Time Series of water quality variables typically possess many of several characteristics which complicate analysis. Of interest to researchers is often the trend over time of the water quality variable. However, sometimes water quality variable levels appear to increase or decrease monotonically for a period of time then switch direction after some intervention affects the factors which have a causal relationship with the level of the variable. Naturally, when analyzed for trend as a whole, these time series usually do not provide significant results. The problem of testing for a change in trend is addressed, and a method for perfoming this test based on a test of equivalence of two modified Kendall's Tau nonparametric correlation coefficients (neither necessarily equal to zero) is presented. The test is made valid for use with serially correlated data by use of a new bootstrap method titled the effective sample size bootstrap. Further issues involved in applying this test to water quality variables are also addressed. / Ph. D.

This simulation study examined the performance of the curve-of-factors growth model when serial correlation and growth processes were present in the first-level factor structure. As previous research has shown (Ferron, Dailey, & Yi, 2002; Kwok, West, & Green, 2007; Murphy & Pituch, 2009) estimates of the fixed effects and their standard errors were unbiased when serial correlation was present in the data but unmodeled. However, variance components were estimated poorly across the examined serial correlation conditions. Two new models were also examined: one curve-of-factors model was fitted with a first-order autoregressive serial correlation parameter, and a second curve-of-factors model was fitted with first-order autoregressive and moving average serial correlation parameters. The models were developed in an effort to measure growth and serial correlation processes within the same data set. Both models fitted with serial correlation parameters were able to accurately reproduce the serial correlation parameter and approximate the true growth trajectory. However, estimates of the variance components and the standard errors of the fixed effects were problematic. The two models also produced inadmissible solutions across all conditions. Of the three models, the curve-of-factors model had the best overall performance. / text

Statistically significant prediction of stock price changes requires security returns' correlation with, or dependence upon, some variable(s) across time. Since a security's past return is commonly employed in forecasting, and because the lack of lower-order correlation does not guarantee higher-order independence, nonlinear testing that focuses on higher-order moments of stock return distributions may reveal exploitable stock return dependencies. This dissertation fits AR models to TAQ data sampled at ten-minute intervals for 20 small-capitalization, 20 mid-capitalization, and 20 large-capitalization NYSE securities, for the years 1993, 1995, 1997, 1999 and 2001. The Hinich Patterson Bicovariance statistic (to reveal nonlinear and linear autocorrelation) is computed for each of the 1243 trading days for each of the 60 securities. This statistic is examined to see if it is more or less likely to occur in securities with differing market capitalization, at various calendar periods, in conjunction with trading volume, or instances of changing investor sentiment, as evidenced by the put-call ratio. There is a statistically significant difference in the level and incidence of nonlinear behavior for the different-sized portfolios. Large-cap stocks exhibit the highest level and greatest incidence of nonlinear behavior, followed by mid-cap stocks, and then small-cap stocks. These differences are most pronounced at the beginning of decade and remain significant throughout the decade. For all size portfolios, nonlinear correlation increases throughout the decade, while linear correlation decreases. Statistical significance between the nonlinear or the linear test statistics and trading volume occur on a year-by-year basis only for small-cap stocks. There is sporadic seasonality significance for all portfolios over the decade, but only the small-cap portfolio consistently exhibits a notable "December effect". The average nonlinear statistic for small-cap stocks is larger in December than for other months of the year. The fourth quarter of the year for small-cap stocks also exhibits significantly higher levels of nonlinearity. An OLS regression of the put/call ratio to proxy for investor sentiment against the H and C statistic was run from October 1995 through December 2001. There are instances of sporadic correlations among the different portfolios, indicating this relationship is more dynamic than previously imagined. / Ph. D.

In a visual search experiment, the subject must find a target item hidden in a display of other items, and their performance is measured by their reaction time (RT). Here I look at how visual search reaction times are correlated with past reaction times. Target-absent RTs (i.e. RTs to displays that have no target) are strongly correlated with past target-absent RTs and, treated as a time series, have a 1/f power spectrum. Target-present RTs, on the other hand, are effectively uncorrelated with past RTs. A model for visual search is presented which generates search RTs with this pattern of correlations and power spectra. In the model, search is conducted by matching search items up with ¿categorizers,¿ which take a certain time to categorize each item as target or distractor; the RT is the sum of categorization times. The categorizers are drawn at random from a pool of active categorizers. After each search, some of the categorizers in the active pool are replaced with categorizers drawn from a larger population of unused categorizers. The categorizers that are not replaced are responsible for the RT correlations and the 1/f power spectrum.

