecological studies. I have taken a Bayesian model fitting approach in this thesis. The predator-prey interactions between the hen harrier (Circus cyaneus) and red grouse (Lagopus lagopus scoticus) are used to demonstrate state-space modelling’s capabilities. The harrier data are believed to be known without error, while missing data make the cyclic dynamics of the grouse harder to model. The grouse-harrier interactions are modelled in a multi-species state-space model, rather than including one species as a covariate in the other’s model. Finally, models are included for the harriers’ alternate prey. The single- and multi-species state-space models for the predator-prey interactions provide insight into the species’ management. The models investigate aspects of the species’ behaviour, from the mechanisms behind grouse cycles to what motivates harrier immigration. The inferences drawn from these models are applicable to management, suggesting actions to halt grouse cycles or mitigate the grouse-harrier conflict. Overall, the multi-species models suggest that two popular ideas for grouse-harrier management, diversionary feeding and habitat manipulation to reduce alternate prey densities, will not have the desired effect, and in the case of reducing prey densities, may even increase the harriers’ impact on grouse chicks.

過去雖有文獻探討國內房地產市場泡沫化問題，卻僅從租金收益的單一角度衡量房價基值，對於自有住宅比例較高的台灣而言，家戶所得不僅代表購屋者的負擔能力，更是構成房價基值的重要因素。有鑑於此，本研究分別從租金收益及家戶所得兩者不同角度下，透過資產市場現值模型，分別建立房價基值模型分析泡沫化現象。此外，過去文獻僅從檢定價格波動穩定性與否或將殘差項視為泡沫來研究泡沫化問題，然泡沫為不可觀察之變數，故本文使用具有可估計不可觀察變數特質的狀態空間模型（STATE-SPACE MODEL），推估泡沫價格，分析在不同時期下泡沫的規模大小。 在實證方面，本研究使用台北市1973Q2至2008Q1共140筆住宅價格資料，發現由租金與所得所計算之房價泡沫規模略為一致。在1988~1990年房市泡沫化時期，所得推估之泡沫規模達到高峰，泡沫價格占市價約47%；而由租金面亦計算出泡沫價格占市價約54%的高比例。而在2008年房價持續上漲的情況下，兩者泡沫價格亦呈現相同上升之走勢，泡沫價格近市價38%，租金推估泡沫價格占市價27%；此結果表示出目前房市有泡沫化之跡象，現階段欲購屋自住者不宜進入市場，宜審慎等待時機。而本文認為房價所得比或是房價租金比皆是作為衡量台北市房地產市場泡沫化現象之重要指標，另外就總體因素分析而言，房價上漲率、貨幣供給額、貸款利率與大盤股價指數皆為影響泡沫之重要因素，且經由實證發現所得所推估之泡沫價格較具有市場代表性。 / The past literatures about Taipei housing price bubble has only been measured the fundamental price by rent. However, the housing owner ratio is so high in Taiwan that housing income is not only regarded as affordability but also an important fundamental factor of housing price. According to the above, we focus on different fundamental models that define market fundamental price to analyses the bubble price from expected present value of both rent and permanent housing income. On the other hand, different from lots of literature testing the housing price volatility or residual to measure bubble prices, because housing bubble is an unobservable variable, we apply State-Space Model which is good for testing an invisible factor to estimate bubble in the housing markets of Taipei. This paper tries to test whether there was a housing price bubble using Taipei housing price index ranged from 1973Q1 to 2008Q1. The findings indicate that there appeared bubble ratio from 1988 to 1990, 47% of the housing price based on housing income and 54 % of the housing price based on rent. In 2008 when housing price continually keeps rising, bubble price ratios are close to 38% and 27% respectively. Those results show that Taipei seems to have sign of a bubble in this moment and housing buyers should concern it with more caution. Secondly, both price-income ratio and price-rent ratio are good indicators to measure housing bubble prices. Beside, we find macro economic factors change, such as the growth rate of housing price, M2, mortgage rate, and stock price index, are important to influence the size of housing bubble. Thirdly, bubble price estimated by housing income has a better performance than rent.

