This paper seeks to further investigate data extracted by the use of Functional Magnetic Resonance Imaging (FMRI) as it is applied to brain tissue and how it measures blood flow to certain areas of the brain following the application of a stimulus. As a precursor to detailed spatial analysis of this kind of data, this paper develops methods of grouping data based on the necessary conditions for spatial statistical analysis. The purpose of this paper is to examine and develop methods that can be used to delineate regions of stationarity. One of the major assumptions used in spatial estimation is that the data field is homogeneous with respect to the mean and the covariance function. As such, any spatial estimation presupposes that these criteria are met. With respect to analyses that may be considered new or experimental, however, there is no evidence that these assumptions will hold.

The unit root revolution in time series modeling has created substantial interest in non- stationarity and its implications for empirical modeling. Beyond the original interest in trend vs. di¤erence non-stationarity, there has been renewed interest in testing and modeling structural breaks. The focus of my dissertation is on testing for departures from stationarity in a broader framework where unit root, mean trends and structural break non-stationarity constitute only a small subset of the possible forms of non-stationarity. In the fi¦rst chapter the most popular testing procedures for the assumption, in view of the fact that general forms of non-stationarity render each observation unique, I develop a testing procedure using a resampling scheme which is based on a Maximum Entropy replication algorithm. The proposed misspecification testing procedure relies on resampling techniques to enhance the informational content of the observed data in an attempt to capture heterogeneity 'locally' using rolling window estimators of the primary moments of the stochastic process. This provides an e¤ective way to enhance the sample information in order to assess the presence of departures from stationarity. Depending on the sample size, the method utilizes overlapping or non-overlapping window estimates. The e¤ectiveness of the testing procedure is assessed using extensive Monte Carlo simulations. The use of rolling non-overlapping windows improves the method by improving both the size and power of the test. In particular, the new test has empirical size very close to the nominal and very high power for a variety of departures from stationarity. The proposed procedure is then applied on seven macroeconomic series in the fourth chapter. Finally, the optimal choice of orthogonal polynomials, for hypothesis testing, is investigated in the last chapter. / Ph. D.

A system with hysteresis is one that exhibits path dependent but rate independent memory. Hysteresis can be observed physically through the magnetization of a ferromagnetic material. In order to mathematically describe systems with hysteresis, we use the Preisach model. A discussion of the Preisach model is given as well as a method for computing the hysteretic transformation of an input variable. The focus of this paper is hysteresis in economics, namely, unemployment. We consider essential time series techniques for analyzing time series data, i.e. unit root testing for stationarity. However, we point out problems in modeling hysteresis with these techniques and argue that unit root tests cannot capture the selective memory of a system with hysteresis. For that, hysteresis in economic time series data is modeled using the Preisach model. We test the explanatory power of the previous unemployment rate on the current unemployment rate using both a hysteretic and non-hysteretic model. We find that the non-hysteretic model is better at explaining current unemployment rates, which suggests hysteresis is not present in the United States unemployment rate. / Master of Science

This thesis is concerned with the econometric modelling of gasoline prices in US. The intention is to characterize the market process in this crucial and significant industry. Overall we have been seeking to identify a mechanism to signal and measure market failure and consequently improve market performance. Firstly we examine the time series properties of gasoline prices using the criteria for perfect arbitrage to test market efficiency from the stationarity of price proportions. This is done by considering market efficiency across in different regions of the US, by applying a range of different stationary tests. In this analysis we collected a comprehensive data set of gasoline prices for all regions of the US mainland for the longest period available. Forni (2004), outlined reasons why the analysis of price proportions may be advantageous; especially when the sample is limited. Stationarity corresponds to a broad market, it is found here that the US gasoline market is on average broad. Except for the Gulf Coast and Lower Atlantic, which may be seen as economically and/or geographically separated, market structure in the rest of the US would not appear to be a problem Next we investigate possible long-run price leadership in the US gasoline market and the inter-relatedness of price behaviour relevant to a competitive market. Following Hunter & Burke (2007) and Kurita (2008) market definition is tested. This is done on an extended regional data set to Kurita and following the analysis in Hunter and Burke on a set of company data for the US.We analysed long-run price leadership through the cointegrated vector auto-regression (VAR) to identify key characteristics of long-run structure in the gasoline market. The analysis of the system of regional prices confirms problems with the Gulf Coast and Lower Atlantic, but also based on the finding that the cointegrating rank is less than N-1 using both types of data ( regional price data and company price data) and the findings on weak exogenity it is suggested that competition across the whole of the US is further limited. We applied further tests to company data on prices and quantity data to investigate further the need to regulate for potential anomalies and to capture more directly consumer harm. The variance screening method applied to recent weekly data indicates that there is too little variation in gasoline prices and this would seem to support the cointegration study. Furthermore we applied a dynamic disequilibrium analysis to attempt to identify long-run demand and supply in the gasoline market. Finding significant variables using the Phillips-Hansen fully modified estimation of the switching regression is necessary to distinguish two long-run equations (S&D). Moreover a comparison is made with a Markov Switching Model (MSM) of prices and this suggests a similar pattern of regime to the quantity information analysed in by our disequilibrium model.

