published_or_final_version / abstract / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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Photocopy of typescript. / Digitized by Kansas Correctional Industries

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.

Graduation date: 2004

The semi-parametric approach to the analysis of proportional hazards survival data is relatively new, having been initiated in 1972 by Sir David Cox, who restricted its use to hypothesis tests and confidence intervals for fixed effects in a regression setting. Practitioners have begun to diversify applications of this model, constructing residuals, modeling the baseline hazard, estimating median failure time, and analyzing experiments with random effects and repeated measures. The main purpose of this thesis is to show that working with an incompletely specified loglikelihood is more fruitful than working with Cox's original partial loglikelihood, in these applications. In Chapter 2, we show that the deviance residuals arising naturally from the partial loglikelihood have difficulties detecting outliers. We demonstrate that a smoothed, nonparametric baseline hazard partially solves this problem. In Chapter 3, we derive new deviance residuals that are useful for identifying the shape of the baseline hazard. When these new residuals are plotted in temporal order, patterns in the residuals mirror patterns in the baseline hazard. In Chapter 4, we demonstrate how to analyze survival data having a split-plot design structure. Using a BLUP estimation algorithm, we produce hypothesis tests for fixed effects, and estimation procedures for the fixed effects and random effects. / Graduation date: 1999

Image processing applications such as image denoising, image segmentation, object detection, object recognition and texture synthesis often require a multi-scale analysis of images. This is useful because different features in the image become prominent at different scales. Traditional imaging models, which have been used for multi-scale analysis of images, have several limitations such as high sensitivity to noise and structural degradation observed at higher scales. Parametric models make certain assumptions about the image structure which may or may not be valid in several situations. Non-parametric methods, on the other hand, are very flexible and adapt to the underlying image structure more easily. It is highly desirable to have effi cient non-parametric models for image analysis, which can be used to build robust image processing algorithms with little or no prior knowledge of the underlying image content. In this thesis, we propose a non-parametric pixel neighbourhood based framework for multi-scale image analysis and apply the model to build image denoising and saliency detection algorithms for the purpose of illustration. It has been shown that the algorithms based on this framework give competitive results without using any prior information about the image statistics.

<p>Automated acoustic sensing systems are required to detect, classify and localize acoustic signals in real-time. Despite the fact that humans are capable of performing acoustic sensing tasks with ease in a variety of situations, the performance of current automated acoustic sensing algorithms is limited by seemingly benign changes in environmental or operating conditions. In this work, a framework for acoustic surveillance that is capable of accounting for changing environmental and operational conditions, is developed and analyzed. The algorithms employed in this work utilize non-stationary and nonparametric Bayesian inference techniques to allow the resulting framework to adapt to varying background signals and allow the system to characterize new signals of interest when additional information is available. The performance of each of the two stages of the framework is compared to existing techniques and superior performance of the proposed methodology is demonstrated. The algorithms developed operate on the time-domain acoustic signals in a nonparametric manner, thus enabling them to operate on other types of time-series data without the need to perform application specific tuning. This is demonstrated in this work as the developed models are successfully applied, without alteration, to landmine signatures resulting from ground penetrating radar data. The nonparametric statistical models developed in this work for the characterization of acoustic signals may ultimately be useful not only in acoustic surveillance but also other topics within acoustic sensing.</p> / Dissertation

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 110-114). Also available in electronic version. Access restricted to campus users.

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 141-146).