本研究透過聯合系統與獨特風險綜合評估違約的強度，假設市場上經濟變數或資訊影響系統之違約強度，然若直接考慮所有經濟變數到模型中將可能會有共線性或維度過高之疑慮，因此透過狀態空間模型來設定狀態變數以及經濟變數之關係並將萃取三大狀態變數分別用以描述市場實質活動面、通貨膨脹以及信用環境。另外，將透過結構式模型來計算獨特性風險大小，當個別潛在的變數低於一定數值將導致個別的違約事件發生。而因布朗運動可能無法描述或校準市場上違約之鋒態以及偏態，將進一步考慮Variance Gamma過程用以更準確描述真實違約狀況。最後透過結合以上兩個風險綜合評估下，考慮一個聯合違約模型來評價信用違約交換之信用價差。 / Systematic and idiosyncratic risks are supposed to jointly trigger the default events. This paper identifies three fundamental risks to capture the systematic movement: real activity, inflation, and credit environment. Since most macroeconomic variables fluctuate together, the state-space model is imposed to extract the three variables from macroeconomic data series. In the idiosyncratic part, the structural model is applied. That is, idiosyncratic default is triggered by the crossing of a barrier. For improvement of the underlying lognormal distribution, we assume the process for the potential variable of the firm follows a Variance Gamma process, sufficient dimensions of which can fit the skewed and leptokurtic distributions. Under the specific setting of combinations of the two risks (the so-called joint default model), we price credit default swaps.

Im Rahmen dieser Dissertation bemühe ich mich, den statistischen Ansatz der zeitkontinuierlichen dynamischen Modellierung, der die Rolle der Zeit explizit berücksichtigt, zu erweitern und praktisch anwendbar zu machen. Diese Dissertation ist so strukturiert, dass ich in Kapitel 1 die Natur dynamischer Modelle bespreche, verschiedene Ansätze zum Umgang mit mehreren Personen betrachte und ein zeitkontinuierliches dynamisches Modell mit Input-Effekten (wie Interventionen) und einem Gaußschen Messmodell detailliert darstelle. In Kapitel 2 beschreibe ich die Verwendung der Software ctsem für R, die als Teil dieser Dissertation entwickelt wurde und die Modellierung von Strukturgleichungen und Mixed-Effects über einen frequentistischen Schätzansatz realisiert. In Kapitel 3 stelle ich einen hierarchischen, komplett Random-Effects beinhaltenden Bayesschen Schätzansatz vor, unter dem sich Personen nicht nur in Interceptparametern, sondern in allen Charakteristika von Mess - und Prozessmodell unterscheiden können, wobei die Schätzung individueller Parameter trotzdem von den Daten aller Personen profitiert. Kapitel 4 beschreibt die Verwendung der Bayesschen Erweiterung der Software ctsem. In Kapitel 5} betrachte ich die Natur experimenteller Interventionen vor dem Hintergrund zeitkontinuierlicher dynamischer Modellierung und zeige Ansätze, die die Art und Weise adressieren, mit der Interventionen auf psychologische Prozesse über die Zeit wirken. Das berührt Fragen, wie: 'Nach welcher Zeit zeigt eine Intervention ihre maximale Wirkung', 'Wie ändert sich die Form des Effektes im Laufe der Zeit' und 'Für wen ist die Wirkung am stärksten oder dauert am längsten an'. Viele Bei-spiele, die sowohl frequentistische als auch bayessche Formen der Software ctsem verwenden, sind enthalten. Im letzten Kapitel fasse ich die Dissertation zusammen, zeige Limitationen der angebotenen Ansätze auf und stelle meine