Theses and Dissertations

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    Financial time series forecasting via RNNs and Wavelet Analysis
    (2022-04-22) Jackson, Mike Demone; Ensor, Katherine B
    Recent successes in both Artificial Neural Networks (ANN) and wavelets have placed these two methods in the spotlight of quantitative traders seeking the best tool to forecast financial time series. The Wavelet Neural Network (W-NN), a prediction model which combines wavelet-based denoising and ANN, has successfully combined the two strategies in order to make accurate predictions of financial time series. We explore how the most recent formulation of the W-NN model, with the Nonlinear Autoregressive Neural Network with Exogenous variables (NARX), is affected by the choice of wavelet thresholding technique when predicting daily returns of American index futures contracts. We explore how the choice of thresholding technique affects the profitability of two technical trading models based on daily return predictions from a NARX-based W-NN. The purpose of this research is twofold: it compares the effect of different wavelet thresholding techniques on a NARX-based W-NN’s forecasting ability on 1-day returns of American index futures contracts and offers two easy-to-implement trading strategies. In the second part of the thesis, we formulate a hybrid NARX-based seasonal predictive model, Seasonal Nonlinear Autoregressive Neural Network with Exogenous Variables (S-NARX ), for end-of-day volume, where end-of-day volume is directly driven by the end of the day auctions. The S-NARX model will seek to take advantage of the information found in the data up until the auction time and high-frequency intraday trading volume’s diurnal seasonal pattern to predict end-of-day volume. Volume is well known to be a leading indicator of price changes and the two metrics are simultaneously positively correlated. Algorithmic traders rely on accurate volume predictions to deploy algorithmic trading algorithms, especially when utilizing a Volume Weighted Average Price (VWAP) algorithm, that allows the execution of large orders with minimal slippage. Fundamental and quantitative investors are also interested in trading volume because it is a measure of trading intensity and an indicator of market liquidity. The S-NARX augments the NARX with the feature set from a seasonal ARMA(P,Q)[s] and offers quantitative traders a flexible machine learning model for forecasting time series with both longer dependencies and seasonality. Finally, we develop an R package that provides the traditional NARX network along with the novel seasonal version of the CoFES S-NARX that augments the NARX feature set with the features from an ARMA(P,0)[s]. The networks are built using the Keras framework in R and utilize the sequential model from this package.
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    Topological Data Analysis and theoretical statistical inference for time series dependent data and error in parametric choices
    (2022-07-14) Aguilar, Alex; Ensor, Katherine
    Topological data analysis extracts topological features by examining the shape of the data through persistent homology to produce topological summaries, such as the persistence landscape. While the persistence landscape makes it easier to conduct statistical analysis, the Strong Law of Large Numbers and a Central Limit Theorem for the persistence landscape applies to independent and identically distributed copies of a random variable. Therefore, we developed a Strong Law of Large Numbers and a Central Limit Theorem for the persistence landscape when the stochastic component of our series is driven by an autoregressive process of order one. Theoretical results for the persistence landscape are demonstrated computationally and applied to financial time series.
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    Two Random Walk Problems
    (2022-04-22) Huang, Dongzhou; Ernst, Philip A.
    Among numerous probabilistic objects, random walk is one of the most fundamental but most favourable. This dissertation concerns two problems related to random walk theory. The first problem regards $d$ independent Bernoulli random walks. We investigate the first “rencontre-time” (i.e. the first time all of the $d$ Bernoulli random walks arrive in the same state) and derive its distribution. Further, relying on the probability generating function, we discuss the probability of the first “rencontre-time” equaling infinity, whose positivity depends on the dimension $d$ and the success-parameters of these $d$ Bernoulli random walks. We then investigate the conditional expectations of the first “rencontre-time” by studying their bounds. In the second problem, we investigate Yule's “nonsense correlation” for two independent Gaussian random walks. The original problem, calculating the second moment of Yule's “nonsense correlation” for two independent Bernoulli random walks, has proved elusive. Relevant work in this topic includes two papers by Ernst et al., with the former first calculating explicitly the second moment of its asymptotic distribution and the latter providing the first approximation to the density of the asymptotic distribution by exploiting its moments up to order 16. We replace the Bernoulli random walks with Gaussian random walks. Relying on the property that the distribution of Gaussian random vector is invariant under orthonormal transformation, we successfully derive the distribution of Yule's “nonsense correlation” of Gaussian random walks. We also provide rates of convergence of the empirical correlation of two independent Gaussian random walks to the empirical correlation of two independent Wiener processes. At the level of distributions, in Wasserstein distance, the convergence rate is the inverse $n^{-1}$ of the number of the data points $n$.
