The main objective of the study was to determine the exchange rate volatility regime for carry trade profitability when using the South African Rand as the target currency. The study used the Logistic Smooth Transition Regression (LSTR) model to test the uncovered interest rate parity (UIP). The Sharpe ratio and the risk adjusted forward premium were used as the transition variables. The transition variable is a function of the transition function, which is used to determine the regime for the UIP. The LSTR model is characterised by three regimes, i.e. the lower regime, the middle regime and the upper regime. The LSTR model was tested for the short-term forward rate maturity of less than one year. The results show that the UIP hypothesis holds in the middle regime for the Rand/USD and the Rand/GBP when using the Sharpe ratio as the transition variable. Meanwhile, the UIP hypothesis does not hold for the Rand/Yen when using the Sharpe ratio as the transition variable for the forward rate maturity of one month, and it does hold for other short-term forward rate maturity of less than one year. The results for the risk adjusted forward premium as the transition variable show that the UIP hypothesis does not hold for all three currencies at various short-term forward rate maturities of less than one year. The research provides the following contributions to new knowledge: (1) Uncovered interest parity hypothesis holds in the middle regime for all periods for the Rand/USD and the Rand/GBP when using the Sharpe ratio as the transition variable with a short-term forward rate maturity of less than one year. (2) Currency carry trade profit taking for the Rand/USD and the Rand/GBP can be achieved in the upper regime. (3) The results for the Rand/Yen are mixed, in that the UIP hypothesis does not hold for other crisis periods as a result of negative Sharpe ratios. However, for the calm periods, UIP hypothesis holds in the middle regime for the Rand/Yen for short-term forward rate maturity of more than one month but less than one year when using the Sharpe ratio as the transition variable. The overall contribution of this study is that for the South African Rand as the target currency, the UIP hypothesis holds for the short-term horizon when using the Sharpe ratio as the transition variable and that this mostly depends more on currency than on horizon. Contrary to other researchers who found that the UIP holds in the long-term maturity with higher Sharpe ratios in the upper regime, this study proved that the UIP holds in the short-term maturity horizon. / Business Management / D.B.L.

South Africa is experiencing a financial skills shortage with a severe shortage of accountants and chartered accountants in particular. The aim of this study was to measure accessibility of public higher education in South Africa, in general and specifically relating to accountancy programmes with special emphasis on chartered accountancy programmes in South Africa, by making use of selected accessibility indicators. Although some of these indicators have been used to measure accessibility of higher education in general both locally and internationally, they are not often used to measure accessibility of a programme for a particular profession such as accountancy or chartered accountancy. This study aimed to fill this gap by measuring the selected accessibility indicators and providing subsequent rankings of the four public universities selected for this study. The results can be used by institutions that offer accountancy and chartered accountancy programmes as well as the South African Institute of Chartered Accountants, as the profession’s Education and Training Quality Assurance body, to evaluate the accessibility of accountancy as well as chartered accountancy programmes. / Financial Accounting / M. Compt. (Applied Accountancy)

<p>Computer programs keep finding their ways into new safety-critical applications, while at the same time growing more complex. This calls for new and better methods to verify the correctness of software. We focus on one approach to verifying systems, namely that of <i>model checking</i>. At first, we investigate two categories of problems related to model checking: <i>games</i> and <i>stochastic infinite-state systems</i>. In the end, we join these two lines of research, by studying <i>stochastic infinite-state games</i>.</p><p>Game theory has been used in verification for a long time. We focus on finite-state 2-player parity and limit-average (mean payoff) games. These problems have applications in model checking for the <i>μ</i>-calculus, one of the most expressive logics for programs. We give a simplified proof of memoryless determinacy. The proof applies <i>both</i> to parity and limit-average games. Moreover, we suggest a strategy improvement algorithm for limit-average games. The algorithm is discrete and strongly subexponential.</p><p>We also consider probabilistic infinite-state systems (Markov chains) induced by three types of models. <i>Lossy channel systems (LCS)</i> have been used to model processes that communicate over an unreliable medium. <i>Petri nets</i> model systems with unboundedly many parallel processes. <i>Noisy Turing machines</i> can model computers where the memory may be corrupted in a stochastic manner. We introduce the notion of <i>eagerness</i> and prove that all these systems are eager. We give a scheme to approximate the value of a reward function defined on paths. Eagerness allows us to prove that the scheme terminates. For probabilistic LCS, we also give an algorithm that approximates the limit-average reward. This quantity describes the long-run behavior of the system.</p><p>Finally, we investigate Büchi games on probabilistic LCS. Such games can be used to model a malicious cracker trying to break a network protocol. We give an algorithm to solve these games.</p>

