Time Series Analysis, Cointegration, and Applications

The two prize winners in Economics this year would describe themselves as "Econometricians," so I thought that I should start by explaining that term. One can begin with the ancient subject of Mathematics which is largely concerned with the discovery of relationships between deterministic variables using a rigorous argument. (A deterministic variable is one whose value is known with certainty.) However, by the middle of the last millennium it became clear that some objects were not deterministic, they had to be described with the use of probabilities, so that Mathematics grew a substantial sub-field known as "Statistics." This later became involved with the analysis of data and a number of methods have been developed for data having what may be called "standard properties."time series; cointegration

Observation of chiral heat transport in the quantum Hall regime

Heat transport in the quantum Hall regime is investigated using micron-scale heaters and thermometers positioned along the edge of a millimeter-scale two dimensional electron system (2DES). The heaters rely on localized current injection into the 2DES, while the thermometers are based on the thermoelectric effect. In the v=1 integer quantized Hall state, a thermoelectric signal appears at an edge thermometer only when it is “downstream,” in the sense of electronic edge transport, from the heater. When the distance between the heater and the thermometer is increased, the thermoelectric signal is reduced, showing that the electrons cool as they propagate along the edge

Smooth critical points of planar harmonic mappings

In a work in 1992, Lyzzaik studies local properties of light harmonic mappings. More precisely, he classifies their critical points and accordingly studies their topological and geometrical behaviours. We will focus our study on smooth critical points of light harmonic maps. We will establish several relationships between miscellaneous local invariants, and show how to connect them to Lyzzaik's models. With a crucial use of Milnor fibration theory, we get a fundamental and yet quite unexpected relation between three of the numerical invariants, namely the complex multiplicity, the local order of the map and the Puiseux pair of the critical value curve. We also derive similar results for a real and complex analytic planar germ at a regular point of its Jacobian level-0 curve. Inspired by Whitney's work on cusps and folds, we develop an iterative algorithm computing the invariants. Examples are presented in order to compare the harmonic situation to the real analytic one.Comment: 36 pages, 5 figure

Modeling Amazon Deforestation for Policy Purposes

Brazil has long ago removed most of the perverse government incentives that stimulated massive deforestation in the Amazon in the 70s and 80s, but one highly controversial policy remains: Road building. While data is now abundantly available due to the constant satellite surveillance of the Amazon, the analytical methods typically used to analyze the impact of roads on natural vegetation cover are methodologically weak and not very helpful to guide public policy. This paper discusses the respective weaknesses of typical GIS analysis and typical municipality level regression analysis, and shows what would be needed to construct an ideal model of deforestation processes. It also presents an alternative approach that is much less demanding in terms of modeling and estimation and more useful for policy makers as well.Deforestation, Amazon, Brazil, econometric modeling

Regeneration of Imperiled Hardwoods in the Eastern United States

Our ability to successfully promote forest stand health and facilitate species under the threat of extinction will hinge on our ability to identify species regeneration requirements in an ever-changing environment. In the first chapter of this dissertation, I address what is known about the nature of threatened and imperiled hardwoods in the eastern United States, and in doing so, I identify several large knowledge gaps in current potentials and methodologies for regenerating them. In my second chapter, I use recent data from the United States Forest Service, Forest Inventory and Analysis program (FIA) to quantify ash regeneration counts across FIA forest type groups containing the emerald ash borer (EAB; Agrilus planipennis Fairmaire) threatened species white ash (Fraxinus americana L.), green ash (Fraxinus pensylvanica Marsh.), black ash (Fraxinus nigra Marsh.), blue ash (Fraxinus quadrangulata Michx.), Carolina ash (Fraxinus caroliniana Mill.), and pumpkin ash (Fraxinus profunda (Bush) Bush). In addition to this baseline calculation of ash regeneration potentials, all other species are quantified to determine overall species composition and levels of inter-specific competition. In the third chapter, Shannon-Wiener species diversity index values are calculated for forest communities containing each of the six ash species above. This facilitates identification of ash-dominated communities and states in need of greater conservation efforts. In the fourth chapter, I use field observations to quantify microsites supporting populations of mountain stewartia (Stewartia ovata (Cav.) Weatherby) across East Tennessee and examine the hypothesis that specific site requirements are limiting stewartia’s distribution and abundance across its natural range. In doing so, I am able to put forth a list of site requirements that may be necessary to guarantee the future regeneration and success of mountain stewartia. In the final chapter, a 25-year data set is used to investigate the success of a novel method for regenerating northern red oak (Quercus rubra L.) in Michigan oak and pine stands. Oak regeneration is more successful in pine stands than in oak stands due to several potential factors. Overall, my dissertation seeks to highlight regeneration requirements, potentials, and methods for regenerating an important group of threatened and imperiled hardwood species

Reducing the Bias of Causality Measures

Measures of the direction and strength of the interdependence between two time series are evaluated and modified in order to reduce the bias in the estimation of the measures, so that they give zero values when there is no causal effect. For this, point shuffling is employed as used in the frame of surrogate data. This correction is not specific to a particular measure and it is implemented here on measures based on state space reconstruction and information measures. The performance of the causality measures and their modifications is evaluated on simulated uncoupled and coupled dynamical systems and for different settings of embedding dimension, time series length and noise level. The corrected measures, and particularly the suggested corrected transfer entropy, turn out to stabilize at the zero level in the absence of causal effect and detect correctly the direction of information flow when it is present. The measures are also evaluated on electroencephalograms (EEG) for the detection of the information flow in the brain of an epileptic patient. The performance of the measures on EEG is interpreted, in view of the results from the simulation study.Comment: 30 pages, 12 figures, accepted to Physical Review