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    Feature Learning and Bayesian Functional Regression for High-Dimensional Complex Data
    (2021-12-02) Zohner, Ye Emma M; Li, Meng; Morris, Jeffrey S.
    In recent years, technological innovations have facilitated the collection of complex, high-dimensional data that pose substantial modeling challenges. Most of the time, these complex objects are strongly characterized by internal structure that makes sparse representations possible. If we can learn a sparse set of features that accurately captures the salient features of a given object, then we can model these features using standard statistical tools including clustering, regression and classification. The key question is how well this sparse set of features captures the salient information in the objects. In this thesis, we develop methodology for evaluating latent feature representations for functional data and for using these latent features within functional regression frameworks to build flexible models. In the first project, we introduce a graphical latent feature representation tool (GLaRe) to learn features and assess how well a given feature learning approach captures the salient information in a data object. In the second project, we build on this feature learning methodology to propose a basis strategy for fitting functional regression models when the domain is a closed manifold. This methodology is applied to MRI data to characterize patterns of infant cortical thickness development in the first two years of life. In the third project, we adapt our feature learning and Bayesian functional regression methodology to high-frequency data streams. We model high-frequency intraocular pressure data streams using custom bases for quantile representations of the underlying distribution, and provide insights into the etiology of glaucoma.
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    Spatiotemporal Extreme Value Modeling with Environmental Applications
    (2021-10-06) Fagnant, Carlynn; Ensor, Katherine B.
    Extreme value analysis (EVA) is essential to evaluate the extreme events brought on by natural hazards in the environment. Particularly, EVA informs risk assessment for communities, which is crucial to protecting people and property. This work focuses on an application to extreme rainfall in the Houston, TX region and Harris County, and performs spatiotemporal extreme value modeling in order to assess the evolution of extremes over time for the region. Rainfall extreme values are compared to previous standards in order to demonstrate the need for updated policies. In addition to the temporal evolution of EVA, a key component of this work is the introduction of new methods to extend extreme value modeling at the point observation level to the areal level. The methods employ spatial statistics change-of-support concepts and the use of the extended Hausdorff distance to provide estimates of the extreme value distribution at the region level. Regional inference provides insight to support policy decisions for communities and cities.
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    Computational and Statistical Methodology for Highly Structured Data
    (2020-09-15) Weylandt, Michael; Ensor, Katherine B
    Modern data-intensive research is typically characterized by large scale data and the impressive computational and modeling tools necessary to analyze it. Equally important, though less remarked upon, is the important structure present in large data sets. Statistical approaches that incorporate knowledge of this structure, whether spatio-temporal dependence or sparsity in a suitable basis, are essential to accurately capture the richness of modern large scale data sets. This thesis presents four novel methodologies for dealing with various types of highly structured data in a statistically rich and computationally efficient manner. The first project considers sparse regression and sparse covariance selection for complex valued data. While complex valued data is ubiquitous in spectral analysis and neuroimaging, typical machine learning techniques discard the rich structure of complex numbers, losing valuable phase information in the process. A major contribution of this project is the development of convex analysis for a class of non-smooth "Wirtinger" functions, which allows high-dimensional statistical theory to be applied in the complex domain. The second project considers clustering of large scale multi-way array ("tensor") data. Efficient clustering algorithms for convex bi-clustering and co-clustering are derived and shown to achieve an order-of-magnitude speed improvement over previous approaches. The third project considers principal component analysis for data with smooth and/or sparse structure. An efficient manifold optimization technique is proposed which can flexibly adapt to a wide variety of regularization schemes, while efficiently estimating multiple principal components. Despite the non-convexity of the manifold constraints used, it is possible to establish convergence to a stationary point. Additionally, a new family of "deflation" schemes are proposed to allow iterative estimation of nested principal components while maintaining weaker forms of orthogonality. The fourth and final project develops a multivariate volatility model for US natural gas markets. This model flexibly incorporates differing market dynamics across time scales and different spatial locations. A rigorous evaluation shows significantly improved forecasting performance both in- and out-of-sample. All four methodologies are able to flexibly incorporate prior knowledge in a statistically rigorous fashion while maintaining a high degree of computational performance.
