The fundamental objective of the analysis of financial time series is to unveil the random mechanism, i.e. the probability law, underlying financial data. The effort to identify the truth that governs the observations involves proposing and estimating reasonable statistical models that well explain the empirical features of data. This thesis develops some new nonparametric tools that can be exploited in this context; the efficacy and validity of their use are supported by computational advancements and surging availability of large/complex (`big') data sets. Chapter 1 investigates the conditional first moment properties of financial returns. We propose multivariate extensions of the popular Variance Ratio (VR) statistic, aiming to test linear predictability of returns and weak-form market efficiency. We construct asymptotic distribution theories for the statistics and scalar functions thereof under the null hypothesis of no predictability. The imposed assumptions are weaker than those widely adopted in the literature, and in our view more credible with regard to the underlying data generating process we expect for stock returns. It is also shown that the limit theories can be extended to the long horizon and large dimension cases, and also to allow for a time varying risk premium. Our methods are applied to CRSP weekly returns from 1962 to 2013; the joint tests of the multivariate hypothesis reject the null at the 1% level for all horizons considered. Chapter 2 is about nonparametric estimation of conditional moments. We propose a local constant type estimator that operates with an infinite number of conditioning variables; this enables a direct estimation of many objects of econometric interest that have dependence upon the infinite past. We show pointwise and uniform consistency of the estimator and establish its asymptotic nomality in various static and dynamic regressions context. The optimal rate of estimation turns out to be of logarithmic order, and the precise rate depends on the Lambert W function, the smoothness of the regression operator and the dependence of the data in a non-trivial way. The theories are applied to investigate the intertemporal risk-return relation for the aggregate stock market. We report an overall positive risk-return relation on the S&P 500 daily data from 1950-2017, and find evidence of strong time variation and counter-cyclical behaviour in risk aversion. Lastly, Chapter 3 concerns nonparametric volatility estimation with high frequency time series. While data observed at finer time scale than daily provide rich information, their distinctive empirical properties bring new challenges in their analysis. We propose a Fourier domain based estimator for multivariate ex-post volatility that is robust to two major hurdles in high frequency finance: asynchronicity in observations and the presence of microstructure noise. Asymptotic properties are derived under some mild conditions. Simulation studies show our method outperforms time domain estimators when two assets with different liquidity are traded asynchronously.

Chan, Hon Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 57-59). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Cluster Analysis in Time Series --- p.1 / Chapter 1.2 --- Dissimilarity Measure --- p.2 / Chapter 1.2.1 --- Euclidean Distance --- p.3 / Chapter 1.2.2 --- Pearson's Correlation Coefficient --- p.3 / Chapter 1.2.3 --- Other Measure --- p.4 / Chapter 1.3 --- Summary --- p.5 / Chapter 2 --- Algorithm and Methodology --- p.8 / Chapter 2.1 --- Algorithm and Methodology --- p.8 / Chapter 2.2 --- Illustrative Examples --- p.14 / Chapter 3 --- Simulation Study --- p.20 / Chapter 3.1 --- Simulation Plan --- p.20 / Chapter 3.2 --- Measure of Performance --- p.24 / Chapter 3.3 --- Simulation Results --- p.27 / Chapter 3.4 --- Results of k-means Clustering --- p.33 / Chapter 4 --- Application on Gene Expression --- p.37 / Chapter 4.1 --- Dataset --- p.37 / Chapter 4.2 --- Parameter Settings --- p.38 / Chapter 4.3 --- Results --- p.38 / Chapter 5 --- Conclusion and Further Research --- p.55

