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In this work, we apply a nonlinear mixture autoregressive (MixAR) model to supplant the Gaussian mixture model for speaker verification. MixAR is a statistical model that is a probabilistically weighted combination of components, each of which is an autoregressive filter in addition to a mean. The probabilistic mixing and the datadependent weights are responsible for the nonlinear nature of the model. Our experiments with synthetic as well as real speech data from standard speech corpora show that MixAR model outperforms GMM, especially under unseen noisy conditions. Moreover, MixAR did not require delta features and used 2.5x fewer parameters to achieve comparable or better performance as that of GMM using static as well as delta features. Also, MixAR suffered less from overitting issues than GMM when training data was sparse. However, MixAR performance deteriorated more quickly than that of GMM when evaluation data duration was reduced. This could pose limitations on the required minimum amount of evaluation data when using MixAR model for speaker verification.

As compared to short-term forecasting (e.g., 1 day), it is often challenging to accurately forecast the volume of precipitation in a medium-term horizon (e.g., 1 week). As a result, fluctuations in water inflow can trigger generation shortage and electricity price spikes in a power system with major or predominant hydro resources. In this paper, we study a two-stage robust scheduling approach for a hydrothermal power system. We consider water inflow uncertainty and employ a vector autoregressive (VAR) model to represent its seasonality and accordingly construct an uncertainty set in the robust optimization approach. We design a Benders' decomposition algorithm to solve this problem. Results are presented for the proposed approach on a real-world case study.

Water quality and river/stream ecosystems are important for all living creatures. To protect human health, aquatic life and the surrounding ecosystem, a considerable amount of time and money has been spent on sampling and monitoring streams and rivers. Water quality monitoring and analysis can help researchers predict and learn from natural processes in the environment and determine human impacts on an ecosystem. Measurements such as temperature, pH, nitrogen concentration, algae and fish count collected along the network are all important factors in water quality analysis. The main purposes of the statistical analysis in this thesis are (1) to assess the relationship between the variable measured in the water (response variable) and other variables that describe either the locations on/along the stream network or certain characteristics at each location (explanatory variable), and (2) to assess the degree of similarity between the response variable values measured at different locations of the stream, i.e. spatial dependence structure. It is commonly accepted that measurements taken at two locations close to each other should have more similarity than locations far away. However, this is not always true for observations from stream networks. Observations from two sites that do not share water flow could be independent of each other even if they are very close in terms of stream distance, especially those observations taken on objects that move passively with the water flow. To model stream network data correctly, it is important to quantify the strength of association between observations from sites that do not share water.

This thesis is mainly concerned with the estimation of parameters of a first-order Smooth Threshold Autoregressive (STAR) model with delay parameter one. The estimation procedures include classical and Bayesian methods from a parametric and a semiparametric point of view.As the theoretical importance of stationarity is a primary concern in estimation of time series models, we begin the thesis with a thorough investigation of necessary or sufficient conditions for ergodicity of a first-order STAR process followed by the necessary and sufficient conditions for recurrence and classification for null-recurrence and transience.The estimation procedure is started by using Bayesian analysis which derives posterior distributions of parameters with a noninformative prior for the STAR models of order p. The predictive performance of the STAR models using the exact one-step-ahead predictions along with an approximation to multi-step-ahead predictive density are considered. The theoretical results are then illustrated by simulated data sets and the well- known Canadian lynx data set.The parameter estimation obtained by conditional least squares, maximum likelihood, M-estimator and estimating functions are reviewed together with their asymptotic properties and presented under the classical and parametric approaches. These estimators are then used as preliminary estimators for obtaining adaptive estimates in a semiparametric setting. The adaptive estimates for a first-order STAR model with delay parameter one exist only for the class of symmetric error densities. At the end, the numerical results are presented to compare the parametric and semiparametric estimates of this model.

Vibroarthrograpyhy (VAG) is an innovative, objective and non-invasive technique to obtain diagnostic information concerning the articular cartilage of knee joints. Knee VAG signals can be detected by putting a contact sensor on the surface of the knee joints during the movement such as flexion and extension. Before this research, there are many VAG group studies that contribute in signal processing and database building. The adaptive segmentation method and autoregressive modeling are developed to segment the nonstationary VAG signals. This thesis tries to investigate the accuracy of some database containing root mean square (RMS) value and intraclass distance (ID) feature parameters of physiological patellofemoral crepitus (PPC) signals. This research is first setting up two diagnosis standards for RMS and ID. According to the two standards, all signals are divided into three types: normal, unknown and injured, and those appear both in normal type of RMS and ID parameters are picked out. The same does the injured type. In conclusion, by checking the anamneses of these signals, we can be aware of the numbers of real normal and real injured in normal type and injured type; therefore the accuracy of the database can be derived. Consequently the accuracy of database in this thesis is quite certifiable.

Former researches provide evidence that invasive species could alter ecosystem’s components, threaten native species and cause economic losses in southern forest lands. The objective of the project is to explore significant driving factors and develop geospatial models for monitoring, predicting and mapping the extent and conditions of major invasive species. In the study area, 16 invasive species were classified into four groups: regionally spreading species, regionally establishing species, locally spreading species and regionally colonizing species by population size and spatial characteristics. According to local Moran’s I, spatial autocorrelation existed in 16 invasive species. Autologistic model and simultaneous autoregressive model were employed to explore the relationships between spatial distribution and a set of indentified variables for Chinese privet, kudzu, Nepalese browntop and tallow tree at plot and county levels. The project showed that human-caused disturbances and forest types were significantly related to the spatial distribution of four invasive species in different scales.