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    Dynamic Multivariate Wavelet Signal Extraction and Forecasting with Applications to Finance
    (2020-04-16) Raath, Kim C; Ensor, Katherine B
    Over the past few years, we have seen an increased need for analyzing the dynamically changing behaviors of economic and financial time series. These needs have led to significant demand for methods that denoise non-stationary time series across time and for specific investment horizons (scales) and localized windows (blocks) of time. This thesis consists of a three-part series of papers. The first paper develops a wavelet framework for the finance and economics community to quantify dynamic, interconnected relationships between non-stationary time series. The second paper introduces a novel continuous wavelet transform, dynamically-optimized, multivariate thresholding method to extract the optimal signal from multivariate time series. Finally, the third paper presents an augmented stochastic volatility wavelet-based forecasting method building on the partial mixture distribution modeling framework introduced in the second paper. Promising results in economics and finance have come from implementing wavelet analysis, however more advanced wavelet techniques are needed as well as more robust statistical analysis tools. In support of this expansion effort, we developed a comprehensive and user-friendly R package, CoFESWave, containing our newly developed thresholding and forecasting methods.
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    Filtering and Estimation for a Class of Stochastic Volatility Models with Intractable Likelihoods
    (2015-08-28) Vankov, Emilian; Ensor, Katherine B
    A new approach to state filtering and parameter estimation for a class of stochastic volatility models for which the likelihood function is unknown is considered. The alpha-stable stochastic volatility model provides a flexible framework for modeling asymmetry and heavy tails, which is useful when modeling financial returns. However, a problem posed by the alpha-stable distribution is the lack of a closed form for the probability density function, which prevents its direct application to standard filtering and estimation techniques such as sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). To circumvent this difficulty, researchers have recently developed various approximate Bayesian computation (ABC) methods, which require only that one is able to simulate data from the model. To obtain filtered volatility estimates, we develop a novel ABC based auxiliary particle filter (APF-ABC). The algorithm we develop can be easily applied to many state space models for which the likelihood function is intractable or computationally expensive. APF-ABC improves on the accuracy through better proposal distributions in cases where the optimal importance density of the filter is unavailable. Further, a new particle based MCMC (PMCMC) method is proposed for parameter estimation in this class of volatility models. PMCMC methods combine SMC with MCMC to produce samples from the joint stationary distribution of the latent states and parameters. If full conditional distributions for all parameters are available then the particle Gibbs sampler is typically adopted; otherwise, the particle marginal Metropolis-Hastings can be used for posterior estimation. Although, several ABC based extensions of PMCMC have been proposed for the symmetric alpha-stable stochastic volatility model, all have used the particle marginal Metropolis-Hastings algorithm due to the inability to obtain full conditional distributions for all parameters in the model. However, the availability of full conditional distributions for a subset of the parameters raises the natural question of whether it is possible to estimate some of the parameters using their full conditionals, while others using a Metropolis-Hastings step. The algorithm that is proposed addresses this exact question. It is shown through a simulation study, that such a strategy can lead to increases in efficiency in the estimation process. Moreover, in contrast to previous works, this thesis studies the asymmetric alpha-stable stochastic volatility model.
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    On longest consecutive patterns in Markov chains
    (2019-11-11) Xia, Yizhou; Ernst, Philip A.
