The thesis concentrates on property of linearity in time series models, its definitions and possibilities of testing. Presented tests focus mainly on the time domain; these are based on various statistical methods such as regression, neural networks and random fields. Their implementation in R software is described. Advantages and disadvantages for tests, which are implemented in more than one package, are discussed. Second topic of the thesis is additivity in nonlinear models. The definition is introduced as well as tests developed for testing its presence. Several test (both linearity and additivity) have been implemented in R for purposes of simulations. The last chapter deals with application of tests to real data. 1

The analysis of time series has long been the subject of interest in different fields. For decades time series were analysed with linear models, which have many advantages. Nevertheless, an issue which has been raised is whether there exist other models that can explain and forecast real data better than linear ones. In this thesis, new nonlinear time series models are suggested, which consist of a nonlinear conditional mean model, such as an ExpAR or an Extended ExpAR, and a nonlinear conditional variance model, such as an ARCH or a GARCH. Since new models are introduced, simulated series of the new models are presented, as it is important in order to see what characteristics real data which could be explained by them should have. In addition, the models are applied to various stationary and nonstationary economic and financial time series and are compared to the classic AR-ARCH and AR-GARCH models, in terms of fitting and forecasting. It is shown that, although it is difficult to beat the AR-ARCH and AR-GARCH models, the ExpAR and Extended ExpAR models and their special cases, combined with conditional heteroscedastic errors, can be useful tools in fitting, describing and forecasting nonlinear behaviour in financial and economic time series, and can provide some improvement in terms of both fitting and forecasting compared to the AR-ARCH and AR-GARCH models.

I study the role of heterogeneity and idiosyncratic risk in Macroeconomics, and their implications on problems of income taxation. In the first chapter, I study the effects of redistributive taxation in an incomplete market economy with heterogeneous agents and idiosyncratic risk. I focus on the role of distortions in labor supply decisions and the interplay of heterogeneity and uninsurable idiosyncratic shocks, conducting the first general equilibrium analysis of a Negative Income Tax (NIT). I show that a NIT is a serious candidate to replace the current income tax in the United States. I find that the optimal NIT has a marginal tax rate of 28% and a transfer of 10% of per capita GDP, roughly $4600. The welfare gains of replacing the current US income tax with a NIT are equivalent to a 6.3% increase in annual consumption in every state of the world. Low-ability agents, in the bottom quintile of the productivity distribution, benefit the most, while high-ability agents are worse off. A consequence of the reform is that the composition of the labor force changes, with high-productivity agents working more, in relative terms, than low-productivity agents. Finally, I find that the riskier the economy, the higher the welfare gains of the NIT as a provider of public insurance. In the second chapter, I study labor income dynamics over the life cycle and introduce a novel methodology that can detect the presence of patterns in the idiosyncratic earnings shocks and recognize economic forces in action. Using a sample from the Panel Study of Income Dynamics (PSID), I estimate a Bayesian Logistic Smoothed Transition Autoregressive model of order 1 (LSTAR(1)) with a rich level of heterogeneity in the innovations. I find that there is a life-cycle pattern in the earning shocks: before the age 29, young workers experience shocks with higher variance and a positive probability of lower persistence than older workers. A comparison with conventional models shows that an incorrect model specification introduces bias in the estimates. The proposed model can be easily approximated with a discrete Markov process. This means that this model can be used by macroeconomists to calibrate income processes.

Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.

