Dissertations / Theses on the topic 'Mixed frequency time series'

La prévision macroéconomique à court terme est un exercice aussi complexe qu’essentiel pour la définition de la politique économique et monétaire. Les crises financières récentes ainsi que les récessions qu’ont endurées et qu’endurent aujourd’hui encore, en ce début d’année 2014, nombre de pays parmi les plus riches, témoignent de la difficulté d’anticiper les fluctuations économiques, même à des horizons proches. Les recherches effectuées dans le cadre de la thèse de doctorat qui est présentée dans ce manuscrit se sont attachées à étudier, analyser et développer des modélisations pour la prévision de croissance économique. L’ensemble d’informations à partir duquel construire une méthodologie prédictive est vaste mais également hétérogène. Celle-ci doit en effet concilier le mélange des fréquences d’échantillonnage des données et la parcimonie nécessaire à son estimation. Nous évoquons à cet effet dans un premier chapitre les éléments économétriques fondamentaux de la modélisation multi-fréquentielle. Le deuxième chapitre illustre l’apport prédictif macroéconomique que constitue l’utilisation de la volatilité des variables financières en période de retournement conjoncturel. Le troisième chapitre s’étend ensuite sur l’inférence bayésienne et nous présentons par ce biais un travail empirique issu de l’adjonction d’une volatilité stochastique à notre modèle. Enfin, le quatrième chapitre propose une étude des techniques de sélection de variables à fréquence multiple dans l’optique d’améliorer la capacité prédictive de nos modélisations. Diverses méthodologies sont à cet égard développées, leurs aptitudes empiriques sont comparées, et certains faits stylisés sont esquissés
Economic downturn and recession that many countries experienced in the wake of the global financial crisis demonstrate how important but difficult it is to forecast macroeconomic fluctuations, especially within a short time horizon. The doctoral dissertation studies, analyses and develops models for economic growth forecasting. The set of information coming from economic activity is vast and disparate. In fact, time series coming from real and financial economy do not have the same characteristics, both in terms of sampling frequency and predictive power. Therefore short-term forecasting models should both allow the use of mixed-frequency data and parsimony. The first chapter is dedicated to time series econometrics within a mixed-frequency framework. The second chapter contains two empirical works that sheds light on macro-financial linkages by assessing the leading role of the daily financial volatility in macroeconomic prediction during the Great Recession. The third chapter extends mixed-frequency model into a Bayesian framework and presents an empirical study using a stochastic volatility augmented mixed data sampling model. The fourth chapter focuses on variable selection techniques in mixed-frequency models for short-term forecasting. We address the selection issue by developing mixed-frequency-based dimension reduction techniques in a cross-validation procedure that allows automatic in-sample selection based on recent forecasting performances. Our model succeeds in constructing an objective variable selection with broad applicability

This doctoral dissertation proposes methodologies which, from a linear or a non-linear approach, accommodate to the information flow and can deal with a large amount of data. The empirical application of the proposed methodologies contributes to answer some of the questions that have emerged or that it has potentiated after the 2008 global crisis. Thus, essential aspects of the macroeconomic analysis are studied, like the identification and forecast of business cycles turning points, the business cycles interactions between countries or the development of tools able to forecast the evolution of key economic indicators based on new data sources, like those which emerge from search engines.