本研究提出UIP、PPP、 MF、TR及TRa五種匯率預測模型，以新台幣兌美元即期匯率、遠期匯率進行避險準確率及避險成效的實證分析。資料期間為1996年12月到2012年10月的新台幣兌美元即期匯率月資料，資料來源為資料庫Datastream。 實證結果發現UIP、PPP、 MF、TR及TRa五種匯率預測模型比較分析中，若以相對購買力平價模型(PPP)進行選擇性避險，再搭配適當避險比率，其報酬率可能由負報酬轉為正報酬；避險績效衡量方面，以相對購買力平價模型搭配完全避險的績效最好。若以不對稱泰勒模型(TRa)進行選擇性避險，再搭配適當避險比率，報酬率明顯由負轉為正；衡量避險績效衡量方面，完全避險在風險降幅及下方動差避險績效衡量下，以不對稱泰勒模型搭配完全避險的績效最好。 / This study provides five exchange rate models to predict future exchange rate (UIP,PPP,MF,Taylor rule and asymmetric Taylor rule). We illustrate these methods by assessing the forecasting performance of five exchange rate models using monthly returns on TWD/US dollar exchange rate. The data are monthly exchange rates ranging from December 1996 to October 2012, using spot and one-month forward exchange rates form Datastream. We find that empirical models based on purchase power parity (PPP) and the asymmetric Taylor rule(TRa) outperform the other models in out-of-sample forecasting using the appropriate hedging ratio. Comparing the hedging performance between PPP and models, we find that the hedging performance by the PPP will get the higher return. However, the hedging performance by the will get the lower volatility.

We implement a package for the construction of a new class of Low Density Parity Check (LDPC) codes based on a new random high girth graph construction technique, and study the performance of the codes so constructed on both the Additive White Gaussian Noise (AWGN) channel as well as the Binary Erasure Channel (BEC). Our codes are “near regular”, meaning thereby that the the left degree of any node in the Tanner graph constructed varies by at most 1 from the average left degree and so also the right degree. The simulations for rate half codes indicate that the codes perform better than both the regular Progressive Edge Growth (PEG) codes which are constructed using a similar random technique, as well as the MacKay random codes. For high rates the ARG (Almost Regular high Girth) codes perform better than the PEG codes at low to medium SNR’s but the PEG codes seem to do better at high SNR’s. We have tried to track both near codewords as well as small weight codewords for these codes to examine the performance at high rates. For the binary erasure channel the performance of the ARG codes is better than that of the PEG codes. We have also proposed a modification of the sum-product decoding algorithm, where a quantity called the “node credibility” is used to appropriately process messages to check nodes. This technique substantially reduces the error rates at signal to noise ratios of 2.5dB and beyond for the codes experimented on. The average number of iterations to achieve this improved performance is practically the same as that for the traditional sum-product algorithm.

This item contains the agenda, minutes, and attachments for the Faculty Senate meeting on this date. There may be additional materials from the meeting available at the Faculty Center.

Computer programs keep finding their ways into new safety-critical applications, while at the same time growing more complex. This calls for new and better methods to verify the correctness of software. We focus on one approach to verifying systems, namely that of model checking. At first, we investigate two categories of problems related to model checking: games and stochastic infinite-state systems. In the end, we join these two lines of research, by studying stochastic infinite-state games. Game theory has been used in verification for a long time. We focus on finite-state 2-player parity and limit-average (mean payoff) games. These problems have applications in model checking for the μ-calculus, one of the most expressive logics for programs. We give a simplified proof of memoryless determinacy. The proof applies both to parity and limit-average games. Moreover, we suggest a strategy improvement algorithm for limit-average games. The algorithm is discrete and strongly subexponential. We also consider probabilistic infinite-state systems (Markov chains) induced by three types of models. Lossy channel systems (LCS) have been used to model processes that communicate over an unreliable medium. Petri nets model systems with unboundedly many parallel processes. Noisy Turing machines can model computers where the memory may be corrupted in a stochastic manner. We introduce the notion of eagerness and prove that all these systems are eager. We give a scheme to approximate the value of a reward function defined on paths. Eagerness allows us to prove that the scheme terminates. For probabilistic LCS, we also give an algorithm that approximates the limit-average reward. This quantity describes the long-run behavior of the system. Finally, we investigate Büchi games on probabilistic LCS. Such games can be used to model a malicious cracker trying to break a network protocol. We give an algorithm to solve these games.

