Application of Block Sieve Bootstrap to Change-Point detection in time series

Since the introduction of CUSUM statistic by E.S. Page (1951), detection of change or a structural break in time series has gained significant interest as its applications span across various disciplines including economics, industrial applications, and environmental data sets. However, many of the early suggested statistics, such as CUSUM or MOSUM, lose their effectiveness when applied to time series data. Either the size or power of the test statistic gets distorted, especially for higher order autoregressive moving average processes. We use the test statistic from Gombay and Serban (2009) for detecting change in the mean of an autoregressive process and show how the application of sieve bootstrap to the time series data can improve the performance of our test to detect change. The effectiveness of the proposed method is illustrated by applying it to economic data sets

Statistical learning methods for functional data with applications to prediction, classification and outlier detection

In the era of big data, Functional Data Analysis has become increasingly important insofar as it constitutes a powerful tool to tackle inference problems in statistics. In particular in this thesis we have proposed several methods aimed to solve problems of prediction of time series, classification and outlier detection from a functional approach. The thesis is organized as follows: In Chapter 1 we introduce the concept of functional data and state the overview of the thesis. In Chapter 2 of this work we present the theoretical framework used to we develop the proposed methodologies. In Chapters 3 and 4 two new ordering mappings for functional data are proposed. The first is a Kernel depth measure, which satisfies the corresponding theoretical properties, while the second is an entropy measure. In both cases we propose a parametric and non-parametric estimation method that allow us to define an order in the data set at hand. A natural application of these measures is the identification of atypical observations (functions). In Chapter 5 we study the Functional Autoregressive Hilbertian model. We also propose a new family of basis functions for the estimation and prediction of the aforementioned model, which belong to a reproducing kernel Hilbert space. The properties of continuity obtained in this space allow us to construct confidence bands for the corresponding predictions in a detracted time horizon. In order to boost different classification methods, in Chapter 6 we propose a divergence measure for functional data. This metric allows us to determine in which part of the domain two classes of functional present divergent behavior. This methodology is framed in the field of domain selection, and it is aimed to solve classification problems by means of the elimination of redundant information. Finally in Chapter 7 the general conclusions of this work and the future research lines are presented.Financial support received from the Spanish Ministry of Economy and Competitiveness ECO2015-66593-P and the UC3M PIF scholarship for doctoral studies.Programa de Doctorado en Economía de la Empresa y Métodos Cuantitativos por la Universidad Carlos III de MadridPresidente: Santiago Velilla Cerdán; Secretario: Kalliopi Mylona; Vocal: Luis Antonio Belanche Muño

Time Series Modelling

The analysis and modeling of time series is of the utmost importance in various fields of application. This Special Issue is a collection of articles on a wide range of topics, covering stochastic models for time series as well as methods for their analysis, univariate and multivariate time series, real-valued and discrete-valued time series, applications of time series methods to forecasting and statistical process control, and software implementations of methods and models for time series. The proposed approaches and concepts are thoroughly discussed and illustrated with several real-world data examples

Bayesian molecular clock dating and the divergence times of angiosperms and primates