<p>This dissertation aims to introduce a new sequential Monte Carlo (SMC) based estimation framework for structural models used in macroeconomics and industrial organization. Current Markov chain Monte Carlo (MCMC) estimation methods for structural models suffer from slow Markov chain convergence, which means parameter and state spaces of interest might not be properly explored unless huge numbers of samples are simulated. This could lead to insurmountable computational burdens for the estimation of those structural models that are expensive to solve. In contrast, SMC methods rely on the principle of sequential importance sampling to jointly evolve simulated particles, thus bypassing the dependence on Markov chain convergence altogether. This dissertation will explore the feasibility and the potential benefits to estimating structural models using SMC based methods.</p><p> Chapter 1 casts the structural estimation problem in the form of inference of hidden Markov models and demonstrates with a simple growth model.</p><p> Chapter 2 presents the key ingredients, both conceptual and theoretical, to successful SMC parameter estimation strategies in the context of structural economic models.</p><p> Chapter 3, based on Chen, Petralia and Lopes (2010), develops SMC estimation methods for dynamic stochastic general equilibrium (DSGE) models. SMC algorithms allow a simultaneous filtering of time-varying state vectors and estimation of fixed parameters. We first establish empirical feasibility of the full SMC approach by comparing estimation results from both MCMC batch estimation and SMC on-line estimation on a simple neoclassical growth model. We then estimate a large scale DSGE model for the Euro area developed in Smets and Wouters (2003) with a full SMC approach, and revisit the on-going debate between the merits of reduced form and structural models in the macroeconomics context by performing sequential model assessment between the DSGE model and various VAR/BVAR models.</p><p> Chapter 4 proposes an SMC estimation procedure and show that it readily applies to the estimation of dynamic discrete games with serially correlated endogenous state variables. I apply this estimation procedure to a dynamic oligopolistic game of entry using data from the generic pharmaceutical industry and demonstrate that the proposed SMC method can potentially better explore the parameter posterior space while being more computationally efficient than MCMC estimation. In addition, I show how the unobserved endogenous cost paths could be recovered using particle smoothing, both with and without parameter uncertainty. Parameter estimates obtained using this SMC based method largely concur with earlier findings that spillover effect from market entry is significant and plays an important role in the generic drug industry, but that it might not be as high as previously thought when full model uncertainty is taken into account during estimation.</p> / Dissertation

To be effective, a linear congruential random number generator (LCG) should produce values that are (a) uniformly distributed on the unit interval (0,1) excluding endpoints and (b) substantially free of serial correlation. It has been found that many statistical methods produce inflated Type I error rates for correlated observations. Theoretically, independently seeding an LCG under the following conditions attenuates serial correlation: (a) simple random sampling of seeds, (b) non-replicate streams, (c) non-overlapping streams, and (d) non-adjoining streams. Accordingly, 4 algorithms (each satisfying at least 1 condition) were developed: (a) zero-leap, (b) fixed-leap, (c) scaled random-leap, and (d) unscaled random-leap. Note that the latter satisfied all 4 independent seeding conditions. To assess serial correlation, univariate and multivariate simulations were conducted at 3 equally spaced intervals for each algorithm (N=24) and measured using 3 randomness tests: (a) the serial correlation test, (b) the runs up test, and (c) the white noise test. A one-way balanced multivariate analysis of variance (MANOVA) was used to test 4 hypotheses: (a) omnibus, (b) contrast of unscaled vs. others, (c) contrast of scaled vs. others, and (d) contrast of fixed vs. others. The MANOVA assumptions of independence, normality, and homogeneity were satisfied. In sum, the seeding algorithms did not differ significantly from each other (omnibus hypothesis). For the contrast hypotheses, only the fixed-leap algorithm differed significantly from all other algorithms. Surprisingly, the scaled random-leap offered the least difference among the algorithms (theoretically this algorithm should have produced the second largest difference). Although not fully supported by the research design used in this study, it is thought that the unscaled random-leap algorithm is the best choice for independently seeding the multiplicative congruential random number generator. Accordingly, suggestions for further research are proposed.