Conventional time series analysis depends heavily on the twin assumptions of linearity and stationarity. However; there are certain cases where sampled data tend to violate the assumptions. In this paper, we use neural networks technology to explore the situation when the assumptions of linearity and stationarity are failed. At the end of the paper, we discuss an illustrative example about the annual expenditures of government and science-education-culture of R.O.C.

In this dissertation, I study the effects of climate change on agricultural total factor productivity and crop yields and their variability. In addition, an examination was conducted on the value of select climate change adaptation strategies in forestry. Across the study, the climate change scenarios analyzed were based on the 2007 Intergovernmental Panel on Climate Change Assessment Report. Climate change impacts on the returns to research investments were examined extending the work of Huffman and Evenson (2006), incorporating climatic effects. The conjecture is that the rate of return of agricultural research is falling due to altered resource allocations and unfavorable weather conditions, arising from the early onset of climate change. This work was done using a panel model of Agricultural Total Factor Productivity (TFP) for the forty-eight contiguous states over 1970?1999. Climatic variables such as temperature and amount and intensity of precipitation were added into the model. The main results are (1) climate change affects research productivity, varying by region; (2) this effect is generally negative; (3) additional investments are needed to achieve pre-climate change TFP rates of growth; and (4) the predicted investment increases are on the order of 18%. The second inquiry involved the impact of historical climatic conditions on the statistical distributions of crop yields through mean and variability. This was done statistically, using historical yields for several crops in the US, and climate variables, with annual observations from 1960 to 2007. The estimation shows that climate change is having an effect on the first two moments of the distribution, concluding that crop yield distributions are not stationary. The implication is that risk analysis must consider means and volatility measures that depend on future climatic conditions. The analysis shows that future mean yields will increase, but volatility will also be greater for the studied crops. These results have strong implication for future crop insurance decisions. Finally, an examination was done on the value of select forestry adaptation strategies in the face of climate change. This work is motivated by the known fact that forestry sector is already heavily adapted to changing climatic conditions. Using the Forestry and Agriculture Sector Optimization Model for the United States (FASOM), I found that rotation age is the most effective adaptation strategy being worth about 60 billion dollars, while changes in species and management intensity are worth about 1.5 billion, and land use change between forestry to agriculture is worth about 200,000.

We consider an online learning scenario in which the learner can make predictions on the basis of a fixed set of experts. We derive upper and lower relative loss bounds for a class of universal learning algorithms involving a switching dynamics over the choice of the experts. On the basis of the performance bounds we provide the optimal a priori discretization of the switching-rate parameter that governs the switching dynamics. We demonstrate the algorithm in the context of wireless networks.

