This thesis is an effort to develop generalized dynamic models for systems with time-varying time delays. Unlike the simple time-delay model characterized by a transportation lag in the case of a fixed time delay, time-varying delays exhibit quite different characteristics, making the development of easy to use models a difficult endeavor. First an algorithm is developed to predict the actual input-output behavior when the input signal is directly fed into a device that characterizes the time-varying delay. Input-output behaviour generated with this algorithm serves as the truth model for subsequent approximate model development. Simulation results for different classes of delay and different inputs were obtained using the truth model. The input functions were limited to steps, ramps and sinusoids. This limited class of inputs and delays defines the scope of this thesis and the results are to be interpreted as such. The methodology adopted to identify the basic underpinnings of models was system identification where input-output data came from the truth model. Models for the aforementioned classes of inputs and delays were then derived using elementary system identification tools. These models were then carefully analyzed to extract trends by changing the delay parameter. A satisfactory trend was observed in the case of linearly varying time delay. A generalized model for the linearly varying time delay with step and polynomial inputs was developed. An attempt was also made at developing a generalized model for sinusoidally time-varying time delays. This study proposes a model for linearly time-varying time delay, whose structure is not surprisingly also dependent on the class of inputs. It is shown that the derived model reduces to the well known model in the case of a fixed delay.

Understanding stock-bond return correlation is a key facet in asset mix, asset allocation and in an investor’s portfolio optimisation strategy. For the last couple of decades, several studies have probed this cardinal relationship. While initial literature tries to understand the fundamental pattern of co-movements, later studies aim to model the economic state variables influencing such time-varying volatility behaviour of stock-bond returns. This study provides a systematic literature review in the field of stock and bond return correlation. The review investigates the existing literature in three key dimensions. First, it examines the effect of macro-economic variables on SB return co-movements. Second, it illustrates the effect of financial integration on the asset correlation dynamics. Third, it reviews the existing models that are employed to estimate the dynamic relationship. In addition to the systematic review, I conduct an empirical analysis of stock-bond return co-movements on U.S. capital market. Both the literature and the empirical investigation substantiate my claims on existing research gaps and respective scope for further research. Evidence shows that existing models impose strong restrictions on past stock-bond return variance dynamics and yield inconclusive results. I, therefore, propose an alternative method, i.e. copula function approach, to model stock and bond time-varying co-movements. Since the previous studies largely focus on developed economies, I suggest an empirically investigation of emerging economies as well. This will allow me to examine the effect of financial integration on the dynamic asset return correlation. Apart from this academic contribution, the study provides an illustration of the economic implications which relate to portfolio optimization and minimal-risk hedge ratio.

In the first part of the thesis, we study the trade-off between the transmission reliability and data rate in high signal-to-noise ratio regime in ad-hoc wireless networks. Bandwidth allocation plays a significant role in this trade-off, since dividing bandwidth reduces the number of users on each band and consequently decreases the interference level, however it also decreases the data rate. Noting that the interference power is substantially influenced by the network density, this trade-off introduces a measure for appropriate bandwidth allocation among users considering the network density. The diversity-multiplexing trade-off is derived for a one-dimensional regular ad-hoc network. In the second part of the thesis, we study the performance of point-to-point and broadcast systems with partial channel state information at the transmitter in a time-varying environment. First, the capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel state information is perfectly known at the receiver and is fed back to the transmitter at the regular time-intervals. The system capacity is investigated in two cases: i) finite state Markov channel, and ii) additive white Gaussian noise channel with time-correlated fading. In a multiuser scenario, we consider a downlink system in which a single-antenna base station communicates with single antenna users, over a time-correlated fading channel. It is assumed that channel state information is perfectly known at each receiver, while the rate of channel variations and the fading gain at the beginning of each frame are known to the transmitter. The asymptotic throughput of the scheduling that transmits to the user with the maximum signal to noise ratio is examined applying variable code rate and/or variable codeword length signaling. It is shown that by selecting a fixed codeword length for all users, the order of the maximum possible throughput (corresponding to quasi-static fading) is achieved.

