A Generalized Quasi-Likelihood Estimator for Nonstationary Stochastic Processes−Asymptotic Properties and Examples

2010 Mathematics Subject Classification: 62F12, 62M05, 62M09, 62M10, 60G42.

The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form

2000 Mathematics Subject Classification: 35J70, 35P15.

Inequalities and Asymptotic Formulae for the Three Parametric Mittag-Leffler Functions

MSC 2010: 33E12, 30A10, 30D15, 30E15

Asymptotic Analysis of a Schrödinger-Poisson System with Quantum Wells and Macroscopic Nonlinearities in Dimension 1

2000 Mathematics Subject Classification: 35Q02, 35Q05, 35Q10, 35B40.

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

2000 Mathematics Subject Classification: 37D40.

Stokes waves revisited:exact solutions in the asymptotic limit

The Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic “secular variation” in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher-ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long-standing theoretical insufficiency by invoking a compact exact n-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third-ordered perturbative solution, that leads to a seamless extension to higher-order (e.g., fifth-order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desired higher-ordered expansion may be compacted within the same representation, but without any aperiodicity in the spectral pattern of the wave guides.

An asymptotic test for the Conditional Value-at-Risk

Conditional Value-at-Risk (equivalent to the Expected Shortfall, Tail Value-at-Risk and Tail Conditional Expectation in the case of continuous probability distributions) is an increasingly popular risk measure in the fields of actuarial science, banking and finance, and arguably a more suitable alternative to the currently widespread Value-at-Risk. In my paper, I present a brief literature survey, and propose a statistical test of the location of the CVaR, which may be applied by practising actuaries to test whether CVaR-based capital levels are in line with observed data. Finally, I conclude with numerical experiments and some questions for future research.

The European Parliament, membership expansions, and organizational change

The European Union (EU) is an extraordinary achievement. From a regional economic organization, it grew into a polity within fifty years. The original EU of six members expanded incrementally to 27 over forty years, and it now comprises a population of almost 500 million people. While the five expansions of the European Economic Community/European Community/European Union (EU) have received considerable scholarly attention, surprisingly little attention has been given to their impacts on "Europe's" only legislative body, currently known as the European Parliament (EP). More specifically, little is known about how waves of new members (from widely diverse parties and national backgrounds) affected—and were affected by—the EP's organizational structure and its internal processes. The purpose of this study therefore is to help fill this gap by describing and explaining how the various EEC/EC/EU expansions or "membership shocks" (1973, 1981, 1986, 1995, and 2004) affected the EP's organizational structure and its internal Rules of Procedure (RoP). The central research question of this dissertation is the following: What were the major structural and procedural effects of the five membership expansions of what eventually became the European Union on the European Parliament? This dissertation answers this question by using concepts and measures drawn from organizational theory. While other studies have applied concepts and hypotheses from organizational theory to legislatures, such an approach has never been used to analyze the EP, which is conceptualized here as a "membership organization." This study, through an analysis of the EP, demonstrates that organization theory can help us fully understand the effects of membership expansions on any membership organization. That is, understanding how this particular organization responded to change can inform not only how others in this class (legislatures) do so, but how this process unfolds in a variety of times and places. The principal findings of this study are as follows: (1) EP staff growth revealed an interesting pattern: Staff did not increase concurrently with EP membership. That is, it turned out that the rate of membership growth exceeded the rate of staff increase, suggesting professionalization of EP staff and their relative empowerment vis-à-vis MEPs; (2) The number of rules and the precision within them increased; (3) the largest number of EP rule changes focused on increasing EP efficiency; and (4) The authority was centralized in the hands of EP leadership, that is, the EP President, the Conference of Presidents and also two major political groups.

Asymptotic Theory for Extended Asymmetric Multivariate GARCH Processes

The paper considers various extended asymmetric multivariate conditional volatility models, and derives appropriate regularity conditions and associated asymptotic theory. This enables checking of internal consistency and allows valid statistical inferences to be drawn based on empirical estimation. For this purpose, we use an underlying vector random coefficient autoregressive process, for which we show the equivalent representation for the asymmetric multivariate conditional volatility model, to derive asymptotic theory for the quasi-maximum likelihood estimator. As an extension, we develop a new multivariate asymmetric long memory volatility model, and discuss the associated asymptotic properties.

Widespread range expansions shape latitudinal variation in insect thermal limits

I thank the authors of previous studies on global variation in insect thermal tolerances who have generously provided open access use of their data sets.

Bond Fund Performance During Recessions and Expansions: Empirical Evidence from a Small Market

This paper provides the first investigation about bond mutual fund performance during recession and expansion periods separately. Based on multi-factor performance evaluation models, results show that bond funds significantly underperform the market during both phases of the business cycle. Nevertheless, unlike equity funds, bond funds exhibit considerably higher alphas during good economic states than during market downturns. These results, however, seem entirely driven by the global financial crisis subperiod. In contrast, during the recession associated to the Euro sovereign debt crisis, bond funds are able to accomplish neutral performance. This improved performance throughout the debt crisis seems to be related to more conservative investment strategies, which reflect an increase in managers’ risk aversion.

Asymptotic Change-Point Analysis of the Dependencies in Time Series

In recent papers, Wied and his coauthors have introduced change-point procedures to detect and estimate structural breaks in the correlation between time series. To prove the asymptotic distribution of the test statistic and stopping time as well as the change-point estimation rate, they use an extended functional Delta method and assume nearly constant expectations and variances of the time series. In this thesis, we allow asymptotically infinitely many structural breaks in the means and variances of the time series. For this setting, we present test statistics and stopping times which are used to determine whether or not the correlation between two time series is and stays constant, respectively. Additionally, we consider estimates for change-points in the correlations. The employed nonparametric statistics depend on the means and variances. These (nuisance) parameters are replaced by estimates in the course of this thesis. We avoid assuming a fixed form of these estimates but rather we use "blackbox" estimates, i.e. we derive results under assumptions that these estimates fulfill. These results are supplement with examples. This thesis is organized in seven sections. In Section 1, we motivate the issue and present the mathematical model. In Section 2, we consider a posteriori and sequential testing procedures, and investigate convergence rates for change-point estimation, always assuming that the means and the variances of the time series are known. In the following sections, the assumptions of known means and variances are relaxed. In Section 3, we present the assumptions for the mean and variance estimates that we will use for the mean in Section 4, for the variance in Section 5, and for both parameters in Section 6. Finally, in Section 7, a simulation study illustrates the finite sample behaviors of some testing procedures and estimates.