Gedanken zu möglichen zukünftigen Entwicklungen dar. / With this dissertation I endeavor to extend, and make practically applicable for psychology, the statistical approach of continuous time dynamic modelling, in which the role of time is made explicit. The structure of this dissertation is such that in Chapter 1, I discuss the nature of dynamic models, consider various approaches to handling multiple subjects, and detail a continuous time dynamic model with input effects (such as interventions) and a Gaussian measurement model. In Chapter 2, I describe the usage of the ctsem software for R developed as part of this dissertation, which provides a frequentist, mixed effects, structural equation modelling approach to estimation. Chapter 3 details a hierarchical Bayesian, fully random effects approach to estimation, allowing for subjects to differ not only in intercept parameters but in all characteristics of the measurement and dynamic models -- while still benefiting from other subjects data for parameter estimation. Chapter 4 describes the usage of the Bayesian extension to the ctsem software. In Chapter 5 I consider the nature of experimental interventions in the continuous time dynamic modelling framework, and show approaches to address questions regarding the way interventions influence psychological processes over time, with questions such as 'how long does a treatment take to reach maximum effect', `how does the shape of the effect change over time', and 'for whom is the effect strongest, or longest lasting'. Many examples using both frequentist and Bayesian forms of the ctsem software are given. For the final chapter I summarise the dissertation, consider limitations of the approaches offered, and provide some thoughts on possible future developments.

違約事件受到系統性風險與獨特性風險的綜合影響。本研究建構一狀態相依公司信用模型，該模型能反映出系統環境對市場造成的影響與個別公司獨特因子帶來的個別衝擊。 本模型透過從總體環境中萃取出的狀態變數來捕捉系統性變化，另外透過Variance Gamma過程來描繪個別公司的獨特因子帶來的影響。Variance Gamma過程可藉由調整分配的鋒態及偏態來調整布朗運動無法反映出的分配，以更貼近真實的市場訊息。 與縮減試模型相較之下，本模型無需參考信評機構的信用評等資訊，僅依賴市場上公開且透明的資訊，並且與結構式模型相同的是其富有經濟意涵。我們可以透過本模型來同時生成公司流動性危機發生機率與預期流動性危機造成的損失，進而利用本模型評價出個別公司信用違約交換的價格。 關鍵字：信用違約交換；系統風險；獨特性風險；狀態空間模型；Variance Gamma 過程 / Systematic and idiosyncratic risks are thought to affect the default events. This study develops a state-dependent corporate credit model that reflects both systematic movement and idiosyncratic shocks. To capture the systematic movement, the model extracts state factors from macroeconomics data. For the idiosyncratic part, the model applied Variance Gamma Process in depicting the potential variable of the firm by altering the distribution’s skewness and kurtosis. The model contains abundant economic significance as structural-form model does. Comparing to the reduced-form model, it does not rely on the information provided by rating agency but use information that is transparent and public. One can generate a firm’s probabilities of liquidity crisis and expected liquidity shortfalls endogenously and concurrently by employing the model. Credit derivative such as Single-name CDS can be priced under the model.