Einleitung & Problemstellung: Beschwerden nach Beschleunigungsverletzungen der Halswirbelsäule sind oft nur unzureichend einzuordnen und diagnostizierbar. Eine eindeutige Diagnostik ist jedoch für eine entsprechende Therapie wie auch möglicherweise entstehende versicherungsrechtliche Forderungen notwendig. Die Entwicklung eines geeigneten Diagnoseverfahrens liegt damit im Interesse von Betroffenen wie auch Kostenträgern. Neben Störungen der Weichteilgewebe ist fast immer die Funktion der Halsmuskulatur in Folge eines Traumas beeinträchtigt. Dabei wird vor allem die sensorische Funktion der HWS-Muskulatur, die an der Regulation des Gleichgewichts beteiligt ist, gestört. In Folge dessen kann angenommen werden, dass es zu einer Beeinträchtigung der Gleichgewichtsregulation kommt. Die Zielstellung der Arbeit lautete deshalb, die möglicherweise gestörte Gleichgewichtsregulation nach einem Trauma im HWS-Bereich apparativ zu erfassen, um so die Verletzung eindeutig diagnostizieren zu können. Methodik: Unter Verwendung eines posturographischen Messsystems mit Kraftmomentensensorik wurden bei 478 Probanden einer Vergleichsgruppe und bei 85 Probanden eines Patientenpools Kraftmomente unter der Fußsohle als Äußerung der posturalen Balanceregulation aufgezeichnet. Die gemessenen Balancezeitreihen wurden nichtlinear analysiert, um die hohe Variabilität der Gleichgewichtsregulation optimal zu beschreiben. Über die dabei gewonnenen Parameter kann überprüft werden, ob sich spezifische Unterschiede im Schwankungsverhalten anhand der plantaren Druckverteilung zwischen HWS-Traumatisierten und den Probanden der Kontrollgruppe klassifizieren lassen. Ergebnisse: Die beste Klassifizierung konnte dabei über Parameter erzielt werden, die das Schwankungsverhalten in Phasen beschreiben, in denen die Amplitudenschwankungen relativ gering ausgeprägt waren. Die Analysen ergaben signifikante Unterschiede im Balanceverhalten zwischen der Gruppe HWS-traumatisierter Probanden und der Vergleichsgruppe. Die höchsten Trennbarkeitsraten wurden dabei durch Messungen im ruhigen beidbeinigen Stand mit geschlossenen Augen erzielt. Diskussion: Das posturale Balanceverhalten wies jedoch in allen Messpositionen eine hohe individuelle Varianz auf, so dass kein allgemeingültiges Schwankungsmuster für eine Gruppengesamtheit klassifiziert werden konnte. Eine individuelle Vorhersage der Gruppenzugehörigkeit ist damit nicht möglich. Die verwendete Messtechnik und die angewandten Auswerteverfahren tragen somit zwar zu einem Erkenntnisgewinn und zur Beschreibung des Gleichgewichtsverhaltens nach HWS-Traumatisierung bei. Sie können jedoch zum derzeitigen Stand für den Einzelfall keinen Beitrag zu einer eindeutigen Bestimmung eines Schleudertraumas leisten. / Introduction & Problem definition: Disorders after acceleration injuries of the cervical spine can often be classified and diagnosed only inadequately. But an explicit diagnosis is necessary as a basis for an adequate therapy as well as for possibly arising demands pursuant to insurance law. The development of suitable diagnosis methods is in the interest of patients as well as the cost units. Apart from disorders of the soft tissues there are almost always impairments of the function of the neck musculature. Particularly the sensory function of the cervical spine musculature, which participates in the regulation of the equilibrium, is disturbed by that. As a result in can be assumed that the postural control is also disturbed. Therefore the aim of this study was to examine the possibly disturbed postural motor balance after a whiplash injury of the cervical spine with the help of apparatus-supported methods to be able to unambigiously diagnose. Methods: postural measuring system based on the force-moment sensortechnique was used to record the postural balance regulation of 478 test persons and 85 patients which had suffered a whiplash injury. Data analysis was accomplished by linear as well as by nonlinear time series methods in order to characterise the balance regulation in an optimal way. Thus it can be determined whether there can be classified specific differences in the plantar pressure distribution covering patients with a whiplash injury and the test persons of the control group. Results: The best classification could be achieved by parameters which describe the variation of the postural balance regulation in phases in which the differences of the amplitudes of the plantar pressure distribution were relatively small. The analyses showed significant differences in the postural motor balance between the group of patients with whiplash injuries and the control group. The most significant differences (highest discriminate rates) could be observed by measurements in both-legged position with closed eyes. Discussion: Although the results achieved support the hypothesis mentioned above, is must be conceded that the postural motor balance showed a high individual variation in all positions of measurement. Therefore no universal variation model could be classified for the entirety of either group. This way an individual forecast of the group membership is impossible. As a result the measurement technology being used and the nonlinear time series analyses can contribute to the gain of knowledge and to the description of the regulation of postural control after whiplash injury. But at present they cannot contribute to an explicit determination of a whiplash injury for a particular case.