In this thesis, we consider plants with uncertain parameters where those parameters may be time-varying; we show that, with reasonable assumptions, we can design a controller that stabilizes such systems while providing near-optimal performance in the face of persistent discontinuities in the time-varying parameters. We consider two classes of uncertainty. The first class is modeled via a (possibly infinite) set of linear time invariant plants - the uncertain time variation consists of unpredictable (but sufficiently slow) switches between those plants. We consider standard LQR performance, and, in the case of a finite set of plants, the more complicated problem of LQR step tracking. Our second class is a time-varying gain margin problem: we consider an reasonably general, uncertain, time-varying function at the input of an otherwise linear time invariant nominal plant. In this second context, we consider the tracking problem wherein the signal to be tracked is modeled by a (stable) filter at the exogenous input and we measure performance via a weighted sensitivity function. The controllers are periodic and mildly nonlinear, with the exception that the controller for the second class is linear.

In the first part of the thesis, we study the trade-off between the transmission reliability and data rate in high signal-to-noise ratio regime in ad-hoc wireless networks. Bandwidth allocation plays a significant role in this trade-off, since dividing bandwidth reduces the number of users on each band and consequently decreases the interference level, however it also decreases the data rate. Noting that the interference power is substantially influenced by the network density, this trade-off introduces a measure for appropriate bandwidth allocation among users considering the network density. The diversity-multiplexing trade-off is derived for a one-dimensional regular ad-hoc network. In the second part of the thesis, we study the performance of point-to-point and broadcast systems with partial channel state information at the transmitter in a time-varying environment. First, the capacity of time-varying channels with periodic feedback at the transmitter is evaluated. It is assumed that the channel state information is perfectly known at the receiver and is fed back to the transmitter at the regular time-intervals. The system capacity is investigated in two cases: i) finite state Markov channel, and ii) additive white Gaussian noise channel with time-correlated fading. In a multiuser scenario, we consider a downlink system in which a single-antenna base station communicates with single antenna users, over a time-correlated fading channel. It is assumed that channel state information is perfectly known at each receiver, while the rate of channel variations and the fading gain at the beginning of each frame are known to the transmitter. The asymptotic throughput of the scheduling that transmits to the user with the maximum signal to noise ratio is examined applying variable code rate and/or variable codeword length signaling. It is shown that by selecting a fixed codeword length for all users, the order of the maximum possible throughput (corresponding to quasi-static fading) is achieved.

In this thesis, we consider plants with uncertain parameters where those parameters may be time-varying; we show that, with reasonable assumptions, we can design a controller that stabilizes such systems while providing near-optimal performance in the face of persistent discontinuities in the time-varying parameters. We consider two classes of uncertainty. The first class is modeled via a (possibly infinite) set of linear time invariant plants - the uncertain time variation consists of unpredictable (but sufficiently slow) switches between those plants. We consider standard LQR performance, and, in the case of a finite set of plants, the more complicated problem of LQR step tracking. Our second class is a time-varying gain margin problem: we consider an reasonably general, uncertain, time-varying function at the input of an otherwise linear time invariant nominal plant. In this second context, we consider the tracking problem wherein the signal to be tracked is modeled by a (stable) filter at the exogenous input and we measure performance via a weighted sensitivity function. The controllers are periodic and mildly nonlinear, with the exception that the controller for the second class is linear.

In the thesis, we investigate transmit beamforming strategies in a wireless cooperative network consisting of one source, one destination and multi relays that adopt amplify-and-forward (AF). In our scheme, small amount of information feedback from the destination, each relays perturbs individually based beamforming coefficient. Perturbation-based beamforming have been proposed in [16], where the authors assume that the channel is time-invariant, and every relay node can not acquire channel state information (CSI) after receiving pilot sequence signals, the relays multiply the pilot sequence with two perturbed beamforming vectors, and forward two weighted training sequence to destination. At the destination, the signal to noise ratio (SNR) of two received training sequence are evaluated and compared. Finally, the destination compare with SNRs. To indicate the result of compared SNRs, destination feedback one-bit message to inform relays the comparison results, and then relays update beamforming vector based on one-bit message. After several iteration, the beamforming vector will approach the optimum one. However, in time-varying environment, the updating rata of beamforming vector in the method with one-bit feedback may be more slowly than rate of channel variation. The contribution of this thesis is to propose transmit beamforming scheme with two-bit or finite-bit feedback to accommodate to the time-varying environment. In our proposed scheme, the destination linearly combines two received sequence corresponding to two different beamforming vectors with various weighting factors. After evaluating and comparing the SNRs of combined signals, the destination notifies the optimum linear combining factors using a multi-bit feedback message. Based on the feedback message, relays can update the beamforming vector correspondingly. In chapter five, it shows through computer simulations that our proposed scheme can raise average SNR and reduce bit error rate effectively.