Advances in sensor technology enable environmental monitoring programmes to record and store measurements at high-temporal resolution over long time periods. These large volumes of high-frequency data promote an increasingly comprehensive picture of many environmental processes that would not have been accessible in the past with monthly, fortnightly or even daily sampling. However, benefiting from these increasing amounts of high-frequency data presents various challenges in terms of data processing and statistical modeling using standard methods and software tools. These challenges are attributed to the large volumes of data, the persistent and long memory serial correlation in the data, the signal to noise ratio, and the complex and time-varying dynamics and inter-relationships between the different drivers of the process at different timescales. This thesis aims at using and developing a variety of statistical methods in both the time and frequency domains to effectively explore and analyze high-frequency time series data as well as to reduce their dimensionality, with specific application to a 3 year hydrological time series. Firstly, the thesis investigates the statistical challenges of exploring, modeling and analyzing these large volumes of high-frequency time series. Thereafter, it uses and develops more advanced statistical techniques to: (i) better visualize and identify the different modes of variability and common patterns in such data, and (ii) provide a more adequate dimension reduction representation to the data, which takes into account the persistent serial dependence structure and non-stationarity in the series. Throughout the thesis, a 15-minute resolution time series of excess partial pressure of carbon dioxide (EpCO2) obtained for a small catchment in the River Dee in Scotland has been used as an illustrative data set. Understanding the bio-geochemical and hydrological drivers of EpCO 2 is very important to the assessment of the global carbon budget. Specifically, Chapters 1 and 2 present a range of advanced statistical approaches in both the time and frequency domains, including wavelet analysis and additive models, to visualize and explore temporal variations and relationships between variables for the River Dee data across the different timescales to investigate the statistical challenges posed by such data. In Chapter 3, a functional data analysis approach is employed to identify the common daily patterns of EpCO2 by means of functional principal component analysis and functional cluster analysis. The techniques used in this chapter assume independent functional data. However, in numerous applications, functional observations are serially correlated over time, e.g. where each curve represents a segment of the whole time interval. In this situation, ignoring the temporal dependence may result in an inappropriate dimension reduction of the data and inefficient inference procedures. Subsequently, the dynamic functional principal components, recently developed by Hor mann et al. (2014), are considered in Chapter 4 to account for the temporal correlation using a frequency domain approach. A specific contribution of this thesis is the extension of the methodology of dynamic functional principal components to temporally dependent functional data estimated using any type of basis functions, not only orthogonal basis functions. Based on the scores of the proposed general version of dynamic functional principal components, a novel clustering approach is proposed and used to cluster the daily curves of EpCO2 taking into account the dependence structure in the data. The dynamic functional principal components depend in their construction on the assumption of second-order stationarity, which is not a realistic assumption in most environmental applications. Therefore, in Chapter 5, a second specific contribution of this thesis is the development of a time-varying dynamic functional principal components which allows the components to vary smoothly over time. The performance of these smooth dynamic functional principal components is evaluated empirically using the EpCO2 data and using a simulation study. The simulation study compares the performance of smooth and original dynamic functional principal components under both stationary and non-stationary conditions. The smooth dynamic functional principal components have shown considerable improvement in representing non-stationary dependent functional data in smaller dimensions. Using a bootstrap inference procedure, the smooth dynamic functional principal components have been subsequently employed to investigate whether or not the spectral density and covariance structure of the functional time series under study change over time. To account for the possible changes in the covariance structure, a clustering approach based on the proposed smooth dynamic functional principal components is suggested and the results of application are discussed. Finally, Chapter 6 provides a summary of the work presented within this thesis, discusses the limitations and implications and proposes areas for future research.

The experimental factors such as the cell type and the treatment may have different impact on expression levels of individual genes which are quantitative measurements from microarrays. The measurements can be collected at a few unevenly spaced time points with replicates. The aim of this study is to consider cell type, treatment and short time series attributes and to infer about their effects on individual genes. A mixed effects model (LME) was proposed to model the gene expression data and the performance of the model was validated by a simulation study. Realistic data sets were generated preserving the structure of the sample real life data studied by Nymark et al. (2007). Predictive performance of the model was evaluated by performance measures, such as accuracy, sensitivity and specificity, as well as compared to the competing method by Smyth (2004), namely Limma. Both methods were also compared on real life data. Simulation results showed that the predictive performance of LME is as high as 99%, and it produces False Discovery Rate (FDR) as low as 0.4% whereas Limma has an FDR value of at least 32%. Moreover, LME has almost 99% predictive capability on the continuous time parameter where Limma has only about 67% and even it cannot handle continuous independent variables.

The concept of cointegration has principally been developed under the assumption that the raw data vector Zt is I(1) and the cointegrating residual et is I(0); we call this framework the CI(l) case. The purpose of this thesis is to consider more general fractional circumstances, where Zt is stationary with long memory and et is stationary with less memory, or where Zt is nonstationary while et is less nonstationary or stationary, possibly with long memory. First we establish weak convergence to what we term "type II fractional Brownian motion" for a wide class of nonstationary fractionally integrated processes, then we go on to investigate the behaviour of the discretely averaged periodogram for processes that are not second order stationary. These results are exploited for the analysis of a procedure originally proposed by Robinson (1994a), which we call Frequency Domain Least Squares (FDLS). FDLS yield estimates of the cointe-grating vector that are consistent for stationary and nonstationary Zt, asymptotically equivalent to OLS in some circumstances, and superior in many others, including the standard CI(1) case; a semiparametric methodology for fractional cointegration analysis is applied to data sets on eleven US macroeconomic variables. Finally, we investigate an alternative definition of fractional cointegration, for which we introduce a continuously averaged version of FDLS, obtaining consistent estimates in both the stationary and the nonstationary case. Asymptotic distributions and Monte Carlo evidence on finite sample performance are also provided.

