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Standard linear modeling approaches make potentially simplistic assumptions regarding the structure of categorical effects that may obfuscate more complex relationships governing data. For example, recent work focused on the two-way unreplicated layout has shown that hidden groupings among the levels of one categorical predictor frequently interact with the ungrouped factor. We extend the notion of a "latent grouping factor'' to linear models in general. The proposed work allows researchers to determine whether an apparent grouping of the levels of a categorical predictor reveals a plausible hidden structure given the observed data. Specifically, we offer Bayesian model selection-based approaches to reveal latent group-based heteroscedasticity, regression effects, and/or interactions. Failure to account for such structures can produce misleading conclusions. Since the presence of latent group structures is frequently unknown a priori to the researcher, we use fractional Bayes factor methods and mixture g-priors to overcome lack of prior information. We provide an R package, slgf, that implements our methodology in practice, and demonstrate its usage in practice. / Doctor of Philosophy / Statistical models are a powerful tool for describing a broad range of phenomena in our world. However, many common statistical models may make assumptions that are overly simplistic and fail to account for key trends and patterns in data. Specifically, we search for hidden structures formed by partitioning a dataset into two groups. These two groups may have distinct variability, statistical effects, or other hidden effects that are missed by conventional approaches. We illustrate the ability of our method to detect these patterns through a variety of disciplines and data layouts, and provide software for researchers to implement this approach in practice.

The traditional approach to standardizing tree-ring time series is to divide raw ring widths by a fitted curve. Although the derived ratios are conceptually elegant and have a more homogenous variance through time than simple differences, residual heteroscedasticity associated with variance dependence on local mean ring width may remain. Incorrect inferences about climate forcing may result if this heteroscedasticity is not corrected for, or at least recognized (with appropriate caveats). A new variance stabilization method is proposed that specifically targets this source of heteroscedasticity. It is based on stabilizing the magnitude of differences from standardization curves to a common reference local mean ring width and uses data pooled from multiple radii. Application of the method to a multi-site kauri (Agathis australis (D. Don) Lindley) data set shows that (a) the heteroscedasticity issue addressed may be generic rather than radius-specific, at least for some species, (b) variance stabilization using pooled data works well for standardization curves of variable flexibility, (c) in the case of kauri, simple ratios do not appear to be significantly affected by this cause of heteroscedasticity, and (d) centennial-scale variance trends are highly sensitive to the analytical methods used to build tree-ring chronologies.

A major objective of this thesis is to study the statistical inference problem for GARCH-type models, including fractionally-integrated (FI) GARCH, fractional (F) GARCH, long-memory (LM) GARCH, and non-stationary GARCH models. / Among various types of generalizations to the ARCH models, fractionally-integrated (FI) GARCH model proposed in Baillie et al. (1996) and Bollerslev and Mikkelson (1996) is one of the most interesting ones as it offered many challenging theretical problems. / Parameters in the ARCH-type models are commonly estimated using the quasi-maximum likelihood estimator (QMLE). To establish consistency and asymptotic normality of the QMLE, one usually has to impose stringent assumptions, see Robinson and Zaffaroni (2006) and Straumann (2005). They have to assume that a stationary solution to the true model exists and this solution has some finite moments. These two assumptions are too restrictive to be applied to FIGARCH models. Formal results of the asymptotic properties of the QMLE of the FIGARCH models are still not available. Progresses on asymptotic theory of QMLE have only been made on certain models that resemble the FIGARCH model, including the FGARCH model of Ding and Granger (1996) and Robinson and Zaffaroni (2006), the LM-GARCH model of Robinson and Zaffaroni (1997) and the non-stationary ARCH model, but not the FIGARCH model itself. / This study attempts to solve the FIGARCH problem and extend the current findings on FGARCH, LM-GARCH and non-stationary GARCH models. We show that if the fractional parameter d is known, the QMLE for the parameters are strongly consistent and asymptotically normal. The results of LM-GARCH (0, d, 0) model in Konlikov (2003a,b) will be generalized to encompass the LM-GARCH(p, d, q) models. We also furnish a general result for non-stationary GARCH (p, q) models, extending the results of Jensen and Rahbek (2004) on weak consistency and asymptotic normality of the QMLE of the non-stationary GARCH (1, 1) models. / Ng, Chi Tim. / "June 2007." / Adviser: Chan Ngai Hang. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0398. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

In this paper we examine, by Monte Carlo simulation, size and power of the Johansens trace test when the error covariance matrix is nonstationary, and we also investigate the properties of three different bootstrap cointegration tests. Earlier studies indicate that the Johansen trace test is not robust in presence of heteroscedasticity, and tests based on resampling methods have been proposed to solve the problem. The tests that are evaluated is the Johansen trace test, nonparametric bootstrap test and two different types of wild bootstrap tests. The wild bootstrap test is a resampling method that attempts to mimic the GARCH model by multiplying each residual by a stochastic variable with an expected value of zero and unit variance. The wild bootstrap tests proved to be superior to the other tests, but not as good as earlier indicated. The more the error terms differs from white noise, the worse these tests are doing. Although the wild bootstrap tests did not do a very bad job, the focus of further investigation should be to derive tests that does an even better job than the wild bootstrap tests examined here.

Thesis (M. Phil.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 87-91).

Thesis (M.Soc.Sc.)--University of Hong Kong, 1989. / Also available in print.

This paper surveys various statistical methods that have been proposed for the examination of the efficiency of financial markets and proposes a novel procedure for testing the predictability of a time series. For illustration, this procedure is applied to Austrian stock return series.