Diss. Stockholm : Handelshögsk., 2003.

This dissertation contains five chapters. An introduction and a summary of the research are given in Chapter 1. The other four chapters present theoretical results on the moment structure of GARCH processes. Some chapters also contain empirical examples in order to illustrate applications of the theory. The focus, however, is mainly on statistical theory. Chapter 2 considers the moments of a family of first-order GARCH processes. First, a general condition of the existence of any integer moment of the absolute values of the observations is given. Second, a general expression of this moments as a function of lower-order moments is derived. Third, the kurtosis and the autocorrelation function of the squared and absolute-valued observations are derived. The results apply to a host of different GARCH parameterizations. Finally, the existence, or the lack of it, of the theoretical counterpart to the so-called Taylor effect for some members of this GARCH family is discussed. The asymmetric power ARCH model is a recent addition to time series models that may be used for predicting volatility. Its performance is compared with that of standard models of conditional heteroskedasticity such as GARCH. This has previously been done empirically. In Chapter 3 the same issue is studied theoretically using unconditional fractional moments for the A-PARCH model that are derived for the purpose. The role of the heteroskedasticity parameter of the A-PARCH process is highlighted and compared with corresponding empirical results involving autocorrelation functions of power-transformed absolute-valued return series.In Chapter 4, a necessary and sufficient condition for the existence of the unconditional fourth moment of the GARCH(p,q) process is given as well as an expression for the moment itself. Furthermore, the autocorrelation function of the centred and squared observations of this process is derived. The statistical theory is further illustrated by a few special cases such as the GARCH(2,2) process and the ARCH(q) process.Nonnegativity constraints on the parameters of the GARCH(p,q) model may be relaxed without giving up the requirement of the conditional variance remaining nonnegative with probability one. Chapter 5 looks into the consequences of adopting these less severe constraints in the GARCH(2,2) case and its two second-order special cases, GARCH(2,1) and GARCH(1,2). This is done by comparing the autocorrelation function of squared observations under these two sets of constraints. The less severe constraints allow more flexibility in the shape of the autocorrelation function than the constraints restricting the parameters to be nonnegative. The theory is illustrated by an empirical example. / Revised versions of chapters 2-5 have been published as:He, C. and T. Teräsvirta, "Properties of moments of a amily of GARCH processes" in Journal of Econometrics, Vol. 92, No. 1, 1999, pp173-192.He, C. and T. Teräsvirta, "Statistical Properties of the Asymmetric Power ARCH Process" in R.F. Engle and H. White (eds) Cointegration, causality, and forecasting. Festschrift in honour of Clive W.J. Granger, chapter 19, pp 462-474, Oxford University Press, 1999.He, C. and T. Teräsvirta, "Fourth moment structure of the GARCH(p,q) process" in Econometric Theory, Vol. 15, 1999, pp 824-846.He, C. and T. Teräsvirta, "Properties of the autocorrelation function of squared observations for second order GARCH processes under two sets of parameter constraints" in Journal of Time Series Analysis, Vol. 20, No. 1, January 1999, pp 23-30.

In this dissertation, three essays are presented that apply recent advances in time-series methods to the analysis of inflation and stock market index data for Taiwan. Specifically, ARCH and GARCH methodologies are used to investigate claims of increased volatility in economic time-series data since 1980. In the first essay, analysis that accounts for structural change reveals that the fundamental relationship between inflation and its variability was severed by policies implemented during economic liberalization in Taiwan in the early 1980s. Furthermore, if residuals are corrected for serial correlation, evidence in favor of ARCH effects is weakened. In the second essay, dynamic linkages between daily stock returns and daily trading volume are explored. Both linear and nonlinear dependence are evaluated using Granger causality tests and GARCH modelling. Results suggest significant unidirectional Granger causality from stock returns to trading volume. In the third essay, comparative analysis of the frequency structure of the Taiwan stock index data is conducted using daily, weekly, and monthly data. Results demonstrate that the relationship between mean return and its conditional standard deviation is positive and significant only for high-frequency daily data.

In this dissertation, three essays are presented that apply recent advances in time-series methods to the analysis of inflation and stock market index data for Taiwan. Specifically, ARCH and GARCH methodologies are used to investigate claims of increased volatility in economic time-series data since 1980. In the first essay, analysis that accounts for structural change reveals that the fundamental relationship between inflation and its variability was severed by policies implemented during economic liberalization in Taiwan in the early 1980s. Furthermore, if residuals are corrected for serial correlation, evidence in favor of ARCH effects is weakened. In the second essay, dynamic linkages between daily stock returns and daily trading volume are explored. Both linear and nonlinear dependence are evaluated using Granger causality tests and GARCH modelling. Results suggest significant unidirectional Granger causality from stock returns to trading volume. In the third essay, comparative analysis of the frequency structure of the Taiwan stock index data is conducted using daily, weekly, and monthly data. Results demonstrate that the relationship between mean return and its conditional standard deviation is positive and significant only for high-frequency daily data.

