D. Phil. / There have been two rather distinct approaches to the analysis of time series: the time domain approach and frequency domain approach. The former is exemplified by the work of Quenouille (1957), Durbin (1960), Box and Jenkins (1970) and Ljung and Box (1979). The principal names associated with the development of the latter approach are Slutsky (1929, 1934), Wiener (1930, 1949), Whittle (1953), Grenander (1951), Bartlett (1948, 1966) and Grenander and Rosenblatt (1957). The difference between these two methods is discussed in Wold (1963). In this thesis, we are concerned with a frequency domain approach. Consider a model of the "signal plus noise" form yt = g (2t — 1 2n ) + 77t t= 1,2,—. ,n (1.1) where g is a function on (0, 1) and Ti t is a white noise process. Our interest is primarily in testing the hypothesis that g is constant, that is, that it does not change over time. There is a vast literature related to this problem in the special case where g is a step function. In that case (1.1) specifies an abrupt change model. Such abrupt change models are treated extensively by Csorgo and Horvath (1997), where an exhaustive bibliography can also be found. The methods associated with the traditional abrupt change models are, almost without exception, time domain methods. The abrupt change model is in many respects too restrictive since it confines attention to signals g that are simple step functions. In practical applications the need has arisen for tests of constancy of the mean against a less precisely specified alternative. For instance, in the study of variables stars in astronomy (Lombard (1998a)) the appropriate alternative says something like: "g is non-constant but slowly varying and of unspecified functional form". To accommodate such alternatives within a time domain approach seems to very difficult, if at all possible. They can, however, be accommodated within a frequency domain approach quite easily, as shown by, for example, Lombard (1998a and 1998b). Tests of the constancy of g using the frequency domain characteristics of the observations have been investigated by a number of authors. Lombard (1988) proposed a test based on the maximum of squared Fourier cosine coefficients at the lowest frequency oscillations. Eubank and Hart (1992) proposed a test which is based on the maximum the averages of Fourier cosine coefficients. The essential idea underlying these tests is that regular variation in the time domain manifests itself entirely at low frequencies in the frequency domain. Consequently, when g is "high frequency" , that is consists entirely of oscillations at high frequencies, the tests of Lombard (1988) and of Eubank and Hart (1992) lose most of their power. The fundamental tool used in frequency domain analysis is the periodogram; see Chapter 2 below for the definition and basic properties of the latter. A new class of tests was suggested by Lombard (1998b) based on the weighted averages of periodogram ordinates. When 7i t in model (1.1) are i.i.d. random variables with zero mean and variance cr-2 , one form of the test statistic is T1r, = Etvk fiy (A0/0-2 - (1.2) k=1 where wk is a sequence of constants that decrease as k increases and m = [i]. The rationale for such tests is discussed in detail in Lombard (1998a and 1998b). The greater part of the present Thesis consists of an investigation of the asymptotic null distributions, and power, of such tests. It is also shown that such tests can be applied directly to other, seemingly unrelated problems. Three instances of the latter type of application that are investigated in detail are (i) frequency domain competitors of Bartlett's test for white noise, (ii) frequency domain-based tests of goodness-of-fit and (iii) frequency domain-based tests of heteroscedasticity in linear or non-linear regression. regression. The application of frequency domain methods to these problems are, to the best of our knowledge, new. Until now, most research has been restricted to the case where m in (1.1) are i.i.d. random variables. As far as the correlated data are concerned, the changepoint problem was investigated by, for instance, Picard (1985), Lombard and Hart (1994) and Bai (1994) using time domain methods. Kim and Hart (1998) proposed two test statistics derived from frequency domain considerations and that are modeled along the lines of the statistics considered by Eubank and Hart (1992) in the white noise case. An analogue of the type of test statistic given in (1.2) for use with correlated data was proposed, and used, by Lombard (1998a). The latter author does not, however, provide statements or proofs regarding the asymptotic properties of the proposed test.