[pt] Desde o século XVI, já existia a idéia de que o poder de compra deveria influenciar no valor de cada moeda. A fim de se entender as relações entre câmbio e inflação, modelos autoregressivos lineares sempre apresentaram dificuldades para superar o passeio aleatório. Possíveis fricções em operações cambiais podem dificultar a arbitragem próxima do câmbio de equilíbrio considerado pelos agentes financeiros. À medida em que se distancia do valor considerado justo, a convergência se torna mais intensa, pois os custos já não seriam uma parcela tão relevante para o lucro potencial da operação. No modelo não-linear proposto, há dois regimes diferentes: um próximo do equilíbrio (comportamento de passeio aleatório) e um comportamento longe dele ocorrendo simultaneamente, mas com pesos variáveis. A depender do nível do câmbio em relação ao equilíbrio, um regime ganha mais peso e outro perde relevância. Essa tese tem o objetivo de avaliar o caráter preditivo do movimento cambiais. O modelo não-linear ESTAR é usado para montar cestas de moedas a serem compradas e vendidas e o retorno advindo de oscilações cambiais é computado. Por fim, incorporamos os efeitos de juros ao modelo para montar portfólios de moedas a fim de simular o retorno de um investimento usando essa estratégia. Para as cestas de moedas, o modelo gerou bons retornos e baixos riscos, tanto em termos de desvio padrão quanto em termos de drawdown. Tal característica foi observada no modelo in-sample e no out-of-sample o que indica um forte caráter preditivo. Levando em conta o efeito dos juros, os portfólios com menos moedas apresentaram retornos positivos, porém essa vantagem é perdida ao se aumentar a quantidade de moedas. / [en] Since the sixteenth century, there was already the idea that purchasing power should influence the value of each currency. In order to understand the relationship between exchange rate and inflation, linear autoregressive models always presented difficulties to beat the random walk. Possible frictions in foreign exchange operations may hinder arbitrage close to the equilibrium exchange rate considered by financial agents. As the exchange rate distances itself from the value considered fair, the convergence becomes more intense, because the costs would no longer be so relevant to the potential profit of the operation. In the proposed nonlinear model, there are two different regimes: one near equilibrium (random walk behavior) and one behavior away from it occurring simultaneously, but with variable weights. For different levels of the exchange rate relative to the equilibrium, one regime gains more weight and the other loses relevance. This thesis aims to evaluate the predictive nature of the exchange rate movement. The nonlinear model ESTAR is used to create baskets of currencies to be bought and sold and the aggregate return based on exchange rate movements is computed. Finally, we consider the interest rate effects on the model to set up currencies portfolios in order to simulate the return on an investment using this strategy. For the baskets of currencies, the model generated good returns and low risks, based on both standard deviation and drawdown. This characteristic was observed in the in-sample model and in the out-of-sample model, which indicates a strong predictive power. Considering the interest effect, portfolios with fewer currencies showed positive returns, but this advantage is lost by increasing the number of currencies.

Master of Science / Department of Statistics / Juan Du / Space and time are often vital components of research data sets. Accounting for and utilizing the space and time information in statistical models become beneficial when the response variable in question is proved to have a space and time dependence. This work focuses on the modeling and analysis of crop yield over space and time. Specifically, two different yield data sets were used. The first yield and environmental data set was collected across selected counties in Kansas from yield performance tests conducted for multiple years. The second yield data set was a survey data set collected by USDA across the US from 1900-2009. The objectives of our study were to investigate crop yield trends in space and time, quantify the variability in yield explained by genetics and space-time (environment) factors, and study how spatio-temporal information could be incorporated and also utilized in modeling and forecasting yield. Based on the format of these data sets, trend of irrigated and dryland crops was analyzed by employing time series statistical techniques. Some traditional linear regressions and smoothing techniques are first used to obtain the yield function. These models were then improved by incorporating time and space information either as explanatory variables or as auto- or cross- correlations adjusted in the residual covariance structures. In addition, a multivariate time series modeling approach was conducted to demonstrate how the space and time correlation information can be utilized to model and forecast yield and related variables. The conclusion from this research clearly emphasizes the importance of space and time components of data sets in research analysis. That is partly because they can often adjust (make up) for those underlying variables and factor effects that are not measured or not well understood.

This paper explores the relationship between household income inequality and macroeconomic uncertainty in the United States. Using a novel large-scale macroeconometric model, we shed light on regional disparities of inequality responses to a national uncertainty shock. The results suggest that income inequality decreases in most states, with a pronounced degree of heterogeneity in terms of the dynamic responses. By contrast, some few states, mostly located in the Midwest, display increasing levels of income inequality over time. Forecast error variance and historical decompositions highlight the importance of uncertainty shocks in explaining income inequality in most regions considered. Finally, we explain differences in the responses of income inequality by means of a simple regression analysis. These regressions reveal that the income composition as well as labor market fundamentals determine the directional pattern of the dynamic responses. / Series: Working Papers in Regional Science