Neste trabalho apresentamos o RL-CD (Reinforcement Learning with Context Detection), um método desenvolvido a fim de lidar com o problema do aprendizado por reforço (RL) em ambientes não-estacionários. Embora os métodos existentes de RL consigam, muitas vezes, superar a não-estacionariedade, o fazem sob o inconveniente de terem de reaprender políticas que já haviam sido calculadas, o que implica perda de desempenho durante os períodos de readaptação. O método proposto baseia-se em um mecanismo geral através do qual são criados, atualizados e selecionados um dentre vários modelos e políticas parciais. Os modelos parciais do ambiente são incrementalmente construídos de acordo com a capacidade do sistema de fazer predições eficazes. A determinação de tal medida de eficácia baseia-se no cálculo de qualidades globais para cada modelo, as quais refletem o ajuste total necessário para tornar cada modelo coerente com as experimentações reais. Depois de apresentadas as bases teóricas necessárias para fundamentar o RL-CD e suas equações, são propostos e discutidos um conjunto de experimentos que demonstram sua eficiência, tanto em relação a estratégias clássicas de RL quanto em comparação a algoritmos especialmente projetados para lidar com cenários não-estacionários. O RL-CD é comparado com métodos reconhecidos na área de aprendizado por reforço e também com estratégias RL multi-modelo. Os resultados obtidos sugerem que o RLCD constitui uma abordagem eficiente para lidar com uma subclasse de ambientes nãoestacionários, especificamente aquela formada por ambientes cuja dinâmica é corretamente representada por um conjunto finito de Modelos de Markov estacionários. Por fim, apresentamos a análise teórica de um dos parâmetros mais importantes do RL-CD, possibilitada pela aproximação empírica de distribuições de probabilidades via métodos de Monte Carlo. Essa análise permite que os valores ideais de tal parâmetro sejam calculados, tornando assim seu ajuste independente da aplicação específica sendo estudada. / In this work we introduce RL-CD (Reinforcement Learning with Context Detection), a novel method for solving reinforcement learning (RL) problems in non-stationary environments. In face of non-stationary scenarios, standard RL methods need to continually readapt themselves to the changing dynamics of the environment. This causes a performance drop during the readjustment phase and implies the need for relearning policies even for dynamics which have already been experienced. RL-CD overcomes these problems by implementing a mechanism for creating, updating and selecting one among several partial models of the environment. The partial models are incrementally built according to the system’s capability of making predictions regarding a given sequence of observations. First, we present the motivations and the theorical basis needed to develop the conceptual framework of RL-CD. Afterwards, we propose, formalize and show the efficiency of RL-CD both in a simple non-stationary environment and in a noisy scenarios. We show that RL-CD performs better than two standard reinforcement learning algorithms and that it has advantages over methods specifically designed to cope with non-stationarity. Finally, we present the theoretical examination of one of RL-CD’s most important parameters, made possible by means of the analysis of probability distributions obtained via Monte Carlo methods. This analysis makes it possible for us to calculate the optimum values for this parameter, so that its adjustment can be performed independently of the scenario being studied.

Neste trabalho apresentamos o RL-CD (Reinforcement Learning with Context Detection), um método desenvolvido a fim de lidar com o problema do aprendizado por reforço (RL) em ambientes não-estacionários. Embora os métodos existentes de RL consigam, muitas vezes, superar a não-estacionariedade, o fazem sob o inconveniente de terem de reaprender políticas que já haviam sido calculadas, o que implica perda de desempenho durante os períodos de readaptação. O método proposto baseia-se em um mecanismo geral através do qual são criados, atualizados e selecionados um dentre vários modelos e políticas parciais. Os modelos parciais do ambiente são incrementalmente construídos de acordo com a capacidade do sistema de fazer predições eficazes. A determinação de tal medida de eficácia baseia-se no cálculo de qualidades globais para cada modelo, as quais refletem o ajuste total necessário para tornar cada modelo coerente com as experimentações reais. Depois de apresentadas as bases teóricas necessárias para fundamentar o RL-CD e suas equações, são propostos e discutidos um conjunto de experimentos que demonstram sua eficiência, tanto em relação a estratégias clássicas de RL quanto em comparação a algoritmos especialmente projetados para lidar com cenários não-estacionários. O RL-CD é comparado com métodos reconhecidos na área de aprendizado por reforço e também com estratégias RL multi-modelo. Os resultados obtidos sugerem que o RLCD constitui uma abordagem eficiente para lidar com uma subclasse de ambientes nãoestacionários, especificamente aquela formada por ambientes cuja dinâmica é corretamente representada por um conjunto finito de Modelos de Markov estacionários. Por fim, apresentamos a análise teórica de um dos parâmetros mais importantes do RL-CD, possibilitada pela aproximação empírica de distribuições de probabilidades via métodos de Monte Carlo. Essa análise permite que os valores ideais de tal parâmetro sejam calculados, tornando assim seu ajuste independente da aplicação específica sendo estudada. / In this work we introduce RL-CD (Reinforcement Learning with Context Detection), a novel method for solving reinforcement learning (RL) problems in non-stationary environments. In face of non-stationary scenarios, standard RL methods need to continually readapt themselves to the changing dynamics of the environment. This causes a performance drop during the readjustment phase and implies the need for relearning policies even for dynamics which have already been experienced. RL-CD overcomes these problems by implementing a mechanism for creating, updating and selecting one among several partial models of the environment. The partial models are incrementally built according to the system’s capability of making predictions regarding a given sequence of observations. First, we present the motivations and the theorical basis needed to develop the conceptual framework of RL-CD. Afterwards, we propose, formalize and show the efficiency of RL-CD both in a simple non-stationary environment and in a noisy scenarios. We show that RL-CD performs better than two standard reinforcement learning algorithms and that it has advantages over methods specifically designed to cope with non-stationarity. Finally, we present the theoretical examination of one of RL-CD’s most important parameters, made possible by means of the analysis of probability distributions obtained via Monte Carlo methods. This analysis makes it possible for us to calculate the optimum values for this parameter, so that its adjustment can be performed independently of the scenario being studied.