    The length of longest consecutive head in Bernoulli trials L(n) has been studied extensively and has been found applications in biology, finance and non-parametric statistics. The study of longest consecutive successes in random trials dates the work of de Moivre. Limiting theorems and large deviation results are provided for L(n) with the assumption of existence of stationary distribution. Given a discrete-time homogeneous Markov chain with initial state i, one extension from previous Bernoulli case is to study the distribution of L(j,n), the length of the longest consecutive visits of this chain to state j until time n. Our work focuses on studying L(j,n) for both homogeneous and time-nonhomogeneous Markov chains. In the existing literature, no limiting theorems of L(j,n) are derived under the case of time nonhomogeneous Markov chains. We are able to solve this by first deriving a new exact formula of the distribution of L(j,n) and then derive an upper and lower bound of P(L(j,n)
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    Essays on Crude Oil Markets and Electricity Access
    (2019-05-13) Volkmar, Peter; Hartley, Peter R
    In the first chapter I discuss how OPEC's internal costs restrict their ability collude. Where membership in 2007 was anchored by three large, low-cost producers in Iran, Venezuela and Saudi Arabia, by 2015 Venezuela and Iran were no longer large producers due to lack of investment and sanctions, respectively. This left Saudi Arabia and Iraq as the only large producers. Using a game theory model, I show that together they did not have the power to enforce quotas among themselves and other OPEC members without Russia's participation. More generally, my model implies that at present, OPEC is unable to enforce quotas without full participation of either Iran or Russia. This situation has been exacerbated, from their perspective, by improved medium- and long-term price responsiveness of non-OPEC crude oil supply, which erodes OPEC market power. However, the model implies that this change in non-OPEC supply is not necessary for destroying OPEC's ability to cartelize. OPEC's current composition has reduced its ability to enforce production quotas among its membership. Many analysts have suggested that OPEC's role as swing producer will be supplanted by tight oil production from the United States. After exploring this possibility in my second chapter I find that tight oil production has not increased non-OPEC supply's short-term price responsiveness, while demand has simultaneously grown more brittle. This implies OPEC's role as swing producer is more important for stabilizing price now than at any point in the past decade. Yet my first chapter shows they are currently ill-prepared for the task. The final chapter constructs a measure of the relative success of different countries in providing access to electrical power, which is in turn a critical determinant of energy poverty. Measuring energy poverty indexing is only helpful if it allows us to discern how lagging countries may be able to attain outcomes like their peers. More specifically, I utilize frontier analysis to develop efficiency ratings in meeting electricity demand that highlight inputs countries are not using efficiently to that end. Charts in the chapter compare 71 countries' existing infrastructure relative to their electrification rates. The Data Envelopment Analysis employed allows comparison between an inefficient country and a group of it economic peers. Additionally, it shows how far from the frontier an under performing country is in each type of input, tracks progress over years and puts bootstrapped confidence intervals on all point estimates.
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    An Old Dog Learns New Tricks: Novel Applications of Kernel Density Estimators on Two Financial Datasets
    (2017-12-01) Ginley, Matthew Cline; Ensor, Katherine B.; Scott, David W.
    In our first application, we contribute two nonparametric simulation methods for analyzing Leveraged Exchange Traded Fund (LETF) return volatility and how this dynamic is related to the underlying index. LETFs are constructed to provide the indicated leverage multiple of the daily total return on an underlying index. LETFs may perform as expected on a daily basis; however, fund issuers state there is no guarantee of achieving the multiple of the index return over longer time horizons. Most, if not all LETF returns data are difficult to model because of the extreme volatility present and limited availability of data. First, to isolate the effects of daily, leveraged compounding on LETF volatility, we propose an innovative method for simulating daily index returns with a chosen constraint on the multi-day period return. By controlling for the performance of the underlying index, the range of volatilities observed in a simulated sample can be attributed to compounding with leverage and the presence of tracking errors. Second, to overcome the limited history of LETF returns data, we propose a method for simulating implied LETF tracking errors while still accounting for their dependence on underlying index returns. This allows for the incorporation of the complete history of index returns in an LETF returns model. Our nonparametric methods are flexible-- easily incorporating any chosen number of days, leverage ratios, or period return constraints, and can be used in combination or separately to model any quantity of interest derived from daily LETF returns. For our second application, we tackle binary classification problems with extremely low class 1 proportions. These ``rare events'' problems are a considerable challenge, which is magnified when dealing with large datasets. Having a minuscule count of class 1 observations motivates the implementation of more sophisticated methods to minimize forecasting bias towards the majority class. We propose an alternative approach to established up-sampling or down-sampling algorithms driven by kernel density estimators to transform the class labels to continuous targets. Having effectively transformed the problem from classification to regression, we argue that under the assumption of a monotonic relationship between predictors and the target, approximations of the majority class are possible in a rare events setting with the use of simple heuristics. By significantly reducing the burden posed by the majority class, the complexities of minority class membership can be modeled more effectively using monotonically constrained nonparametric regression methods. Our approach is demonstrated on a large financial dataset with an extremely low class 1 proportion. Additionally, novel features engineering is introduced to assist in the application of the density estimator used for class label transformation.
