The reliability of monetary policy as an economic stabilisation tool depends on the understanding of the empirical effects of policy intervention on macroeconomic aggregates. Since investigating the interdependencies between macroeconomic variables necessarily involves studying their interactions over time, time series analysis is an important tool. This thesis sets out to examine the presence and effects of nonstationarity in the form of a structural break in a basic VAR of four endogenous variables. Specifically, the transmission of a monetary policy shock on the macroeconomic aggregate of 11 Euro Area countries is estimated for the period 1999–2017, employing variables based on previous studies. A Quandt-Andrews breakpoint test is used to identify the break date, and a comparison is made between the periods. This study finds support for the presence of a break in the regression estimate from the breakpoint test, although the reults from the IRFs cannot be shown to be statistically significant, nor to be bias-free.

Statistical modeling of a nonstationary spatial extremal dependence structure is a challenging problem. In practice, parametric max-stable processes are commonly used for modeling spatially-indexed block maxima data, where the stationarity assumption is often made to make inference easier. However, this assumption is unreliable for data observed over a large or complex domain. In this work, we develop a computationally-efficient method to estimate nonstationary extremal dependence using max-stable processes, which builds upon and extends an approach recently proposed in the classical geostatistical literature. More precisely, we divide the spatial domain into a fine grid of subregions, each having its own set of dependence-related parameters, and then impose LASSO ($L_1$) or Ridge ($L_2$) penalties to obtain spatially-smooth estimates. We then also subsequently merge the subregions sequentially together with a new algorithm to enhance the model's performance. Here we focus on the popular Brown-Resnick process, although extensions to other classes of max-stable processes are also possible. We discuss practical strategies for adequately defining the subregions and merging them back together. To make our method suitable for high-dimensional datasets, we exploit a pairwise likelihood approach and discuss the choice of pairs to achieve reasonable computational and statistical efficiency. We apply our proposed method to a dataset of annual maximum temperature in Nepal and show that our approach fits reasonably and realistically captures the complex non-stationarity in the extremal dependence.

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The leading cause of bridge failure has often been identified as bridge scour, which is generally defined as the erosion or removal of streambed and/or bank material around bridge foundations due to flowing water. These scour critical bridges are particularly vulnerable during extreme flood events, and pose a major risk to human life, transportation infrastructure, and economic sustainability. Climate change is increasing the intensity and persistence of large flow events throughout the world, further straining bridge infrastructure. Retrofitting the thousands of undersized and scour critical bridges to more rigorous standards is prohibitively expensive, and current countermeasures inadequately address the core problems related to bridge scour. This research tested the efficacy of using approach embankments as intentional sacrificial "fuses" to protect the integrity of bridges with minimal damage during large flow events by allowing the streams to access their natural floodplain and reduce channel velocities. The concept was evaluated using the Hydrologic Engineering Center's River Analysis System (HEC-RAS) models. Steady flow models were developed for three specific bridges on two river reaches. Bayesian streamflow return period estimators were developed for both river reaches using available United States Geological Survey (USGS) stream gauge data to evaluate sacrificial embankments under non-stationary climatic conditions. Fuse placement was determined to be a cost effective scour mitigation strategy for bridges with suboptimal hydraulic capacity and unknown or shallow foundations. Additional benefits of fuses include reductions in upstream flood stage and velocity.