Neste trabalho apresentamos o RL-CD (Reinforcement Learning with Context Detection), um método desenvolvido a fim de lidar com o problema do aprendizado por reforço (RL) em ambientes não-estacionários. Embora os métodos existentes de RL consigam, muitas vezes, superar a não-estacionariedade, o fazem sob o inconveniente de terem de reaprender políticas que já haviam sido calculadas, o que implica perda de desempenho durante os períodos de readaptação. O método proposto baseia-se em um mecanismo geral através do qual são criados, atualizados e selecionados um dentre vários modelos e políticas parciais. Os modelos parciais do ambiente são incrementalmente construídos de acordo com a capacidade do sistema de fazer predições eficazes. A determinação de tal medida de eficácia baseia-se no cálculo de qualidades globais para cada modelo, as quais refletem o ajuste total necessário para tornar cada modelo coerente com as experimentações reais. Depois de apresentadas as bases teóricas necessárias para fundamentar o RL-CD e suas equações, são propostos e discutidos um conjunto de experimentos que demonstram sua eficiência, tanto em relação a estratégias clássicas de RL quanto em comparação a algoritmos especialmente projetados para lidar com cenários não-estacionários. O RL-CD é comparado com métodos reconhecidos na área de aprendizado por reforço e também com estratégias RL multi-modelo. Os resultados obtidos sugerem que o RLCD constitui uma abordagem eficiente para lidar com uma subclasse de ambientes nãoestacionários, especificamente aquela formada por ambientes cuja dinâmica é corretamente representada por um conjunto finito de Modelos de Markov estacionários. Por fim, apresentamos a análise teórica de um dos parâmetros mais importantes do RL-CD, possibilitada pela aproximação empírica de distribuições de probabilidades via métodos de Monte Carlo. Essa análise permite que os valores ideais de tal parâmetro sejam calculados, tornando assim seu ajuste independente da aplicação específica sendo estudada. / In this work we introduce RL-CD (Reinforcement Learning with Context Detection), a novel method for solving reinforcement learning (RL) problems in non-stationary environments. In face of non-stationary scenarios, standard RL methods need to continually readapt themselves to the changing dynamics of the environment. This causes a performance drop during the readjustment phase and implies the need for relearning policies even for dynamics which have already been experienced. RL-CD overcomes these problems by implementing a mechanism for creating, updating and selecting one among several partial models of the environment. The partial models are incrementally built according to the system’s capability of making predictions regarding a given sequence of observations. First, we present the motivations and the theorical basis needed to develop the conceptual framework of RL-CD. Afterwards, we propose, formalize and show the efficiency of RL-CD both in a simple non-stationary environment and in a noisy scenarios. We show that RL-CD performs better than two standard reinforcement learning algorithms and that it has advantages over methods specifically designed to cope with non-stationarity. Finally, we present the theoretical examination of one of RL-CD’s most important parameters, made possible by means of the analysis of probability distributions obtained via Monte Carlo methods. This analysis makes it possible for us to calculate the optimum values for this parameter, so that its adjustment can be performed independently of the scenario being studied.