This thesis investigates both theoretical and practical aspects of the design and analysis of modern error-control coding schemes, namely low-density parity-check (LDPC) codes and rateless codes for unequal error protection (UEP). It also studies the application of modern error-control codes in efficient data dissemination in wireless ad-hoc and sensor networks. Two methodologies for the design and analysis of UEP-LDPC codes are proposed. For these proposed ensembles, density evolution formulas over the binary erasure channel are derived and used to optimize the degree distribution of the codes. Furthermore, for the first time, rateless codes that can provide UEP are developed. In addition to providing UEP, the proposed codes can be used in applications for which unequal recovery time is desirable, i.e., when more important parts of data are required to be recovered faster than less important parts. Asymptotic behavior of the UEP-rateless codes under the iterative decoding is investigated. In addition, the performance of the proposed codes is examined under the maximum-likelihood decoding, when the codes have short to moderate lengths. Results show that UEP-rateless codes are able to provide very low error rates for more important bits with only a subtle loss in the performance of less important bits. Moreover, it is shown that given a target bit error rate, different parts of the information symbols can be decoded after receiving different numbers of encoded symbols. This implies that information can be recovered in a progressive manner, which is of interest in many practical applications such as media-on-demand systems. This work also explores fundamental research problems related to applying error-control coding such as rateless coding to the problem of reliable and energy-efficient broadcasting in multihop wireless ad-hoc sensor networks. The proposed research touches on the four very large fields of wireless networking, coding theory, graph theory, and percolation theory. Based on the level of information that each node has about the network topology, several reliable and energy-efficient schemes are proposed, all of which are distributed and have low complexity of implementation. The first protocol does not require any information about the network topology. Another protocol, which is more energy efficient, assumes each node has local information about the network topology. In addition, this work proposes a distributed scheme for finding low-cost broadcast trees in wireless networks. This scheme takes into account various parameters such as distances between nodes and link losses. This protocol is then extended to find low-cost multicast trees. Several schemes are extensively simulated and are compared.