This dissertation collects two papers regarding the econometric and economic theory and testing of the predictability of asset returns. It is widely accepted that stock returns are not only predictable but highly so. This belief is due to an abundance of existing empirical literature fi nding often overwhelming evidence in favor of predictability. The common regressors used to test predictability (e.g., the dividend-price ratio for stock returns) are very persistent and their innovations are highly correlated with returns. Persistence when combined with a correlation between innovations in the regressor and asset returns can cause substantial over-rejection of a true null hypothesis. This result is both well documented and well known. On the other hand, stochastic volatility is both broadly accepted as a part of return time series and largely ignored by the existing econometric literature on the predictability of returns. The severe e ffect that stochastic volatility can have on standard tests are demonstrated here. These deleterious e ffects render standard tests invalid. However, this problem can be easily corrected using a simple change of chronometer. When a return time series is read in the usual way, at regular intervals of time (e.g., daily observations), then the distribution of returns is highly non-normal and displays marked time heterogeneity. If the return time series is, instead, read according to a clock based on regular intervals of volatility, then returns will be independent and identically normally distributed. This powerful result is utilized in a unique way in each chapter of this dissertation. This time-deformation technique is combined with the Cauchy t-test and the newly introduced martingale estimation technique. This dissertation nds no evidence of predictability in stock returns. Moreover, using martingale estimation, the cause of the Forward Premium Anomaly may be more easily discerned.

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This dissertation proposes new statistical methods for modeling and inference for two specific types of time series: integer-valued data and multivariate nonstationary extreme data. We rely on the class of integer-valued autoregressive (INAR) processes for the former, proposing a novel, flexible and elegant way of modeling count phenomena. As for the latter, we are interested in the human brain and its multi-channel electroencephalogram (EEG) recordings, a natural source of extreme events. Thus, we develop new extreme value theory methods for analyzing such data, whether in modeling the conditional extremal dependence for brain connectivity or clustering extreme brain communities of EEG channels. Regarding integer-valued time series, INAR processes are generally defined by specifying the thinning operator and either the innovations or the marginal distributions. The major limitations of such processes include difficulties deriving the marginal properties and justifying the choice of the thinning operator. To overcome these drawbacks, this dissertation proposes a novel approach for building an INAR model that offers the flexibility to prespecify both marginal and innovation distributions. Thus, the thinning operator is no longer subjectively selected but is rather a direct consequence of the marginal and innovation distributions specified by the modeler. Novel INAR processes are introduced following this perspective; these processes include a model with geometric marginal and innovation distributions (Geo-INAR) and models with bounded innovations. We explore the Geo-INAR model, which is a natural alternative to the classical Poisson INAR model. The Geo-INAR process has interesting stochastic properties, such as MA($\infty$) representation, time reversibility, and closed forms for the $h$-th-order transition probabilities, which enables a natural framework to perform coherent forecasting. In the front of multivariate nonstationary extreme data, the focus lies on multi-channel epilepsy data. Epilepsy is a chronic neurological disorder affecting more than 50 million people globally. An epileptic seizure acts like a temporary shock to the neuronal system, disrupting normal electrical activity in the brain. Epilepsy is frequently diagnosed with EEGs. Current statistical approaches for analyzing EEGs use spectral and coherence analysis, which do not focus on extreme behavior in EEGs (such as bursts in amplitude), neglecting that neuronal oscillations exhibit non-Gaussian heavy-tailed probability distributions. To overcome this limitation, this dissertation proposes new approaches to characterize brain connectivity based on extremal features of EEG signals. Two extreme-valued methods to study alterations in the brain network are proposed. One method is Conex-Connect, a pioneering approach linking the extreme amplitudes of a reference EEG channel with the other channels in the brain network. The other method is Club Exco, which clusters multi-channel EEG data based on a spherical $k$-means procedure applied to the "pseudo-angles," derived from extreme amplitudes of EEG signals. Both methods provide new insights into how the brain network organizes itself during an extreme event, such as an epileptic seizure, in contrast to a baseline state.