Thesis (M.S.)--University of Missouri--Rolla, 2007.
Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed March 18, 2008) Includes bibliographical references (p. 89-90).

Complex-valued representation of a two-component real-valued time series yields additional physical insights that are lost otherwise. The spectral representation theorem allows us to study covariance stationary complex-valued random sequences in the frequency domain, and this is known as rotary spectral analysis. It is a widely-used technique for studying elliptical motions in ocean currents, wind etc. An important and useful parameter in rotary spectral analysis of scalar complex-valued time series is the rotary coefficient. It measures the tendency of vectors to rotate in a clockwise or counter-clockwise manner. We derive the theoretical distribution of the rotary coefficient estimator and apply our results to ocean current speed and direction measurements at six depths in the Labrador Sea. Canonical correlation techniques are commonly employed in the analysis of a pair of vector-valued random variables. We introduce a framework to extend classical multivariate analysis techniques such as canonical correlation analysis, partial least squares, and multivariate linear regression, to define coherence - a measure of correlation in the frequency domain. In the statistical analysis of complex-valued time series, we refer to a time series as proper/improper according to whether it is uncorrelated/correlated with its complex conjugate. In earlier work, complex-valued signals were assumed to be proper for the simple reason that it led to a simpler algebra. However, the loss in performance caused by overlooking the potential impropriety of such data is realized to be significant, and therefore, when the data is improper, information contained in the complementary covariance structure must be considered. Since impropriety in the time domain may not necessarily correspond to impropriety at all frequencies, we propose a generalized likelihood ratio test which may be used to test propriety of a discrete time complex-valued process at a given frequency. Finally, the idea of vector circulant embedding is exploited to yield a frequency domain bootstrap methodology. With the help of three example parameters involved in the study of multi-channel complex-valued time series, we illustrate how our method allows us to draw statistical inference such as confidence intervals. Our method can prove useful in cases where no theoretical distributional results are available, or to check the effect of nuisance parameter estimates where theoretical results are available.

This volume contains four essays on various topics in the field of financial econometrics. All four discuss the properties of high frequency financial data and its implications on the model choice when an estimate of the capital asset return volatility is in focus. The interest lies both in characterizing "stylized facts" in such series with time series models and in predicting volatility. The first essay, entitled A Survey of Recent Papers Considering the Standard & Poor 500 Composite Stock Index, presents recent empirical findings and stylized facts in the financial market from 1987 to 1996 and gives a brief introduction to the research field of capital asset return volatitlity models and properties of high frequency financial data. As the title indicates, the survey is restricted to research on the well known Standard & Poor 500 index. The second essay, with the title, Stylized Facts of Daily Return Series and the Hidden Markov Model, investigates the properties of the hidden Markov Model, HMM, and its capability of reproducing stylized facts of financial high frequency data. The third essay, Modelling the Conditional Mean and Conditional Variance: A combined Smooth Transition and Hidden Markov Approach with an Application to High Frequency Series, investigates the consequences of combining a nonlinear parameterized conditional mean with an HMM for the conditional variance when characterization of stylized facts is considered. Finally, the fourth essay entitled, Volatility Forecasting for Option Pricing on Exchange Rates and Stock Prices, investigates the volatility forecasting performance of some of the most frequently used capital asset return volatility models such as the GARCH with normal and t-distributed errors, the EGARCH and the HMM. The prediction error minimization approach is also investigated. Each essay is self-contained and could, in principle, be read in any order chosen by the reader. This, however, requires a working knowledge of the properties of the HMM. For readers less familiar with the research field the first essay may serve as an helpful introduction to the following three essays.

Diss. Stockholm : Handelshögsk.