Regression testing of an evolving software system may involve significant challenges. While, there would be a requirement of maximising the probability of finding out if the latest changes to the system has broken some existing feature, it needs to be done as economically as possible. A particularly important class of software systems are API libraries. Such libraries would typically constitute a very important component of many software systems. High quality requirements make it imperative to continually optimise the internal implementation of such libraries without affecting the external interface. Therefore, it is preferred to guide the regression testing by some kind of formal specification of the library. The testing problem comprises of three parts: computation of test data, execution of test, and analysis of test results. Current research mostly focuses on the first part. The objective of test data computation is to maximise the probability of uncovering bugs, and to do it with as few test cases as possible. The problem of test data computation for regression testing is to select a subset of the original test suite running which would suffice to test for bugs probably inserted in the modifications done after the last round of testing. A variant of this problem is that of regression testing of API libraries. The regression testing of an API is usually done by making function calls in such a way that the sequence of function calls thus made suffices a test specification. The test specification in turn embodies some concept of completeness. In this thesis, we focus on the problem of test sequence computation for the regression testing of API libraries. At the heart of this method lies the creation of a state space model of the API library by reverse engineering it by executing the system, with guidance from an formal API specification. Once the state space graph is obtained, it is used to compute test sequences for satisfying some test specification. We analyse the theoretical complexity of the problem of test sequence computation and provide various heuristic algorithms for the same. State space explosion is a classical problem encountered whenever there is an attempt of creating a finite state model of a program. Our method also faces this limitation. We explore a simple and intuitive method of ameliorating this problem – by simply reducing the size of the state vector. We develop the theoretical insights into this method. Also, we present experimental results indicating the practical effectiveness of this method. Finally, we bring all this together into the design and implementation of a tool called Modest.

The first two articles build procedures to simulate vector of univariate states and estimate parameters in nonlinear and non Gaussian state space models. We propose state space speci fications that offer more flexibility in modeling dynamic relationship with latent variables. Our procedures are extension of the HESSIAN method of McCausland[2012]. Thus, they use approximation of the posterior density of the vector of states that allow to : simulate directly from the state vector posterior distribution, to simulate the states vector in one bloc and jointly with the vector of parameters, and to not allow data augmentation. These properties allow to build posterior simulators with very high relative numerical efficiency. Generic, they open a new path in nonlinear and non Gaussian state space analysis with limited contribution of the modeler. The third article is an essay in commodity market analysis. Private firms coexist with farmers' cooperatives in commodity markets in subsaharan african countries. The private firms have the biggest market share while some theoretical models predict they disappearance once confronted to farmers cooperatives. Elsewhere, some empirical studies and observations link cooperative incidence in a region with interpersonal trust, and thus to farmers trust toward cooperatives. We propose a model that sustain these empirical facts. A model where the cooperative reputation is a leading factor determining the market equilibrium of a price competition between a cooperative and a private firm / Les deux premiers articles élaborent des procédures de simulation du vecteur d'état et d'estimation des paramètres dans des modèles espace-états non linéaires et non-Gaussiens. Nous proposons des spécifi cations des modèles espace-états qui offrent plus de flexibilité dans la modélisation des relations dynamiques avec variables latentes. Les procédures d'estimation des paramètres dans ces modèles sont une extension de la méthode HESSIAN de McCausland[2012]. Ainsi, elles utilisent une approximation de la densité à posteriori du vecteur d'état qui permet de : simuler directement de la loi à posteriori du vecteur d'état, de simuler en seul bloc le vecteur d'état et de le simuler conjointement avec le vecteur de paramètres, et de ne pas admettre l'introduction d'inconnues additionnelles. Ces propriétés permettent d'obtenir des simulateurs à posteriori avec une efficacité numérique relative très élevée. Les procédures d'estimation élaborées sont génériques. Elles ouvrent ainsi une voie pour une analyse des modèles espace-états non linéaires et non-Gaussiens sans une grande contribution du modélisateur. Le troisième article est une contribution dans l'analyse des marchés agricoles. Les firmes privées coexistent avec les coopératives de fermiers dans les marchés agricoles en Afrique subsaharienne. Les firmes privées accaparent les plus grandes parts de marché, alors que certains modèles théoriques prédisent leur disparition une fois confrontées aux coopératives agricoles. Par ailleurs, certaines observations et études empiriques lient la forte incidence d'une coopérative dans une région à la confiance interpersonnelle entre les personnes de cette région, et par conséquent la confiance de ces personnes envers les coopératives existantes. Nous proposons un modèle théorique qui cadre mieux avec ces observations empiriques. Un modèle où la réputation de la coopérative est un facteur déterminant de l'équilibre de marché dans la compétition sur le prix à la livraison entre celle-ci et une firme privée.