The explosive increase of molecular sequence data has produced unprecedented opportunities for addressing a number of evolutionary problems. Specially, the species divergence time estimation is fundamental because our understanding of history of life depends critically on knowledge of the ages of major clades. This thesis explores the use of molecular data (genome-scale datasets), combined with statistical summaries of the fossil record, to date the origin of angiosperms (flowering plants) and the divergence times of its major groups in an attempt to resolve the apparent conflict between the molecular dates and fossil evidence. Moreover, because fossil calibrations are the major source of information for resolving the distances between molecular sequences into estimates of absolute times and absolute rates in molecular clock dating analysis, several strategies for converting fossil calibrations into the prior on times are evaluated. Chapter one introduces the diversity and evolution of angiosperms, reviews the current literature that is based predominantly on systematics, phylogenetics, palaeobotany and plant molecular evolution. In introducing the early evolution of angiosperms this chapter highlights the questions associated with the origin of angiosperms and presents aims of the thesis. Chapter two focuses on molecular clock dating methods. It discusses different approaches for estimating divergence times, with emphasis on Bayesian molecular clock dating methods. Chapter three uses a powerful Bayesian method to analyze a molecular dataset of 83 genes from 644 taxa of vascular plants, combined with a suite of 52 fully-justified fossil calibrations to disentangle the pattern of angiosperm diversification. The results indicate that crown angiosperms originated during the Triassic to the Jurassic interval, long prior to the Cretaceous Terrestrial Revolution. This analysis demonstrates that even though many sources of uncertainty are explored, attempts to control for these factors still do not bring clock estimates and earliest confident fossil occurrences into agreement. A post-Jurassic origin of angiosperms was rejected, supporting the notion of a cryptic early history of angiosperms. The main factors affecting the estimates in this study are also discussed. Subsequently, in chapter four different strategies for summarizing fossil information to construct calibration priors were assessed employing an a priori procedure for deriving accurate calibration densities in Bayesian divergence dating. In general, truncation has a great impact on calibrations so that the effective priors on the calibration node ages after the truncation can be very different from the user-specified calibration densities. The different strategies for generating the effective prior also had considerable impact, leading to very different marginal effective priors. Arbitrary parameters used to implement minimum-bound calibrations were found to have a strong impact upon the prior and posterior of the divergence times. The results highlight the importance of inspecting the joint time prior used by the dating program before any Bayesian dating analysis. Finally, chapter five draws together key finding from chapters three and four, and reviews how this work advances our understanding of the origin and evolution of angiosperms and on molecular clock dating using fossil calibrations. This chapter also highlights new gaps in our understanding of early evolution of angiosperms and in the implementation of fossil calibrations in Bayesian molecular clock dating, and discusses several areas for future research. Overall, this thesis highlights that more room for improvement might lie in refining our knowledge and use of fossil calibrations, the resulting improvements to molecular estimates of timescales will lead to a better understanding of angiosperm evolution. I speculate that these results will also shed light on dating discrepancies in other major clades

Essays on fiscal sustainability in Europe

Fiscal sustainability is present when the current government debt equates to the present value of future budget surpluses or their excess over deficits but since 1970 the EU countries on average had a surplus budget only in one year. The first aim of the thesis is to see whether Europe has achieved fiscal sustainability, whereas the second aim is to analyse the effects of Maastricht and the Stability and Growth Pact to this end. Another research aim is to present a formal fiscal sustainability assessment for the EU accession countries. Finally, the thesis bridges fiscal and external sustainability and studies the economy-wide sustainability separately in 'old' Europe and the accession countries. [Continues.

Influence of hydrodynamics on the larval supply to hydrothermal vents on the East Pacific Rise

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2007Examination of the scales at which larval supply varies spatially and temporally, and correlation with concurrent physical observations can provide insights into larval transport mechanisms that contribute to structuring marine benthic communities. In order to facilitate field studies, this thesis first provides new morphological and genetic identifications for hydrothermal vent gastropod larvae along the northern East Pacific Rise. Daily and weekly variability in the supply of hydrothermal vent gastropod larvae to two hydrothermal vents, 1.6 km apart on the East Pacific Rise, were quantified concurrently with current velocity observations. The magnitude and temporal pattern of larval supply differed between vent sites, despite their close proximity. A strong correlation between along-axis flow and daily larval supply suggested that larval supply occurred primarily via along-axis transport between local sources 1-2 km apart. However, weekly larval supply appeared to be driven by larger spatial scales through losses associated with cross-axis flows and the passage of mesoscale eddies. Tracer movement within a quasi-geostrophic eddy model was consistent with the observations of decreased larval supply concurrent with an eddy observed via satellite altimetry. The tracer movement also indicated that deep eddy-induced flow could facilitate a long-distance dispersal event, enhancing dispersal between vents 100s km apart.Financial support was provided by a National Defense Science and Engineering Graduate Fellowship, the WHOI Academic Programs Office, a WHOI Ocean Venture Fund award, the Ocean Life Institute, the Deep Ocean Exploration Institute, and NSF grants OCE0424953 and NSF OCE9712233 to L.S. Mullineaux