Dans cette thèse nous combinons les processus à mémoire longue ainsi que les modèles à changement de régime markovien afin d’étudier la dynamique non linéaire des rentabilités des hedge funds et leur exposition au risque de marché. L’attractivité des hedge funds réside dans leur capacité à générer des rentabilités décorrélées avec celles des actifs traditionnels tout en permettant d’améliorer les rentabilités et/ou de réduire le risque, indépendamment des conditions de marché. Cependant, certaines spécificités des rentabilités des hedge funds (non linéarité, asymétrie et présence d’une forte autocorrélation émanant des problèmes d’illiquidités) remettent en cause cet aspect qui n’est valable que dans un univers gaussien. Nous adoptons de ce fait une approche économétrique permettant de réconcilier la notion de mémoire longue et celle de la persistance pure des performances. Nous mettons l’accent sur le risque de confusion entre vraie mémoire longue et mémoire longue fallacieuse dans la mesure où certains processus peuvent générer des caractéristiques similaires à celles des processus à mémoire longue. Il ressort de cette étude non seulement l’insuffisance des modèles standards à prendre en compte les caractéristiques des séries des rentabilités financières mais aussi la pertinence du recours aux modèles mixtes pour mieux cerner l’ensemble de ces spécificités dans un cadre unifié. Le modèle Beta Switching ARFIMA-FIGARCH que nous proposons révèle la complexité de la dynamique des rentabilités des hedge funds. Il est donc nécessaire de mieux appréhender cette dynamique afin d'expliquer convenablement les interactions qui existent entre les hedge funds eux-mêmes et entre les hedge funds et les marchés standards. La composante mémoire longue est prise en compte à la fois au niveau de la moyenne conditionnelle à travers le processus ARFIMA ainsi qu’au niveau de la variance conditionnelle à travers plusieurs spécifications des processus hétéroscédastiques fractionnaires notamment les processus FIGARCH, FIAPARCH et HYGARCH. Cette modélisation mieux adaptée aux spécificités des hedge funds met en évidence le risque caché de ces derniers et représente une nouvelle perspective vers laquelle les gérants et les responsables d’agence pourraient s’orienter. / In this thesis we combine long memory processes and regime switching models to study the nonlinear dynamics of hedge funds returns and their exposure to market risk. The attractiveness of hedge funds lies in their ability to generate returns uncorrelated to those of traditional assets while allowing to improve returns and/or reduce the risk, regardless of market conditions. However, some specificity of returns of hedge funds as their nonlinear and asymmetric nature as well as the presence of a strong autocorrelation in related to illiquidity problems make this aspect only valid in a Gaussian framework. In this study, we adopt an econometric approach that reconciles the notion of long memory and that of pure performance persistence. In this regard, we focus on the risk of confusion between real and spurious long memory long memory since certain processes can generate similar characteristics to that of long memory processes. It appears from this study not only the inadequacy of standard models to take into account the characteristics of the series of financial returns but also the relevance of using mixed models to better understand all of these features within a unified framework. The Beta Switching ARFIMA-FIGARCH mode we suggest reveals the complexity of hedge fund return dynamics and proves the need to better understand the dynamics of returns of hedge funds in order to explain the interactions between hedge funds themselves and between hedge funds and standard markets. The long memory component is taken into account both at the conditional mean through the ARFIMA process and at the conditional variance through several specifications heteroscedatic fractional processes including FIGARCH, FIAPARCH and HYGARCH models. This model take into account several features of hedge fund returns, highlights their hidden risks and represents a new perspective to which managers could move.