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    Dynamic Characterization of Multivariate Time Series
    (2017-12-01) MELNIKOV, OLEG; Ensor, Katherine B
    The standard non-negative matrix factorization focuses on batch learning assuming that the fixed global latent parameters completely describe the observations. Many online extensions assume rigid constraints and smooth continuity in observations. However, the more complex time series processes can have multivariate distributions switch between a finite number of states or regimes. In this paper we proposes a regime-switching model for non-negative matrix factorization and present a method of forecasting in this lower-dimensional regime-dependent space. The time dependent observations are partitioned into regimes to enhance factors' interpretability inherent in non-negative matrix factorization. We use weighted non-negative matrix factorization to handle missing values and to avoid needless contamination of observed structure. Finally, we propose a method of forecasting from the regime components via threshold autoregressive model and projecting the forecasts back to the original target space. The computation speed is improved by parallelizing weighted non-negative matrix factorization over multiple CPUs. We apply our model to hourly air quality measurements by building regimes from deterministically identified day and night observations. Air pollutants are then partitioned, factorized and forecasted, mostly outperforming the results standard non-negative matrix factorization with respect of the Frobenius norm of the error. We also discuss the shortcomings of the new model.
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    Robust Discriminant Analysis and Clustering by a Partial Minimum Integrated Squared Error Criterion
    (2017-08-10) Adler, Yeshaya Adam; Scott, David W.; Ensor, Katherine B.; Lane, David M.
    In parametric supervised classification and unsupervised clustering traditional methods are often inadequate when data are generated under departures from normality assumptions. A class of density power divergences was introduced by Basu et al. (1998) to alleviate these problems. This class of estimators is indexed by a parameter α which balances efficiency versus robustness. It includes the maximum likelihood as a limiting case as α ↓ 0, and the special case known as L2E where α = 1 (Scott, 2001), which has been studied for its robustness properties. In this thesis, we develop two methods which utilize L2E estimation to perform discriminant analysis and modal clustering. Robust versions of discriminant analysis built on the Bayesian model usually supplant the maximum likelihood estimates by plugging robust alternatives into the discriminant rule. We develop robust discriminant analysis which does not rely on multiple plug-in estimates but rather jointly estimates model parameters. We apply these methods to simulated and applied cases and show them to be robust to departures from normality. In the second application, we explore the problem of obtaining all possible modes of a kernel density estimate. We introduce a clustering method based on the stochastic mode tree, originally developed in an unpublished manuscript of Scott and Szewczyk (2000). This method applies the multivariate partial density component L2E estimator, which includes maximum likelihood estimation as a limiting case, of Scott (2004) to locally probe the data and find all potential modes of a density. We provide an efficient implementation of the stochastic mode tree which is re-purposed to cluster the data according to its modal hierarchy. We explore the behavior of this clustering method with simulations and applied data. We develop an interactive exploratory visualization tool which relates the modal clustering of a density to the optimal weights of individual partial density components. We show how this method can be used to interactively prune the stochastic mode tree to obtain a desired cluster hierarchy. Finally, we show our hierarchical mode clustering to be useful in image thresholding and segmentation.