When testing for the equality of regression slopes based on ordinary least squares (OLS) estimation, extant research has shown that the standard F performs poorly when the critical assumption of homoscedasticity is violated, resulting in increased Type I error rates and reduced statistical power (Box, 1954; DeShon & Alexander, 1996; Wilcox, 1997). Overton (2001) recommended weighted least squares estimation, demonstrating that it outperformed OLS and performed comparably to various statistical approximations. However, Overton's method was limited to two groups. In this study, a generalization of Overton's method is described. Then, using a Monte Carlo simulation, its performance was compared to three alternative weight estimators and three other methods. The results suggest that the generalization provides power levels comparable to the other methods without sacrificing control of Type I error rates. Moreover, in contrast to the statistical approximations, the generalization (a) is computationally simple, (b) can be conducted in commonly available statistical software, and (c) permits post hoc analyses. Various unique findings are discussed. In addition, implications for theory and practice in psychology and future research directions are discussed.

Using terminal sires for crossbreeding is standard practice in the UK sheep industry, where over 70% of market lambs have terminal sire breeding. Thus, selection focusing on terminal sires will translate to changes in the entire industry. Consumers perceive lamb meat as fatty and demand for it has decreased. A lean growth index was developed for terminal sire breeds to increase carcass lean content while keeping fat constant at a constant age end point. The purposes of this study were: to evaluate the effects of index selection of terminal sires on their crossbred offspring up to harvest; to evaluate the effectiveness of the index within the terminal sire breeds; to evaluate the presence and consequences of heterogeneous environmental variances and genetics by environment interactions (GxE) on genetic evaluation. The most widely used breeds of terminal sires in the UK are Charollais, Suffolk, and Texel. These breeds participated in sire referencing schemes from the early 1990s by sharing rams selected on the lean growth index. From 1999 to 2002 approximately 15 high and 15 low lean growth index score rams per breed were selected from their sire referencing schemes and mated to Welsh and Scottish Mule ewes. Their crossbred offspring were reared on 3 farms in the UK under commercial conditions. In total, 6,515 lambs were born between 2000 and 2003. Lambs were weighed at birth (BWT), 5 weeks (5WT), and 10 weeks (10WT). The average daily gain (ADG) from birth to 10 weeks was calculated. Lambs were finished to an estimated 11% subcutaneous fat by visual examination. At harvest, they were weighed (HWT), ultrasonically scanned for muscle (UMD) and fat (UFD) depth, and assessed for condition score and conformation. Lambs sired by high index rams were on average, across breeds, heavier at all ages (P < 0.01) with 0.07 ± 0.03, 0.3 ± 0.1, 0.4 ± 0.1, and 1.2 ± 0.2 kg greater BWT, 5WT, 10WT, and HWT respectively. Their ADG was 5.1 ± 1.9 g/d greater than low index sired lambs. They had thicker UMD (0.7 ± 0.2 mm) and thinner UFD (0.08 ± 0.01 mm). High vs. low index sired lambs took the same amount of days to reach harvest fatness. Suffolk-sired lambs were on average heavier, with greater ADG, whereas Charollais-sired lambs were lightest with smallest ADG. Texel-sired lambs had thicker UMD than Charollais (0.7 ± 0.2 mm; P < 0.001) but were not different than Suffolk. Charollais-sired lambs had greater UFD than both Texel- (0.098 ± 0.016 mm) and Suffolk- (0.061 ± 0.017 mm) sired lambs (P < 0.001). Texel-sired lambs reached harvest condition faster than the other breeds (P < 0.01). Index selection produced heavier and leaner lambs at finishing. Producers have flexibility in choosing the terminal sire that best fits their production system. Heteroscedascity and GxE were found to be more important for ultrasonic traits than weight traits. Fitting a farm by sire random interaction component improved model fit, but only accounted for less than 2% of the variation in weight traits. For ultrasonic traits, it accounted for at least 10% of the variation. When fitting traits as separate but correlated by farm, genetic correlations among traits were mostly above 0.8, indicating no GxE. Reactions norms for sires were fitted. For weight traits and UMD, sires had positive slopes (were environmentally sensitive) that were similar in value, thus performance improved with improving environments. For UFD, reaction norm slopes varied form negative to positive, indicating GxE. Consequences of heteroscedasticity are not large for these data, and any consequence of GxE on breeding goals should be evaluated before explicitly modeling it in genetic evaluation. There was evidence of genetic variation in sensitivity of sires; therefore, they could be selected to be more or less sensitive depending on economic considerations. / Ph. D.