Data described by econometric models typically contains autocorrelation and/or heteroskedasticity of unknown form and for inference in such models it is essential to use covariance matrix estimators that can consistently estimate the covariance of the model parameters. Hence, suitable heteroskedasticity-consistent (HC) and heteroskedasticity and autocorrelation consistent (HAC) estimators have been receiving attention in the econometric literature over the last 20 years. To apply these estimators in practice, an implementation is needed that preferably translates the conceptual properties of the underlying theoretical frameworks into computational tools. In this paper, such an implementation in the package sandwich in the R system for statistical computing is described and it is shown how the suggested functions provide reusable components that build on readily existing functionality and how they can be integrated easily into new inferential procedures or applications. The toolbox contained in sandwich is extremely flexible and comprehensive, including specific functions for the most important HC and HAC estimators from the econometric literature. Several real-world data sets are used to illustrate how the functionality can be integrated into applications. / Series: Research Report Series / Department of Statistics and Mathematics

In this diploma thesis we explain the main principles and properties of bootstrap methods, that can be used to conduct the statistical inference in linear and nonlinear financial time series. We will introduce basic ideas of bootstrap methods for the case when observations can be considered as independent random variables, and afterwards we will describe more advanced methods, that can be successfully used when we are dealing with time series. Thesis deals with both parametric bootstrap methods, that we can use when the underlying parametric model of observations is available, as well as with nonparametric bootstrap methods that are used when more general nonparametric model of time series data is considered. The main objective is to compare particular bootstrap methods and show the usage of these methods on real world data. There is also a basic time series theory included in the work. 1

Two score tests for heteroskedasticity in the errors of a bivariate Probit model are developed, and numerous simulations are performed. These tests are based on an outer product of the gradient estimate of the information matrix, and are constructed using an artificial regression. The empirical sizes of both tests are found to be well-behaved, settling down to the nominal size under the asymptotic distribution as the sample size approaches 1000 observations. Similarly, the empirical powers of both tests increase quickly with sample size. The largest improvement in power occurs as the sample size increases from 250 to 500. An application with health care data from the German Socioeconomic Panel is performed, and strong evidence of heteroskedasticity is detected. This suggests that the maximum likelihood estimator for the standard bivariate Probit model will be inconsistent in this particular case. / Graduate / 0501

This paper measures the effects of the risk of war on nine U.S. financial variables using a heteroskedasticity-based estimation technique. The results indicate that increases in the risk of war cause declines in Treasury yields and equity prices, a widening of lower-grade corporate spreads, a fall in the dollar, and a rise in oil prices. This "war risk factor" accounted for a considerable portion of the variance of these financial variables over the ten weeks leading up to the onset of war with Iraq.

This thesis deals with the nominal and real convergence for Czech Republic and the Euro zone. It also includes analysis of synchronization of economic development in Czech and European economies for identifying potential risks associated with introducing the euro in the CR. The thesis describes different types of convergence and the relevant indicators with their historical evolution and hypothesis about future trends. The empirical part of the paper analyzes some selected indicators using econometric VAR models and linear and non-linear models of conditional heteroskedasticity. A suitable model for the analyzed data is chosen which gives a comparison of development in the Czech Republic and the EU. Especially time series causality, the existence of cointegration and conditional variance processes are observed. In conclusion there's a summary of all theoretical and modelled outputs with the risk evaluation of joining the monetary union.

Made available in DSpace on 2014-06-12T18:29:15Z (GMT). No. of bitstreams: 2 arquivo4279_1.pdf: 1161561 bytes, checksum: 80aee0b17f88de11dd7d0999ad1594a1 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2008 / Esta tese de doutorado trata da realização de inferências no modelo de regressão linear sob heteroscedasticidade de forma desconhecida. No primeiro capítulo, nós desenvolvemos estimadores intervalares que são robustos à presença de heteroscedasticidade. Esses estimadores são baseados em estimadores consistentes de matrizes de covariâncias propostos na literatura, bem como em esquemas bootstrap. A evidência numérica favorece o estimador intervalar HC4. O Capítulo 2 desenvolve uma seqüência corrigida por viés de estimadores de matrizes de covariâncias sob heteroscedasticidade de forma desconhecida a partir de estimador proposto por Qian eWang (2001). Nós mostramos que o estimador de Qian-Wang pode ser generalizado em uma classe mais ampla de estimadores consistentes para matrizes de covariâncias e que nossos resultados podem ser facilmente estendidos a esta classe de estimadores. Finalmente, no Capítulo 3 nós usamos métodos de integração numérica para calcular as distribuições nulas exatas de diferentes estatísticas de testes quasi-t, sob a suposição de que os erros são normalmente distribuídos. Os resultados favorecem o teste HC4