With increasing public sensitivity and concern on environmental issues, huge amounts of spatial data have been collected from location based social network applications to scientific data. This has encouraged formation of large spatial data set and generated considerable interests for identifying novel and meaningful patterns. Allowing correlated observations weakens the usual statistical assumption of independent observations, and complicates the spatial analysis. This research focuses on the construction of efficient and effective approaches for three main mining tasks, including spatial outlier detection, robust inference for spatial dataset, and spatial prediction for large multivariate non-Gaussian data. spatial outlier analysis, which aims at detecting abnormal objects in spatial contexts, can help  extract important knowledge in many applications. There exist the well-known masking and swamping problems in most approaches, which can't still satisfy certain requirements aroused recently. This research focuses on development of spatial outlier detection techniques for three aspects, including spatial numerical outlier detection, spatial categorical outlier detection and identification of the number of spatial numerical outliers. First, this report introduces Random Walk based approaches to identify spatial numerical outliers. The Bipartite and an Exhaustive Combination weighted graphs are modeled based on spatial and/or non-spatial attributes, and then Random walk techniques are performed on the graphs to compute the relevance among objects. The objects with lower relevance are recognized as outliers. Second, an entropy-based method is proposed to estimate the optimum number of outliers. According to the entropy theory, we expect that, by incrementally removing outliers, the entropy value will decrease sharply, and reach a stable state when all the outliers have been removed. Finally, this research designs several Pair Correlation Function based methods to detect spatial categorical outliers for both single and multiple attribute data. Within them, Pair Correlation Ratio(PCR) is defined and estimated for each pair of categorical combinations based on their co-occurrence frequency at different spatial distances. The observations with the lower PCRs are diagnosed as potential SCOs. Spatial kriging is a widely used predictive model whose predictive accuracy could be significantly compromised if the observations are contaminated by outliers. Also, due to spatial heterogeneity, observations are often different types. The prediction of multivariate spatial processes plays an important role when there are cross-spatial dependencies between multiple responses. In addition, given the large volume of spatial data, it is computationally challenging. These raise three research topics: 1).robust prediction for spatial data sets; 2).prediction of multivariate spatial observations; and 3). efficient processing for large data sets. First, increasing the robustness of spatial kriging model can be systematically addressed by integrating heavy tailed distributions. However, it is analytically intractable inference. Here, we presents a novel robust and reduced Rank spatial kriging Model (R$^3$-SKM), which is resilient to the influences of outliers and allows for fast spatial inference. Second, this research introduces a flexible hierarchical Bayesian framework that permits the simultaneous modeling of mixed type variable. Specifically, the mixed-type attributes are mapped to latent numerical random variables that are multivariate Gaussian in nature. Finally, the knot-based techniques is utilized to model the predictive process as a reduced rank spatial process, which projects the process realizations of the spatial model to a lower dimensional subspace. This projection significantly reduces the computational cost. / Ph. D.