Fung, Yu Hin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 39-40). / Abstracts in English and Chinese. / List of Figures --- p.v / List of Tables --- p.vii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Extremogram --- p.3 / Chapter 2.1 --- Strictly Stationary --- p.3 / Chapter 2.2 --- Regularly Varying: A time series {Xt} --- p.3 / Chapter 2.3 --- (Upper) tail dependence --- p.5 / Chapter 2.4 --- Extremogram --- p.6 / Chapter 3 --- Simulated Models --- p.9 / Chapter 3.1 --- Autoregressive (AR) Process --- p.9 / Chapter 3.1.1 --- The simulation --- p.9 / Chapter 3.1.2 --- Theoretical findings --- p.11 / Chapter 3.2 --- Moving Average (MA) Process --- p.12 / Chapter 3.2.1 --- The simulation --- p.12 / Chapter 3.3 --- GARCH and SV --- p.25 / Chapter 4 --- Applications to Market Data --- p.29 / Chapter 4.1 --- Case study: 2011 Japan Earthquake EOD data --- p.29 / Chapter 4.1.1 --- Data description --- p.29 / Chapter 4.1.2 --- Results --- p.30 / Chapter 4.2 --- Case study: TEPCO multi-timeframe analysis --- p.31 / Chapter 4.2.1 --- Data description --- p.31 / Chapter 4.2.2 --- Results --- p.32 / Chapter 5 --- Summary --- p.37 / References --- p.39

Digitized by Kansas Correctional Industries

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This thesis will take a look at the roots of modern-day information geometry and some applications into statistical modeling. In order to truly grasp this field, we will first provide a basic and relevant introduction to differential geometry. This includes the basic concepts of manifolds as well as key properties and theorems. We will then explore exponential families with applications of probability distributions. Finally, we select a few time series models and derive the underlying geometries of their manifolds.

Using C. Fefferman's embedding of a charge space in a measure space allows us to apply standard interpolation theorems to the establishment of norm inequalities for Besicovitch almost periodic functions. This yields a significant improvement to the results of A. Avantaggiati, G. Bruno and R. Iannacci. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2019. / FAU Electronic Theses and Dissertations Collection

Three macroeconomic issues are examined in separate self-contained studies. The first study tests the business cycle theory with application of an enhanced Augmented Dickey-Fuller test on the U.S. time series of real gross national product. Unlike previous studies, the null hypothesis of a unit root is rejected. The second study tests for IS-LM conditions in the U.S. during the post-Bretton Woods era by combining the Johansen's approach to cointegration with bootstrap algorithms. The estimated model produces a dynamic version of the IS-LM that permits short-term evaluations of fiscal and monetary policies. The third study seeks to explain the observed persistence in the Bolivan dollarization process. It is found that dollarization is now an irreversible process, with the Bolivian economy in transition toward equalization with U.S. prices and interest rates.

Web Services can be seen from two views ? one that it is a purely technological advance and the other that it is a capability that an organisation can deploy to meet a business objective. Much has been said about the first view but not much has been said about the second view. The underlying premise of this research is that in the context of an ever-increasing competitive environment, an organisation needs to take into account these important aspects: What is the business strategy of the organisation, which adopts Web Services? Does the IT align with the business strategy of the organisation? The aim of this research is to capture and describe business-IT problems in the context of strategic requirements and Web Services. As a means to align a Web Services initiative with business strategy, we propose a Requirements Engineering framework to capture the business objectives of an organisation from strategy to implementation. The methodology that we propose provides a roadmap from business strategy, to the strategic objectives to implementation in four dimensions: innovation, customer relationship management, infrastructure management and financials. The proposed framework extends the e-Business Modelling Ontology (eBMO) of Pigneur and Osterwalder by applying Bleistein et al?s Progression of Problems to understand the strategic objectives and the business context. We have presented 2 examples as proof of concept. We have experimented with our methodology on Amazon.com and Dell.com ?cases developed from the literature? as these organisations are aggressively pursuing Web Services as a part of their IT and business strategy. We use the Problem Frames approach to capture the business objectives and the problem context of an organisation deploying Web Services and to create a strategic alignment between the business strategy and the information technology. The approach presented in this thesis is used to understand Amazon and Dell?s strategy and strategic objectives. It was possible to capture strategic objectives and the strategic context through combination of the eBMO and Progression of Problems. It was also possible to trace this to Web Services requirement description through application of Problem Frames. The framework combines with Bleistein et al?s Progression of Problems at the strategic level and applies Problem Frames at the operational level. It takes the problem-oriented view of the whole process, but does not apply Problem Frames throughout, at least not in their original formulation by Jackson.

Department of Civil, Surveying and Environmental Engineering. Includes bibliographical references (leaves R-1--R-9)