The thesis investigates relationship between daily stock return volatility of Dow Jones Industrial Average stocks and data obtained on Twitter, the social media network. The Twitter data set contains a number of tweets, categorized according to their polarity, i.e. positive, negative and neutral sentiment of tweets. We construct two classes of models, GARCH and ARFIMA, where for either of them we research basic model setting and setting with additional Twitter variables. Our goal is to compare, which of them predicts the one day ahead volatility most precisely. Besides, we provide commentary regarding the effects of Twitter volume variables on future stock volatility. The analysis has revealed that the best performing model, given the length and structure of our data set, is the ARFIMA model augmented on Twitter volume residuals. In the context of the thesis, Twitter volume residuals represent unexpected activity on the social media network and are obtained as residuals from Twitter volume autoregression. Plain ARFIMA model was the second best and plain volume augmented ARFIMA was in third place. This means that all three ARFIMA models outperformed all three GARCH models in our research. Regarding the Twitter estimation parameters, we found that higher the activity the higher tomorrow's stock...

Over the last few decades, numerous studies have adopted efficiency and productivity techniques to examine and evaluate the overall performance of banking industries to inform policy effect as well as identify the best practice. The majority of banking efficiency and productivity studies focus on the developed US and European countries. There are only limited studies in the Asian banking industries but no cross-country comparison in major Asian economies. To fill this literature gap, this thesis attempts to measure and compare the cost efficiency and total factor productivity change in ten Asian banking sectors using an unbalanced panel data set consisting of 280 commercial banks over the period of 1998 to 2005. It is widely agreed that cross-country differences play an important part in examining banks performance in international comparison. They can influence the frontier technology as additional explanatory variables or they can enter inefficiency directly as a measure of determinants or heteroscedasticity. Both cases are considered in the empirical sections of this thesis. In the former case, the empirical results from systematic comparisons of panel data stochastic frontier models with and without incorporating these cross-country heterogeneities suggests that cross-country differences are important sources to explain banks performances therefore they should not be neglected. The overall cost efficiency in these Asian banking industries is 0.5897 with a decreasing trend, despite positive technical progress and slight economies of scale. The total factor productivity change is measured by using a new cost-based total factor productivity index, an index number counterpart of Bauer's (1990) total differential approach. A five-way decomposition is also provided with the attempt to identify the main contributors to the productivity change. Overall, Asian banking industries have experienced positive but not substantial productivity change from 1998-05. In the latter case, a general model that considers exogenous influences in both inefficiency and random noise error term is constructed and compared against other alternative specifications. The empirical results favour this general model and the overall and country-specific cost efficiency and total factor productivity are then estimated and calculated.

Doctor of Philosophy / Department of Statistics / Weixing Song / The regression model has been given a considerable amount of attention and played a significant role in data analysis. The usual assumption in regression analysis is that the variances of the error terms are constant across the data. Occasionally, this assumption of homoscedasticity on the variance is violated; and the data generated from real world applications exhibit heteroscedasticity. The practical importance of detecting heteroscedasticity in regression analysis is widely recognized in many applications because efficient inference for the regression function requires unequal variance to be taken into account. The goal of this thesis is to propose new testing procedures to assess the adequacy of fitting parametric variance function in heteroscedastic regression models. The proposed tests are established in Chapter 2 using certain minimized L[subscript]2 distance between a nonparametric and a parametric variance function estimators. The asymptotic distribution of the test statistics corresponding to the minimum distance estimator under the fixed model and that of the corresponding minimum distance estimators are shown to be normal. These estimators turn out to be [sqrt]n consistent. The asymptotic power of the proposed test against some local nonparametric alternatives is also investigated. Numerical simulation studies are employed to evaluate the nite sample performance of the test in one dimensional and two dimensional cases. The minimum distance method in Chapter 2 requires the calculation of the integrals in the test statistics. These integrals usually do not have a tractable form. Therefore, some numerical integration methods are needed to approximate the integrations. Chapter 3 discusses a nonparametric empirical smoothing lack-of-fit test for the functional form of the variance in regression models that do not involve evaluation of integrals. empirical smoothing lack-of-fit test can be treated as a nontrivial modification of Zheng (1996)'s nonparametric smoothing test and Koul and Ni (2004)'s minimum distance test for the mean function in the classic regression models. The asymptotic normality of the proposed test under the null hypothesis is established. Consistency at some fixed alternatives and asymptotic power under some local alternatives are also discussed. Simulation studies are conducted to assess the nite sample performance of the test. The simulation studies show that the proposed empirical smoothing test is more powerful and computationally more efficient than the minimum distance test and Wang and Zhou (2006)'s test.