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    Characterizing Production in the Barnett Shale Resource: Essays on Efficiency, Operator Effects and Well Decline
    (2016-04-21) Seitlheko, Likeleli; Hartley, Peter R
    This dissertation is composed of three papers in the field of energy economics. The first paper estimates revenue and technical efficiency for more than 11,000 wells that were drilled in the Barnett between 2000 and 2010, and also examines how the efficiency estimates differ among operators. To achieve this objective, we use stochastic frontier analysis and a two-stage semi-parametric approach that consists of data envelopment analysis in the first stage and a truncated linear regression in the second stage. The stochastic frontier analysis (SFA) and data envelopment analysis (DEA) commonly identify only two operators as more revenue and technically efficient than Devon, the largest operator in the Barnett. We further find that operators have generally been effective at responding to market incentives and producing the revenue-maximizing mix of gas and oil given the reigning prices. Furthermore, coupled with this last result is the insight that most of the revenue inefficiency is derived from technical inefficiency and not allocative inefficiency. The second paper uses multilevel modeling to examine relative operator effects on revenue generation and natural gas output during the 2000-2010 period. The estimated operator effects are used to determine which operators were more effective at producing natural gas or generating revenue from oil and gas. The operators clump together into three groups – average, below average, and above average – and the effects of individual operators within each group are largely indistinguishable from one another. Among the operators that are estimated to have above average effects in both the gas model and the revenue model are Chesapeake, Devon, EOG and XTO, the top four largest operators in the Barnett. The results also reveal that between-operator differences account for a non-trivial portion of the residual variation in gas or revenue output that remains after controlling for well-level characteristics, and prices in the case of the revenue model. In the third paper, we estimate an econometric model describing the decline of a “typical” well in the Barnett shale. The data cover more than 15,000 wells drilled in the Barnett between 1990 and mid-2011. The analysis is directed at testing the hypothesis proposed by Patzek, Male and Marder (2014) that linear flow rather than radial flow – the latter of which is consistent with Arps (1945) system of equations – governs natural gas production within hydraulically fractured wells in extremely low permeability shale formations. To test the hypothesis, we use a fixed effects linear model with Driscoll-Kraay standard errors, which are robust to autocorrelation and cross-sectional correlation, and estimate the model separately for horizontal and vertical wells. For both horizontal and vertical shale gas wells in the Barnett, we cannot reject the hypothesis of a linear flow regime. This implies that the production profile of a Barnett well can be projected – within some reasonable margin of error – using the decline curve equation of Patzek, Male and Marder (2014) once initial production is known. We then estimate productivity tiers by sampling from the distribution of the length normalized initial production of horizontal wells and generate type curves using the decline curve equation of Patzek, Male and Marder (2014). Finally, we calculate the drilling cost per EUR (expected ultimate recovery) and the breakeven price of natural gas for all the tiers.
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    Impact of News on Crude Oil Futures
    (2017-04-21) Han, Yu; Ensor, Katherine; Ostdiek, Barbara; Turnbull, Stuart
    Crude oil futures are worlds the most actively traded commodity futures, with more than 3 billion barrels per year in open interest. In this thesis we use related news to model the price dynamics of oil futures. We examine the empirical patterns of oil market news data processed by Thompson Reuters News Analytics, plus the intraday trading data of the WTI futures price traded on NYMEX. Then we build a three factor stochastic model for futures prices on the whole curve, using interest rate, convenience yield and spot price. The Kalman filter was used to obtain quasi-maximum likelihood estimators. We found that news can significantly explain the price movements and volatility clustering, as well as its skewness and kurtosis. We also found that negative news has an higher explanatory power of price dynamics than positive news, indicating an asymmetrical behavior of information with different tones.
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    Approximate dynamic factor models for mixed frequency data
    (2015-10-15) Zhao, Xin; Ensor, Katherine; Kimmel, Marek; Sizova, Natalia
    Time series observed at different temporal scales cannot be simultaneously analyzed by traditional multivariate time series methods. Adjustments must be made to address issues of asynchronous observations. For example, many macroeconomic time series are published quarterly and other price series are published monthly or daily. Common solutions to the analysis of asynchronous time series include data aggregation, mixed frequency vector autoregressive models, and factor models. In this research, I set up a systematic approach to the analysis of asynchronous multivariate time series based on an approximate dynamic factor model. The methodology treats observations of various temporal frequencies as contemporaneous series. A two-step model estimation and identification scheme is proposed. This method allows explicit structural restrictions that account for appropriate temporal ordering of the mixed frequency data. The methodology consistently estimates the dynamic factors, however, no prior knowledge on the factors is required. To ensure a computationally efficient robust algorithm and model specification, I make use of modern penalized likelihood methodologies. The fitted model captures the effects of temporal relationships across the asynchronous time series in an interpretable manner. The methodology is studied through simulation and applied to several examples. The simulations and examples demonstrate good performance in model specification, estimation and out-of-sample forecasting.