This thesis focuses on the analysis of Catastrophe bond mutual funds [CBMFs] and is organized into four chapters. The first chapter, "An identification-robust analysis of Catastrophe bond mutual funds: zero-beta neutrality under tradability", offers identification-robust evidence on whether CBMFs are zero-beta based on the analysis with only tradable risk factors. Statistical significance of factor risk premiums and cross-sectional loadings is examined in a multivariate, identification-robust setting to inform on the zero-beta performance of CBMFs. The latter is assessed against the Capital Asset Pricing Model [CAPM] without the risk-less asset proposed by Black (1972) [BCAPM], Quadratic CAPM, Cummins-Weiss, Fama-French-Carhart benchmarks and models with Fontaine and Garcia (2012) and Pástor and Stambaugh (2003) liquidity factors. Multiple markets are considered individually and jointly. Beta pricing inference proceeds using the method of Beaulieu, Dufour and Khalaf (2013) robust to weak identification. Instead of non-tradable factors, their mimicking portfolio returns are used in the analysis to facilitate tradable-only factor setting. Results indicate that coskewness, funding liquidity and fixed-income factors are often priced or incur significant factor betas. There is also evidence of risk premiums and joint beta significance for stock, corporate bond and commercial mortgage-backed securities benchmarks. Empirical findings overall suggests that CBMFs underperformed as zero-beta assets. The second chapter, "Zero-beta inference on Catastrophe bond mutual funds: identification- robust evidence with non-tradable factors", examines formally the zero-beta neutrality of CBMFs allowing for some risk factors to be non-tradable. Zero-beta analysis focuses on cross-sectional betas with their joint significance tested for each factor. This is augmented with inference on risk prices and the zero-beta rate to assess whether factor risks are priced. CBMFs are modeled in the QCAPM setting with either stock, corporate bond, government bond or commercial mortgage-backed security [CMBS] market return and its square as respectively tradable and non-tradable factors. The zero-beta performance of CBMFs is also assessed against an extended BCAPM benchmark with either Fontaine and Garcia (2012) or Pástor and Stambaugh (2003) non-tradable liquidity factor considered in addition to the tradable market return. Inference on risk prices and the zero-beta rate builds on the method of Beaulieu, Dufour and Khalaf (2018) which remains exact and simultaneous for any sample size even if the parameter recovery is impaired. Empirically, although identification strength diminishes in the setting with non-tradable factors, relaxing tradability improves model fit across all benchmarks. In particular, QCAPM (reix gardless of the market) is no longer rejected for any period and so is the model with the funding liquidity factor. Goodness-of-fit also improves for the model with the marketwide liquidity factor. In periods for which models were rejected under factor tradability, allowing for some factors to be non-tradable also yields set estimates for the zero-beta rate and risk prices that are informative for beta pricing. In particular, this reveals evidence of priced coskewness risk across all markets over the long-run and for stock, corporate bond and CMBS benchmarks after the 2007-09 US recession. In the same periods, funding liquidity risk is also priced and so is the marketwide liquidity risk over the full sample. Given significant betas on the market return, the latter prevails as a relevant factor even in a setting with other factors being non-tradable. Overall, there is evidence suggesting that CBMFs deviated from performing as zero-beta investments with coskewness and liquidity as contributing factors. These results reinforce findings in the Chapter 1. The third chapter, "An alpha and risk analysis of Catastrophe bond mutual funds: exact, simultaneous inference", examines CBMFs in terms of their ability to produce a positive alpha and the extent of their sensitivity to the developments in financial markets. Inference on alphas and the riskiness of CBMFs relies on exact, simultaneous confidence sets assembled respectively for cross-sectional intercepts and factor loadings in the multivariate linear regression [MLR] model. Set construction proceeds using the analytical inversion procedure of Beaulieu, Dufour and Khalaf (2018) in a Least-Squares case and its extension to a Student-t setting. Proposed in this chapter, the extension involves replacing the Fisher-based cut-off point in the analytical solution of Beaulieu, Dufour and Khalaf (2018) with its simulation-based counterpart obtained under Student-t errors. The empirical analysis of CBMFs reveals evidence of a positive alpha following the 2011 Tohoku earthquake in Japan and indicate that CBMFs are likely to have at most moderate sensitivity to fluctuations in financial markets. These results are robust against CAPM, QCAPM and Fama-French benchmarks and observed in both Gaussian and Student-t settings. The fourth chapter, "Endogeneity in a zero-beta analysis: joint, finite sample inference on Catastrophe bond mutual funds", revisits the zero-beta assessment of CBMFs taking into account factor endogeneity. In particular, this chapter extends the univariate Durbin-Wu-Hausman [DWH] test (Durbin, 1954; Wu, 1973; Hausman, 1978) of exogeneity to a multivariate setting. Unlike the univariate DWH test, the proposed multivariate extension allows to assess factor exogeneity jointly across equations. This chapter also proposes an extended version of the multivariate Wilks-based instrumental variables [IV] test of Dufour, Khalaf and Kichian (2013) to a setting with regressors, and consequently their instruments, that remain the same across equations. Both extended tests allow for possibly non-Gaussian errors and maintain size correctness for a sample with any number of observations even in the setting with weak instruments. Applying the extended methods to the analysis CBMFs provides evidence against joint factor exogeneity in some cases across CAPM and QCAPM in both Gaussian and Student-t settings. In some periods when the joint factor exogeneity is rejected, results for the zero-beta analysis differ depending on whether the IV-based or non-IV test was applied. Unlike in the case without instrumenting, extended Wilks-based IV test of joint beta significance is significant at the 5% level before the 2007-09 US recession for both CAPM and QCAPM regardless of the distributional setting (Gaussian or Student-t). The same result also obtains for QCAPM during the economic downturn. Over the long-run, there is evidence of jointly significant factor loadings obtained with and without instrumenting. Overall, empirical results suggest that performance of CBMFs differs from that of zero-beta assets.