M.Com. (Economic Development and Policy Issues) / This research analyses the effect of exchange rate volatility on exports using a sample of nine emerging countries – Argentina, Brazil, India, Indonesia, Mexico, Malaysia, Poland, South Africa and Thailand – between 1995 and 2010. The study uses panel data models, with a standard exports equation with exports performance determined by exchange rate volatility, the level of exchange rate, demand conditions in major countries as well as terms of trade. Exchange rate volatility is measured by Generalised Autoregressive Conditional Heteroscedasticity (GARCH) and conventional standard deviation in order to determine if the instrument of volatility used influences the nature of the relationship between exchange rate volatility and exports. The results show that exchange rate volatility has a significant negative effect on the performance of exports regardless of the measure of volatility used. The Pedroni residual cointegration method was used to test for panel cointegration to determine if there is a long-run relationship among the variables, and the test showed that a long-run relationship does exists. Generally, the study concludes that policy mix that will reduce exchange rate volatility (such as managed exchange rate regimes) and relatively competitive exchange rates are essential for emerging markets in order to sustain their exports performance.

Esta dissertação flexibiliza a suposição de normalidade, dispondo de distribuições assimétricas em modelos de crescimento. Propõe uma abordagem bayesiana para ajuste de modelos não lineares quando a suposição de normalidade para os erros não é razoável e/ou apresentam heteroscedasticidade. Assim, adota-se as distribuições skew-normal e skew-t para as situações em que é necessário modelar dados com caudas mais pesadas ou mais leves que a normal e assimétricos; sendo que é considerado também a presença de heteroscedasticidade. Diferentes funções são utilizadas na estrutura multiplicativa para modelar a variância. Com esse objetivo, métodos de inferência na abordagem bayesiana são desenvolvidos para estimar os parâmetros dos modelos de regressão não linear com os erros seguindo as distribuições citadas anteriormente. A metodologia visa aplicação à curvas de crescimento para dados de árvores / This paper relaxes the assumption of normality, featuring asymmetric distributions in growth models. Proposes a Bayesian approach to fit nonlinear models when the assumption of normality for the errors is not reasonable and/or exhibit heteroscedasticity. Thus, we adopt the skew-normal and skew-t distributions for situations where it is necessary to model data with tails heavier or lighter than normal and asymmetric, which is considered also the presence of heteroscedasticity. Different functions are used to model the multiplicative structure of variance. With this objective, methods of inference in the Bayesian approach are developed to estimate the parameters of nonlinear regression models with errors following the distributions listed above. The methodology is intended to apply to the growth curves for trees data sets

Orientador: Luzia Aparecida Trinca / Resumo: Nas mais diversas áreas do conhecimento se procura aumentar a eficiência dos delineamentos experimentais, principalmente, para minimizar os custos das pesquisas. O uso dos delineamentos ótimos, com seus diferentes critérios de otimização, é fundamental para se obter resultados que maximizam a informação em estudos experimentais. A maioria dos métodos pressupõe homogeneidade de variâncias, a qual nem sempre é veri cada no conjunto de dados. O objetivo deste trabalho é desenvolver uma metodologia para construção de delineamentos ótimos exatos e cientes em situações de variância não homogênea. Assume-se que linearidade e homoscedasticidade são obtidas via o uso de transformações da família Box-Cox e, além de critérios de otimização puros, critérios compostos que combinam duas propriedades são propostos. Resultados para vários exemplos sob os modelos de primeira e segunda ordem são obtidos e discutidos. / Abstract: In several areas of knowledge we seek to increase the efficiency of experimental designs, mainly in order to minimize the costs of reaserch. The use of optimal design with different optimization criteria is fundamental to obtain results that maximize the information in experimental studies. Most of the methods assume homogeneity of variances, which is not always verified in the data set. The goal of this work is to develop a methodology to construct exact optimal or efficient designs in situations of nonhomogeneous variance. It is assumed that application of a transformation from the Box-Cox family accomplish both linearity and homocedasticity. Pure design criterion as well as compound criteria using two desired properties are used. Results for several examples assuming first and second order models are presented and discussed. / Doutor