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    Robust Methods for Forecast Aggregation
    (2014-08-18) Ramos, Jaime J; Scott, David W.; Lane, David; Thompson, James R
    This study introduces a new forecast aggregation technique. Adding to the well- known difficulties and uncertainty involved in the forecasting process, the aggregation of hundreds or thousands of forecasters’ opinions and expert predictions on social, economical and political matters makes the process even more difficult. Simple quan- titative data analytics, least squares regression, and maximum likelihood estimations are not sufficient to handle the dynamics of such data, which includes outliers, clusters of opinions, extreme values, and abrupt change of mind and predictions of forecasters influenced by news, recent events, collaboration or feedback from experts. The meth- ods developed in this work are based on a particular minimum-distance technique called L2E, which is popular in nonparametric density estimation that makes the aggregation robust to clusters of opinions and dramatic changes. Variance-stabilizing transformations are introduced to attain homoscedasticity for L2E regression improv- ing parameter estimation and overall aggregation. New normalization approaches are proposed to use when the aggregated values are unsuitable probabilities, such as values ∈/ [0, 1] and/or do not add to 1. Finally, data visualization techniques and graphical user interfaces (GUIs) are discussed as aid to decision makers in order to understand “single” aggregated forecast values, obtained from the original big data set analyzed, and the trend of such aggregated forecasts over the forecasting period.
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    Identifying and Dealing with the Approach of Bears and their Departure
    (2013-05-29) Affinito, Ricardo; Thompson, James R.; Ensor, Katherine B.; Williams, Edward E.
    Based on the identification of market dynamics, capital allocation in long positions can be dynamically controlled by means of interrupting an otherwise strictly-long investment strategy allowing for an overall improved risk profile and faster response times during periods of persistent negative market returns. Herein, a portfolio selection methodology updating a reasonably diversified selection of competing S&P 500 constituents within and across various predefined industry groups and which produced above average long-term returns with minimized downside-risk, is proposed. Within the various predefined groups of stocks, Simugram methods are used to model and optimize on the distribution of returns up to and including a horizon of interest. Improvements to previous methods are focused toward calibrating the sampling distribution based on an empirical dataset within the various groups comprising the investor's portfolio, optionally allowing for a varying sampling frequency as dictated by the various group dynamics. By combining within-group optimization alongside with the capability of exiting aggressive long-strategies at seemingly riskier times, focus is on providing more frequent updates on a list of constituents with improved performance in both terms of risk and return.
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    Robust GARCH methods and analysis of partial least squares regression
    (2014-04-24) Egbulefu, Joseph; Cox, Dennis D.; Ensor, Katherine B.; El-Gamal, Mahmoud A.
    New approaches to modeling volatility are evaluated and properties of partial least squares (PLS) regression are investigated. Common methods for modeling volatility, the standard deviation of price changes over a period, that account for the heavy tails of asset returns rely on maximum likelihood estimation using a heavy-tailed distribu- tion. A fractional power GARCH model is developed for robust volatility modeling of heavy tailed returns using a fractional power transform and Gaussian quasi maximum likelihood estimation. Furthermore, a smooth periodic GARCH model, incorporating seasonal trends by wavelet analysis, is developed and shown to outperform existing approaches in long-horizon volatility forecasting. PLS is a latent variable method for regression with correlated predictors. Previous approaches to derive the asymptotic covariance of PLS regression coefficients rely on restrictive assumptions. The asymptotic covariance of PLS coefficients are derived under general conditions. PLS regression is applied to variable selection in the context of index tracking.
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    Robust Parametric Functional Component Estimation Using a Divergence Family
    (2013-09-16) Silver, Justin; Scott, David W.; Ensor, Katherine B.; Brown, James N.
    The classical parametric estimation approach, maximum likelihood, while providing maximally efficient estimators at the correct model, lacks robustness. As a modification of maximum likelihood, Huber (1964) introduced M-estimators, which are very general but often ad hoc. Basu et al. (1998) developed a family of density-based divergences, many of which exhibit robustness. It turns out that maximum likelihood is a special case of this general class of divergence functions, which are indexed by a parameter alpha. Basu noted that only values of alpha in the [0,1] range were of interest -- with alpha = 0 giving the maximum likelihood solution and alpha = 1 the L2E solution (Scott, 2001). As alpha increases, there is a clear tradeoff between increasing robustness and decreasing efficiency. This thesis develops a family of robust location and scale estimators by applying Basu's alpha-divergence function to a multivariate partial density component model (Scott, 2004). The usefulness of alpha values greater than 1 will be explored, and the new estimator will be applied to simulated cases and applications in parametric density estimation and regression.