The United States is the world's largest oil consumer demanding about twenty five percent of the total world oil production. Whenever there are difficulties to supply the increasing quantities of oil demanded by the market, the price of oil escalates leading to what is known as oil price spikes or oil price shocks. The last oil price shock which was the longest sustained oil price run up in history, began its course in year 2004, and ended in 2008. This last oil price shock initiated recognizable changes in transportation dynamics: transit operators realized that commuters switched to transit as a way to save gasoline costs, consumers began to search the market for more efficient vehicles leading car manufactures to close 'gas guzzlers' plants, and the government enacted a new law entitled the Energy Independence Act of 2007, which called for the progressive improvement of the fuel efficiency indicator of the light vehicle fleet up to 35 miles per gallon in year 2020. The past trend of gasoline consumption will probably change; so in the context of the problem a gasoline consumption model was developed in this thesis to ascertain how some of the changes will impact future gasoline demand. Gasoline demand was expressed in oil equivalent million barrels per day, in a two steps Ordinary Least Square (OLS) explanatory variable model. In the first step, vehicle miles traveled expressed in trillion vehicle miles was regressed on the independent variables: vehicles expressed in million vehicles, and price of oil expressed in dollars per barrel. In the second step, the fuel consumption in million barrels per day was regressed on vehicle miles traveled, and on the fuel efficiency indicator expressed in miles per gallon. The explanatory model was run in EVIEWS that allows checking for normality, heteroskedasticty, and serial correlation. Serial correlation was addressed by inclusion of autoregressive or moving average error correction terms. Multicollinearity was solved by first differencing. The 36 year sample series set (1970-2006) was divided into a 30 years sub-period for calibration and a 6 year "hold-out" sub-period for validation. The Root Mean Square Error or RMSE criterion was adopted to select the "best model" among other possible choices, although other criteria were also recorded. Three scenarios for the size of the light vehicle fleet in a forecasting period up to 2020 were created. These scenarios were equivalent to growth rates of 2.1, 1.28, and about 1 per cent per year. The last or more optimistic vehicle growth scenario, from the gasoline consumption perspective, appeared consistent with the theory of vehicle saturation. One scenario for the average miles per gallon indicator was created for each one of the size of fleet indicators by distributing the fleet every year assuming a 7 percent replacement rate. Three scenarios for the price of oil were also created: the first one used the average price of oil in the sample since 1970, the second was obtained by extending the price trend by exponential smoothing, and the third one used a longtime forecast supplied by the Energy Information Administration. The three scenarios created for the price of oil covered a range between a low of about 42 dollars per barrel to highs in the low 100's. The 1970-2006 gasoline consumption trend was extended to year 2020 by ARIMA Box-Jenkins time series analysis, leading to a gasoline consumption value of about 10 millions barrels per day in year 2020. This trend line was taken as the reference or baseline of gasoline consumption. The savings that resulted by application of the explanatory variable OLS model were measured against such a baseline of gasoline consumption. Even on the most pessimistic scenario the savings obtained by the progressive improvement of the fuel efficiency indicator seem enough to offset the increase in consumption that otherwise would have occurred by extension of the trend, leaving consumption at the 2006 levels or about 9 million barrels per day. The most optimistic scenario led to savings up to about 2 million barrels per day below the 2006 level or about 3 millions barrels per day below the baseline in 2020. The "expected" or average consumption in 2020 is about 8 million barrels per day, 2 million barrels below the baseline or 1 million below the 2006 consumption level. More savings are possible if technologies such as plug-in hybrids that have been already implemented in other countries take over soon, are efficiently promoted, or are given incentives or subsidies such as tax credits. The savings in gasoline consumption may in the future contribute to stabilize the price of oil as worldwide demand is tamed by oil saving policy changes implemented in the United States.

No / In a visual search experiment, the subject must find a target item hidden in a display of other items, and their performance is measured by their reaction time (RT). Here I look at how visual search reaction times are correlated with past reaction times. Target-absent RTs (i.e. RTs to displays that have no target) are strongly correlated with past target-absent RTs and, treated as a time series, have a 1/f power spectrum. Target-present RTs, on the other hand, are effectively uncorrelated with past RTs. A model for visual search is presented which generates search RTs with this pattern of correlations and power spectra. In the model, search is conducted by matching search items up with "categorizers," which take a certain time to categorize each item as target or distractor; the RT is the sum of categorization times. The categorizers are drawn at random from a pool of active categorizers. After each search, some of the categorizers in the active pool are replaced with categorizers drawn from a larger population of unused categorizers. The categorizers that are not replaced are responsible for the RT correlations and the 1/f power spectrum.