Tang Him John. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 76-80). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgment --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.2 / Chapter 1.1.1 --- Linear Time Series --- p.2 / Chapter 1.1.2 --- Mixture Models --- p.3 / Chapter 1.1.3 --- EM algorithm --- p.6 / Chapter 1.1.4 --- Model Selection --- p.6 / Chapter 1.2 --- Main Objectives --- p.7 / Chapter 1.3 --- Outline of this thesis --- p.7 / Chapter 2 --- Finite Gaussian Mixture ARMA-GARCH Model --- p.9 / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.1.1 --- "AR, MA, and ARMA" --- p.10 / Chapter 2.1.2 --- Stationarity --- p.11 / Chapter 2.1.3 --- ARCH and GARCH --- p.12 / Chapter 2.1.4 --- Gaussian mixture --- p.13 / Chapter 2.1.5 --- EM and GEM algorithms --- p.14 / Chapter 2.2 --- Finite Gaussian Mixture ARMA-GARCH Model --- p.16 / Chapter 2.3 --- Estimation of Gaussian mixture ARMA-GARCH model --- p.17 / Chapter 2.3.1 --- Autocorrelation and Stationarity --- p.20 / Chapter 2.3.2 --- Model Selection --- p.24 / Chapter 2.4 --- Experiments: First Step Prediction --- p.26 / Chapter 2.5 --- Chapter Summary --- p.28 / Chapter 2.6 --- Notations and Terminologies --- p.30 / Chapter 2.6.1 --- White Noise Time Series --- p.30 / Chapter 2.6.2 --- Lag Operator --- p.30 / Chapter 2.6.3 --- Covariance Stationarity --- p.31 / Chapter 2.6.4 --- Wold's Theorem --- p.31 / Chapter 2.6.5 --- Multivariate Gaussian Density function --- p.32 / Chapter 3 --- Finite Mixture-of-Expert ARMA-GARCH Model --- p.33 / Chapter 3.1 --- Introduction --- p.33 / Chapter 3.1.1 --- Mixture-of-Expert --- p.34 / Chapter 3.1.2 --- Alternative Mixture-of-Expert --- p.35 / Chapter 3.2 --- ARMA-GARCH Finite Mixture-of-Expert Model --- p.36 / Chapter 3.3 --- Estimation of Mixture-of-Expert ARMA-GARCH Model --- p.37 / Chapter 3.3.1 --- Model Selection --- p.38 / Chapter 3.4 --- Experiments: First Step Prediction --- p.41 / Chapter 3.5 --- Second Step and Third Step Prediction --- p.44 / Chapter 3.5.1 --- Calculating Second Step Prediction --- p.44 / Chapter 3.5.2 --- Calculating Third Step Prediction --- p.45 / Chapter 3.5.3 --- Experiments: Second Step and Third Step Prediction . --- p.46 / Chapter 3.6 --- Comparison with Other Models --- p.50 / Chapter 3.7 --- Chapter Summary --- p.57 / Chapter 4 --- Stable Estimation Algorithms --- p.58 / Chapter 4.1 --- Stable AR(1) estimation algorithm --- p.59 / Chapter 4.2 --- Stable AR(2) Estimation Algorithm --- p.60 / Chapter 4.2.1 --- Real p1 and p2 --- p.61 / Chapter 4.2.2 --- Complex p1 and p2 --- p.61 / Chapter 4.2.3 --- Experiments for AR(2) --- p.63 / Chapter 4.3 --- Experiment with Real Data --- p.64 / Chapter 4.4 --- Chapter Summary --- p.65 / Chapter 5 --- Conclusion --- p.66 / Chapter 5.1 --- Further Research --- p.69 / Chapter A --- Equation Derivation --- p.70 / Chapter A.1 --- First Derivatives for Gaussian Mixture ARMA-GARCH Esti- mation --- p.70 / Chapter A.2 --- First Derivatives for Mixture-of-Expert ARMA-GARCH Esti- mation --- p.71 / Chapter A.3 --- First Derivatives for BYY Harmony Function --- p.72 / Chapter A.4 --- First Derivatives for stable estimation algorithms --- p.73 / Chapter A.4.1 --- AR(1) --- p.74 / Chapter A.4.2 --- AR(2) --- p.74 / Bibliography --- p.80