The spectral analysis method is an important tool in time series analysis and the spectral density plays a crucial role on the spectral analysis. However, one of limitations of the spectral density is that the spectral density reflects only the covariance structure among several dependence measures in the time series data. To overcome this restriction, we define two spectral densities, the quantile spectral density and the association spectral density. The quantile spectral density can model the pairwise dependence structure and provide identification of nonlinear time series and the association spectral density allows detecting periodicities on different parts of the domain of the time series. We propose the estimators for the quantile spectral density and the association spectral density and derive their sampling properties including asymptotic normality. Furthermore, we use the quantile spectral density to develop a goodness-of-fit tests for time series and explain how this test can be used for comparing the sequential dependence structure of two time series. The asymptotic sampling properties of the test statistic are derived under the null and alternative hypothesis, and a bootstrap procedure is suggested to obtain finite sample approximation. The method is illustrated with simulations and some real data examples. Besides the exploration of the new spectral densities, we consider general quadratic forms of alpha-mixing time series and derive asymptotic normality of these forms under the relatively weak assumptions.

Wheat is an extremely important agricultural commodity, due to its crucial role in everyday nutrition, food security, and in terms of incomes of a large body of farmers worldwide. This study examines the dynamics of wheat prices in Turkey in a framework that allows for regime switching. Due to their simplicity, threshold autoregressive (TAR) models are used to capture the effects of factors such as transaction costs and other institutional arrangements that generate discontinuous adjustment to equilibrium price level. The results are compared with standard linear model estimations. Results indicate that there is strong evidence for asymmetric adjustment of wheat prices in Turkey to the equilibrium price, hence models allowing for regime switching are more preferable over the linear ones. However, the diagnostics of the TAR model reveal that specification of a TAR model allowing for more than two regimes, or a smooth transition autoregressive (STAR) model that allows for smooth transition through a continuum of regimes might be more appropriate.

This paper reexamines the long-run real interest rate parity of the OECD countries by using the unit root test proposed by Ng and Perron (2001) and by the application of simulation to establish the small sample distribution under the null and the alternative hypothesis. By using the small sample distribution of the unit root statistics, we can make sure that first, size distortions are not the reasons contributing to the rejection of the fact that the alternative hypothesis is unit root. Second, the inference that the low power is not necessary causes the not rejecting the alternative hypothesis is correct. If still can not decide which distributions might cause the real interest difference series by comparing the unit root statistics and the relative location of the small sample distribution, we test that whether the series are asymmetric in those countries which we can not decide what kind of distributions they are by the threshold autoregression model proposed by Caner and Hansen (2001). Finally, the empirical results indicate that the RIPH holds in Australia¡BBelgium¡BCanada¡BFinland¡BFrance¡BGermany¡BJapan and Sweden whenever data frequency under linear time series model. Under quarterly data of Italy and United Kingdom and monthly data of Denmark, it turns out that the data have the traits of nonlinear time series model. Besides, the evidence of supporting the long-run real interest rate parity can not be reached and the phenomena that partial unit root exist in United Kingdom and Denmark.

This thesis explores the interaction between virtual and actual realms in architecture through digital design process and developing environment qualities thereby. The focus will be on the projects that are designed in digital medium to be generated in physical environment. By examining the design attitude of selected four projects in this context, this thesis claims that the two realms of virtual and actual are interdependent. The framework of the study is based on Gilles Deleuze&rsquo / s definitions of &ldquo / actualization of the virtual&rdquo / , and &ldquo / realization of the possible&rdquo / . In this study, besides its connotations of digital technology, the concept of virtual is highlighted with its meaning of &ldquo / potential&rdquo / . The philosophical discourse on virtual and actual proves that the relation between these two realms has a potential to generate new conceptual fields. According to this study, for architecture &ldquo / actualization of the virtual&rdquo / , cultivates the &ldquo / unforeseen relations and new connections&rdquo / in terms of new understandings of space and time. This study introduces the conceptual pairs of form-unform, autoplastic-alloplastic space and linear-nonlinear time to develop discussions on the concerned process. The aim is to explore new space and time considerations both in the design process and in the physical architectural environment generated by this process. The emphasis will be on how responsive and interactive environments speculate the established conceptions of space and time in-between virtual and actual realms. This thesis claims that the architectural projects between virtual and actual are subject to break the traditional understandings of space and time.

Abstract This thesis considers some linear and nonlinear time series models. In the linear case, the analysis of a large number of short time series generated by a first order autoregressive type model is considered. The conditional and exact maximum likelihood procedures are developed to estimate parameters. Simulation results are presented and compare the bias and the mean square errors of the parameter estimates. In Chapter 3, five important nonlinear models are considered and their time series properties are discussed. The estimating function approach for nonlinear models is developed in detail in Chapter 4 and examples are added to illustrate the theory. A simulation study is carried out to examine the finite sample behavior of these proposed estimates based on the estimating functions.