Multi-antenna wireless communication systems that employ a large number of antennas have recently stirred a lot of research interest. This is mainly due to the possibility of achieving very high spectral efficiency, power efficiency, and link reliability in such large-scale multiple-input multiple-output (MIMO) systems. An emerging architecture for large-scale multiuser MIMO communications is one where each base station (BS) is equipped with a large number of antennas (tens to hundreds of antennas) and the user terminals are equipped with fewer antennas (one to four antennas) each. The backhaul communication between base stations is also carried out using large number of antennas. Because of the high dimensionality of large-scale MIMO signals, the computational complexity of various transceiver operations can be prohibitively large. Therefore, low complexity techniques that scale well for transceiver signal processing in such large-scale MIMO systems are crucial. The transceiver operations of interest include signal encoding at the transmitter, and channel estimation, detection and decoding at the receiver. This thesis focuses on the design and analysis of novel low-complexity transceiver signal processing schemes for large-scale MIMO systems. In this thesis, we consider two types of large-scale MIMO systems, namely, massive MIMO systems and generalized spatial modulation MIMO (GSM-MIMO) systems. In massive MIMO, the mapping of information bits to modulation symbols is done using conventional modulation alphabets (e.g., QAM, PSK). In GSM-MIMO, few of the avail-able transmit antennas are activated in a given channel use, and information bits are conveyed through the indices of these active antennas, in addition to the bits conveyed through conventional modulation symbols. We also propose a novel modulation scheme named as precoder index modulation, where information bits are conveyed through the index of the chosen precoder matrix as well as the modulation symbols transmitted. Massive MIMO: In this part of the thesis, we propose a novel MIMO receiver which exploits channel hardening that occurs in large-scale MIMO channels. Channel hardening refers to the phenomenon where the off-diagonal terms of HH H become much weaker compared to the diagonal terms as the size of the channel gain matrix H increases. We exploit this phenomenon to devise a low-complexity channel estimation scheme and a message passing algorithm for signal detection at the BS receiver in massive MIMO systems. We refer to the proposed receiver as the channel hardening-exploiting message passing (CHEMP) receiver. The key novelties in the proposed CHEMP receiver are: (i) operation on the matched filtered system model, (ii) Gaussian approximation on the off-diagonal terms of the HH H matrix, and (iii) direct estimation of HH H instead of H and use of this estimate of HH H for detection The performance and complexity results show that the proposed CHEMP receiver achieves near-optimal performance in large-scale MIMO systems at complexities less than those of linear receivers like minimum mean squared error (MMSE) receiver. We also present a log-likelihood ratio (LLR) analysis that provides an analytical reasoning for this better performance of the CHEMP receiver. Further, the proposed message passing based detection algorithm enables us to combine it with low density parity check (LDPC) decoder to formulate a joint message passing based detector-decoder. For this joint detector-decoder, we design optimized irregular binary LDPC codes specific to the massive MIMO channel and the proposed receiver through EXIT chart matching. The LDPC codes thus obtained are shown to achieve improved coded bit error rate (BER) performance compared to off-the-shelf irregular LDPC codes. The performance of the CHEMP receiver degrades when the system loading factor (ratio of the number of users to the number of BS antennas) and the modulation alpha-bet size are large. It is of interest to devise receiver algorithms that work well for high system loading factors and modulation alphabet sizes. For this purpose, we propose a low-complexity factor-graph based vector message passing algorithm for signal detection. This algorithm uses a scalar Gaussian approximation of interference on the basic sys-tem model. The performance results show that this algorithm performs well for large modulation alphabets and high loading factors. We combine this detection algorithm with a non-binary LDPC decoder to obtain a joint detector-decoder, where the field size of the non-binary LDPC code is same as the size of the modulation alphabet. For this joint message passing based detector-decoder, we design optimized non-binary irregular LDPC codes tailored to the massive MIMO channel and the proposed detector. GSM-MIMO: In this part of the thesis, we consider GSM-MIMO systems in point-to-point as well as multiuser communication settings. GSM-MIMO has the advantage of requiring only fewer transmit radio frequency (RF) chains than the number of transmit antennas. We analyze the capacity of point-to-point GSM-MIMO, and obtain lower and upper bounds on the GSM-MIMO system capacity. We also derive an upper bound on the BER performance of maximum likelihood detection in GSM-MIMO systems. This bound is shown to be tight at moderate to high signal-to-noise ratios. When the number of transmit and receive antennas are large, the complexity of en-coding and decoding of GSM-MIMO signals can be prohibitively high. To alleviate this problem, we propose a low complexity GSM-MIMO encoding technique that utilizes com-binatorial number system for bits-to-symbol mapping. We also propose a novel layered message passing (LaMP) algorithm for decoding GSM-MIMO signals. Low computational complexity is achieved in the LaMP algorithm by detecting the modulation bits and the antenna index bits in two deferent layers. We then consider large-scale multiuser GSM-MIMO systems, where multiple users employ GSM at their transmitters to communicate with a BS having a large number of receive antennas. For this system, we develop computationally efficient message passing algorithms for signal detection using vector Gaussian approximation of interference. The performance results of these algorithms show that the GSM-MIMO system outperforms the massive MIMO system by several dBs for the same spectral efficiency. Precoder index modulation: It is known that the performance of a communication link can be enhanced by exploiting time diversity without reducing the rate of transmission using pseudo random phase preceding (PRPP). In order to further improve the performance of GSM-MIMO, we apply PRPP technique to GSM-MIMO systems. PRPP provides additional diversity advantage at the receiver and further improves the performance of GSM-MIMO systems. For PRPP-GSM systems, we propose methods to simultaneously precode both the antenna index bits and the modulation symbols using rectangular precoder matrices. Finally, we extend the idea of index modulation to pre-coding and propose a new modulation scheme referred to as precoder index modulation (PIM). In PIM, information bits are conveyed through the index of a prehared PRPP matrix, in addition to the information bits conveyed through the modulation symbols. PIM is shown to increase the achieved spectral efficiency, in addition to providing diver-sity advantages.

Prevailing low fertility rates in several European states, such as Germany, have been studied widely in recent years. Findings include discrepancies between fertility preference and actual family size as well as between fertility intentions and fertility behavior; an ‘unmet need’ for children found on the individual and the societal level. Fertility preference is specified as the individual ideal number of children, and fertility intentions as the long- or short-term plans to have a child. Apart from investigating the rates of realization, these measures have been understudied. The objective of this study is to illuminate a new angle of low fertility rates in Germany by reviewing fertility measures previously considered to be stable predictors of fertility behavior. The aim is to investigate the stability of fertility preferences and of positive short-term fertility intentions of Germans in their reproductive age. According to the Theory of Planned Behavior and the life-course perspective, attitudes and experiences can influence fertility preferences and short-term fertility intentions. In this study, the suspected connection between unstable preferences and intentions and certain attitudes towards and experiences with the career, working life, and childcare situation is examined. These processes are expected to differ between men and women, and between childless individuals, parents with one child and parents with more than one child. Using data from seven survey waves of the German family panel pairfam, fixed-effects and random-effects regression models are run separately for women and men and for those of different parities. The results suggest that those with high career importance and those who expect or perceive a negative effect of children on the career are more likely to have unstable positive intentions. Although fertility preferences are shown to be somewhat unstable, no relevant relationships can be found. The differences between the findings on men and women regarding relevant determinants and direction of the relationships are unexpectedly small. Childless individuals are as likely to hold unstable preferences and intentions as parents.