This study tests whether contagion effects existed during the ¡§subprime mortgage crisis¡¨ among the equity markets of the US, the EU, Asia and emerging markets. The time-varying correlation coefficients are estimated by the dynamic conditional correlation (DCC) of Engle (2002), using a multivariate GJR-GARCH with AR (1) model. The empirical findings show that the conditional correlation coefficients of stock returns between the U.S. and others countries were positive and that the contagion effect exists among stock markets. Financial markets displayed contagion effects, in that the global equity markets were confronted with elevated systematic risk at the same time. Therefore, this study further examines the role of systematic risk in the equity market of each country. I used the rolling formulae, the MV-DGP, and DCC-GARCH (1, 1) models to estimate the CAPM beta and downside betas. This study found higher systematic risk (downside systematic risk) in the stock markets of the United States, Germany, France and Brazil, which had beta values nearly above one, while the Chinese stock market had the lowest systemic risk and served as a hedge for investors and fund managers. Finally, the results demonstrate that DCC-HW beta can capture some downside linkages between the market portfolios and expected stock returns, while these linkages cannot likely be captured by the CAPM beta.

Scholarship shows that the social construction of crime is responsible for the public’s demand for tougher criminal justice policies. Yet, there remains disagreement over several key issues regarding the relationship between strategic communication and the punitiveness of the mass public. Little is known about the magnitude and direction of changes in punitive sentiment over the last 50 years. Moreover, there is disagreement over when the public began to demand punitive solutions to crime over alternative policies. Many scholars point the racial turmoil of the 1960s, but none have shown conclusive evidence of any fundamental change in punitive sentiment. Finally, there is disagreement over what type of strategic appeal is most effective at shaping public opinion. The argument of this research is that the democratic nature of American pol- itics creates an environment where the competition of ideas flourish. Political ac- tors can use several types of strategic communication (agenda-setting, persuasion, priming, framing) to shape political outcomes. The effectiveness of an appeal does not remain constant over time, but should evolve around systematic social changes— environmental conditions and social norms. Thus, there is a time varying relationship between various appeals and public opinion. A content analysis of crime news in the New York Times provides measures of four types of strategic messages. Instrumental factors such as the economy and public policy are also shown to influence the public’s desire for punitive criminal justice policies. A Bayesian changepoint model provides a means to test when, if any,fundamental change occurred in the public’s punitive sentiment. Contrary to most accounts, the changepoint model identifies 1972 as having the highest probability of a breakpoint suggesting a public backlash against the Supreme Court’s Furman vs. Georgia decision to abolish the death penalty. Estimates from a state-space model show that different types of messages in the media shape punitive sentiment and that the effectiveness of racial primes and presidential attention to crime changes over time. Moreover, these changes are shown to be a function of changes in social context and norms suggesting ways to improve political communication.

The work presented in this dissertation can be grouped around two major themes. The first theme relates to the asset allocation and the second theme relates to risk management. In Chapter Three, we investigate the dynamics of foreign exchange and stock returns based on an extended version of Sentana and Wadhwani (1992) model. This study is mainly driven by the wish to explain two major stylized facts that puzzled the older models. We find evidence to support that only intertemporal variation in the foreign exchange risk premium can be explained by time¡Vvarying covariance priced risk factors. Furthermore, we also find that the first order autocorrelation of both foreign exchange and stock market returns in Taiwan is negatively related to the level of conditional volatility and covariance. This time-varying nature of the serial correlation pattern is consistent with our model where some traders follow feedback strategies. The three nested asset pricing models with four models of conditional second moments are strongly rejected. We conclude that our extended Sentana and Wadhwani model is more adequate in explaining the dynamics of foreign exchange and stock markets. In Chapter Four, we investigate the risk management of futures market and spot market returns. There is widespread evidence that the volatility of stock returns display an asymmetric response to good and bad news. This paper attempted and found the asymmetric behavior co-existence in spot as well as future markets. By using the Asymmetric Dynamic Model (ADC) proposed by Kroner and Ng (1998), we estimated the conditional covariance matrix asymmetric and calculated dynamic optimal hedge ratios. With the help of that asymmetric model, our ¡§out of sample¡¨ dynamic hedging strategy out-performed that of normally dynamic hedging strategies. However, while taking the transaction costs into consideration, the performance was even worse than that of the static strategy.