Cette thèse développe des méthodes bootstrap pour les modèles à facteurs qui sont couram- ment utilisés pour générer des prévisions depuis l'article pionnier de Stock et Watson (2002) sur les indices de diffusion. Ces modèles tolèrent l'inclusion d'un grand nombre de variables macroéconomiques et financières comme prédicteurs, une caractéristique utile pour inclure di- verses informations disponibles aux agents économiques. Ma thèse propose donc des outils éco- nométriques qui améliorent l'inférence dans les modèles à facteurs utilisant des facteurs latents extraits d'un large panel de prédicteurs observés. Il est subdivisé en trois chapitres complémen- taires dont les deux premiers en collaboration avec Sílvia Gonçalves et Benoit Perron. Dans le premier article, nous étudions comment les méthodes bootstrap peuvent être utilisées pour faire de l'inférence dans les modèles de prévision pour un horizon de h périodes dans le futur. Pour ce faire, il examine l'inférence bootstrap dans un contexte de régression augmentée de facteurs où les erreurs pourraient être autocorrélées. Il généralise les résultats de Gonçalves et Perron (2014) et propose puis justifie deux approches basées sur les résidus : le block wild bootstrap et le dependent wild bootstrap. Nos simulations montrent une amélioration des taux de couverture des intervalles de confiance des coefficients estimés en utilisant ces approches comparativement à la théorie asymptotique et au wild bootstrap en présence de corrélation sérielle dans les erreurs de régression. Le deuxième chapitre propose des méthodes bootstrap pour la construction des intervalles de prévision permettant de relâcher l'hypothèse de normalité des innovations. Nous y propo- sons des intervalles de prédiction bootstrap pour une observation h périodes dans le futur et sa moyenne conditionnelle. Nous supposons que ces prévisions sont faites en utilisant un ensemble de facteurs extraits d'un large panel de variables. Parce que nous traitons ces facteurs comme latents, nos prévisions dépendent à la fois des facteurs estimés et les coefficients de régres- sion estimés. Sous des conditions de régularité, Bai et Ng (2006) ont proposé la construction d'intervalles asymptotiques sous l'hypothèse de Gaussianité des innovations. Le bootstrap nous permet de relâcher cette hypothèse et de construire des intervalles de prédiction valides sous des hypothèses plus générales. En outre, même en supposant la Gaussianité, le bootstrap conduit à des intervalles plus précis dans les cas où la dimension transversale est relativement faible car il prend en considération le biais de l'estimateur des moindres carrés ordinaires comme le montre une étude récente de Gonçalves et Perron (2014). Dans le troisième chapitre, nous suggérons des procédures de sélection convergentes pour les regressions augmentées de facteurs en échantillons finis. Nous démontrons premièrement que la méthode de validation croisée usuelle est non-convergente mais que sa généralisation, la validation croisée «leave-d-out» sélectionne le plus petit ensemble de facteurs estimés pour l'espace généré par les vraies facteurs. Le deuxième critère dont nous montrons également la validité généralise l'approximation bootstrap de Shao (1996) pour les regressions augmentées de facteurs. Les simulations montrent une amélioration de la probabilité de sélectionner par- cimonieusement les facteurs estimés comparativement aux méthodes de sélection disponibles. L'application empirique revisite la relation entre les facteurs macroéconomiques et financiers, et l'excès de rendement sur le marché boursier américain. Parmi les facteurs estimés à partir d'un large panel de données macroéconomiques et financières des États Unis, les facteurs fortement correlés aux écarts de taux d'intérêt et les facteurs de Fama-French ont un bon pouvoir prédictif pour les excès de rendement. / This thesis develops bootstrap methods for factor models which are now widely used for generating forecasts since the seminal paper of Stock and Watson (2002) on diffusion indices. These models allow the inclusion of a large set of macroeconomic and financial variables as predictors, useful to span various information related to economic agents. My thesis develops econometric tools that improves inference in factor-augmented regression models driven by few unobservable factors estimated from a large panel of observed predictors. It is subdivided into three complementary chapters. The two first chapters are joint papers with Sílvia Gonçalves and Benoit Perron. In the first chapter, we study how bootstrap methods can be used to make inference in h-step forecasting models which generally involve serially correlated errors. It thus considers bootstrap inference in a factor-augmented regression context where the errors could potentially be serially correlated. This generalizes results in Gonçalves and Perron (2013) and makes the bootstrap applicable to forecasting contexts where the forecast horizon is greater than one. We propose and justify two residual-based approaches, a block wild bootstrap (BWB) and a dependent wild bootstrap (DWB). Our simulations document improvement in coverage rates of confidence intervals for the coefficients when using BWB or DWB relative to both asymptotic theory and the wild bootstrap when serial correlation is present in the regression errors. The second chapter provides bootstrap methods for prediction intervals which allow relaxing the normality distribution assumption on innovations. We propose bootstrap prediction intervals for an observation h periods into the future and its conditional mean. We assume that these forecasts are made using a set of factors extracted from a large panel of variables. Because we treat these factors as latent, our forecasts depend both on estimated factors and estimated regression coefficients. Under regularity conditions, Bai and Ng (2006) proposed the construction of asymptotic intervals under Gaussianity of the innovations. The bootstrap allows us to relax this assumption and to construct valid prediction intervals under more general conditions. Moreover, even under Gaussianity, the bootstrap leads to more accurate intervals in cases where the cross-sectional dimension is relatively small as it reduces the bias of the ordinary least squares estimator as shown in a recent paper by Gonçalves and Perron (2014). The third chapter proposes two consistent model selection procedures for factor-augmented regressions in finite samples.We first demonstrate that the usual cross-validation is inconsistent, but that a generalization, leave-d-out cross-validation, selects the smallest basis of estimated factors for the space spanned by the true factors. The second proposed criterion is a generalization of the bootstrap approximation of the squared error of prediction of Shao (1996) to factor-augmented regressions which we also show is consistent. Simulation evidence documents improvements in the probability of selecting the smallest set of estimated factors than the usually available methods. An illustrative empirical application that analyzes the relationship between expected stock returns and macroeconomic and financial factors extracted from a large panel of U.S. macroeconomic and financial data is conducted. Our new procedures select factors that correlate heavily with interest rate spreads and with the Fama-French factors. These factors have strong predictive power for excess returns.