<p>This dissertation is a collection of four essays on nonstationary time series econometrics, which are grouped into four chapters. The first chapter investigates the inference in mildly explosive autoregressions under unconditional heteroskedasticity. The second chapter develops a new approach to forecasting a highly persistent time series that employs feasible generalized least squares (FGLS) estimation of the deterministic components in conjunction with Mallows model averaging. The third chapter proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by nonstationary volatility. The last chapter studies the problem of testing partial parameter stability in cointegrated regression models.</p>

Neste trabalho, apresentamos uma extensão da análise bayesiana objetiva feita em Fonseca et al. (2008), baseada nas distribuições a priori de Jeffreys para o modelo de regressão linear com erros t-Student, para os quais consideramos a suposição de heteoscedasticidade. Mostramos que a distribuição a posteriori dos parâmetros do modelo regressão gerada pela distribuição a priori é própria. Através de um estudo de simulação, avaliamos as propriedades frequentistas dos estimadores bayesianos e comparamos os resultados com outras distribuições a priori encontradas na literatura. Além disso, uma análise de diagnóstico baseada na medida de divergência Kullback-Leiber é desenvolvida com a finalidade de estudar a robustez das estimativas na presença de observações atípicas. Finalmente, um conjunto de dados reais é utilizado para o ajuste do modelo proposto. / In this work , we present an extension of the objective bayesian analysis made in Fonseca et al. (2008), based on Jeffreys priors for linear regression models with Student t errors, for which we consider the heteroscedasticity assumption. We show that the posterior distribution generated by the proposed Jeffreys prior, is proper. Through simulation study , we analyzed the frequentist properties of the bayesian estimators obtained. Then we tested the robustness of the model through disturbances in the response variable by comparing its performance with those obtained under another prior distributions proposed in the literature. Finally, a real data set is used to analyze the performance of the proposed model . We detected possible in uential points through the Kullback -Leibler divergence measure, and used the selection model criterias EAIC, EBIC, DIC and LPML in order to compare the models.

Neste trabalho, apresentamos uma extensão da análise bayesiana objetiva feita em Fonseca et al. (2008), baseada nas distribuições a priori de Jeffreys para o modelo de regressão linear com erros t-Student, para os quais consideramos a suposição de heteoscedasticidade. Mostramos que a distribuição a posteriori dos parâmetros do modelo regressão gerada pela distribuição a priori é própria. Através de um estudo de simulação, avaliamos as propriedades frequentistas dos estimadores bayesianos e comparamos os resultados com outras distribuições a priori encontradas na literatura. Além disso, uma análise de diagnóstico baseada na medida de divergência Kullback-Leiber é desenvolvida com a finalidade de estudar a robustez das estimativas na presença de observações atípicas. Finalmente, um conjunto de dados reais é utilizado para o ajuste do modelo proposto. / In this work , we present an extension of the objective bayesian analysis made in Fonseca et al. (2008), based on Jeffreys priors for linear regression models with Student t errors, for which we consider the heteroscedasticity assumption. We show that the posterior distribution generated by the proposed Jeffreys prior, is proper. Through simulation study , we analyzed the frequentist properties of the bayesian estimators obtained. Then we tested the robustness of the model through disturbances in the response variable by comparing its performance with those obtained under another prior distributions proposed in the literature. Finally, a real data set is used to analyze the performance of the proposed model . We detected possible in uential points through the Kullback -Leibler divergence measure, and used the selection model criterias EAIC, EBIC, DIC and LPML in order to compare the models.

Submitted by Luciana Sebin (lusebin@ufscar.br) on 2016-09-26T18:57:40Z No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-27T19:59:56Z (GMT) No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-27T20:00:01Z (GMT) No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) / Made available in DSpace on 2016-09-27T20:00:08Z (GMT). No. of bitstreams: 1 DissACRS.pdf: 1390452 bytes, checksum: a5365fdbf745228c0174f2643b3f7267 (MD5) Previous issue date: 2016-02-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this work , we present an extension of the objective bayesian analysis made in Fonseca et al. (2008), based on Je reys priors for linear regression models with Student t errors, for which we consider the heteroscedasticity assumption. We show that the posterior distribution generated by the proposed Je reys prior, is proper. Through simulation study , we analyzed the frequentist properties of the bayesian estimators obtained. Then we tested the robustness of the model through disturbances in the response variable by comparing its performance with those obtained under another prior distributions proposed in the literature. Finally, a real data set is used to analyze the performance of the proposed model . We detected possible in uential points through the Kullback -Leibler divergence measure, and used the selection model criterias EAIC, EBIC, DIC and LPML in order to compare the models. / Neste trabalho, apresentamos uma extensão da análise bayesiana objetiva feita em Fonseca et al. (2008), baseada nas distribuicões a priori de Je reys para o modelo de regressão linear com erros t-Student, para os quais consideramos a suposicão de heteoscedasticidade. Mostramos que a distribuiçãoo a posteriori dos parâmetros do modelo regressão gerada pela distribuição a priori e própria. Através de um estudo de simulação, avaliamos as propriedades frequentistas dos estimadores bayesianos e comparamos os resultados com outras distribuições a priori encontradas na literatura. Além disso, uma análise de diagnóstico baseada na medida de divergência Kullback-Leiber e desenvolvida com analidade de estudar a robustez das estimativas na presença de observações atípicas. Finalmente, um conjunto de dados reais e utilizado para o ajuste do modelo proposto.