Spatial analysis of species for which there is limited quantity of data, termed as the data-poor species, has been challenging due to limited information, especially lack of spatially explicit information. However, these species are frequently of high ecological, conservation and management interest. In this study, I used two empirical examples to demonstrate spatial analysis for two kinds of data-poor species. One example was seabird bycatch from the U.S. Atlantic pelagic longline fishery, which focused on rare events/species for which data are generally characterized by a high percentage of zero observations. The other example was endangered white abalone off the California coast, which focused on endangered species whose data are very limited. With the seabird bycatch example, I adopted a spatial filtering technique to incorporate spatial patterns and to improve model performance. The model modified with spatial filters showed superior performance over other candidate models. I also applied the geographically weighted approach to explore spatial nonstationarity in seabird bycatch, i.e., spatial variation in the parameters that describe relationships between biological processes and environmental factors. Estimates of parameters exhibited high spatial variation. With the white abalone example, I demonstrated the spatially explicit hierarchical demographic model and conducted a risk assessment to evaluate the efficacy of hypothetical restoration strategies. The model allowed for the Allee effect (i.e., density-dependent fertilization success) by using spatial explicit density estimates. Restoration efforts directed at larger-size individuals may be more effective in increasing population density than efforts focusing on juveniles. I also explored the spatial nonstationarity in white abalone catch data. I estimated the spatially explicit decline rate and linked the decline rate to environmental factors including water depth, distance to California coast, distance to land, sea surface temperature and chlorophyll concentration. The decline rate showed spatial variation. I did not detect any significant associations between decline rate and these five environmental factors. Through such a study, I am hoping to provide insights on applying or adapting existing methods to model spatial dynamics of data-poor species, and on utilizing information from such analyses to aid in their conservation and management. / Ph. D.

The general topic of this work is to reveal the potential relationship between tiredness cause by hypokinetic monotonous loading and breathing. The aim was to determine if there are suitable respiratory parameters that would indicate this tirednes and, if so, then verify their validity for predicting the tiredness phenomena accompanying huge range of everyday human activities. The performed experiment was attended by five volunteers who absolved measurements of electrical activity of brain, of breathing and of chest volume changes. The course of the experiment and the behaviour of probands were recorded by a camera. In the first part of each maesuremnt, a specified monotonous task (Task Tracking) was performed. The probands have had to follow the target moving with pseudocasual direction and speed by the cursor on the monitor. This task currently reflected the level of reliability and quality of the performed aktivity. In the second part of measurement, the probands had just to relax and watch a movie. Both parts were measured in two conditions - alert and tired (after 24 hours of sleep deprivation) proband. The data were compared with each other and evaluated. The measurements and the results showed that the rate of the tiredness can be fairly reliably assessed by monitoring of the volume...

A procedure was developed for dealing with two problems that have impeded the use of quantal parameters in studies of transmitter release. The first, involving temporal and spatial biasing in the estimates for the number of functional release sites (n̄) and probability of release (p̄), was addressed by reducing temporal variance experimentally and calculating the bias produced by spatial variance in p (var(s)p). The second, involving inaccuracies in the use of nerve-evoked endplate potentials (EPPs), was circumvented by using only miniature EPPs (MEPPs). Intracellular recordings were made from isolated frog cutaneous pectoris, after decapitation and pithing of the animals, and the concentration of K+ ([K+]) was raised to 10 mM to increase the level of transmitter release. The number of quanta released (m̄) by the EPP was replaced by the number of MEPPs in a fixed time interval (bin), and 500 sequential bins used for each quantal estimate. With the use of 50-ms bins, estimates for var(s)p were consistently negative. This was due to too large a bin (and introduction of undetected temporal variance) because the use of smaller bins (5 ms) produced positive estimates of var(s)p. Increases in m, n, and p but not var(s)p were found in response to increases in [K+] or [Ca2+]/[Co2+]. La3+ (20 μM) produced increases in m and n, which peaked after 20 min and declined toward zero. There were also large increases in p and var(s)p, which peaked and declined only to initial control values. The increase in var(s)p was presumed to reflect La3+-induced release of Ca2+ from intracellular organelles. The results suggest that this approach may be used to obtain unbiased estimates of n̄ and p̄ and that the estimates of var(s)p may be useful for studying Ca2+ release from intraterminal organelles.