This thesis aims at investigating different forms of residuals from a general time series model with conditional mean and conditional variance fitted by the Gaussian quasi-maximum likelihood method. We investigated the limiting distributions of autocorrelation and partial autocorrelation functions under different forms of residuals. Based on them we devised some individual portmanteau tests and two mixed portmanteau tests. We started by exploring the asymptotic normalities of the residual autocorrelation functions, the squared residual autocorrelation functions and absolute residual autocorrelation functions from the fitted time series model. This leads to three individual portmanteau tests. Then we generalized them to their counterparts of partial autocorrelation functions, and this results in another three individual portmanteau tests. We carried out simulations studies to compare the six individual portmanteau tests and find that some tests are sensitive to mis-specification in the conditional mean while other tests are effective to detect mis-specification in the conditional variance. However, for the case that the mis-specifications happen in both conditional mean and variance, none of these individual portmanteau tests present remarkable power. Based on this, we continued to investigate the joint limiting distributions of the residual autocorrelation functions and absolute residual autocorrelation functions of the fitted model since the former one is powerful to identify mis-specification in the conditional mean and the latter one works well when the conditional variance is mis-specified. This leads to two mixed portmanteau tests for diagnostic checking of the fitted model. Simulation studies are carried out to check the asymptotic theory and to assess the performance of the mixed portmanteau tests. It shows that the mixed portmanteau tests have the power to detect mis-specification in the conditional mean and conditional variance respectively while it is feasible to detect both of them.
published_or_final_version
Statistics and Actuarial Science
Master
Master of Philosophy

Dans les séries temporelles neurophysiologiques, on observe de fortes oscillations neuronales, et les outils d'analyse sont donc naturellement centrés sur le filtrage à bande étroite.Puisque cette approche est trop réductrice, nous proposons de nouvelles méthodes pour représenter ces signaux.Nous centrons tout d'abord notre étude sur le couplage phase-amplitude (PAC), dans lequel une bande haute fréquence est modulée en amplitude par la phase d'une oscillation neuronale plus lente.Nous proposons de capturer ce couplage dans un modèle probabiliste appelé modèle autoregressif piloté (DAR). Cette modélisation permet une sélection de modèle efficace grâce à la mesure de vraisemblance, ce qui constitue un apport majeur à l'estimation du PAC.%Nous présentons différentes paramétrisations des modèles DAR et leurs algorithmes d'inférence rapides, et discutons de leur stabilité.Puis nous montrons comment utiliser les modèles DAR pour l'analyse du PAC, et démontrons l'avantage de l'approche par modélisation avec trois jeux de donnée.Puis nous explorons plusieurs extensions à ces modèles, pour estimer le signal pilote à partir des données, le PAC sur des signaux multivariés, ou encore des champs réceptifs spectro-temporels.Enfin, nous proposons aussi d'adapter les modèles de codage parcimonieux convolutionnels pour les séries temporelles neurophysiologiques, en les étendant à des distributions à queues lourdes et à des décompositions multivariées. Nous développons des algorithmes d'inférence efficaces pour chaque formulations, et montrons que l'on obtient de riches représentations de façon non-supervisée
In neurophysiological time series, strong neural oscillations are observed in the mammalian brain, and the natural processing tools are thus centered on narrow-band linear filtering.As this approach is too reductive, we propose new methods to represent these signals.We first focus on the study of phase-amplitude coupling (PAC), which consists in an amplitude modulation of a high frequency band, time-locked with a specific phase of a slow neural oscillation.We propose to use driven autoregressive models (DAR), to capture PAC in a probabilistic model. Giving a proper model to the signal enables model selection by using the likelihood of the model, which constitutes a major improvement in PAC estimation.%We first present different parametrization of DAR models, with fast inference algorithms and stability discussions.Then, we present how to use DAR models for PAC analysis, demonstrating the advantage of the model-based approach on three empirical datasets.Then, we explore different extensions to DAR models, estimating the driving signal from the data, PAC in multivariate signals, or spectro-temporal receptive fields.Finally, we also propose to adapt convolutional sparse coding (CSC) models for neurophysiological time-series, extending them to heavy-tail noise distribution and multivariate decompositions. We develop efficient inference algorithms for each formulation, and show that we obtain rich unsupervised signal representations

Statistics
Ph.D.
This thesis proposes novel methods to address specific challenges in analyzing the frequency- and time-domain properties of nonstationary time series data motivated by the study of electrophysiological signals. A new method is proposed for the simultaneous and automatic analysis of the association between the time-varying power spectrum and covariates. The procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines. The approach is formulated in a fully Bayesian framework, in which the number and locations of partition points are random, and fit using reversible jump Markov chain Monte Carlo techniques. Estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes. The new methodology is used to analyze the association between the time-varying spectrum of heart rate variability and self-reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse. Another method proposed in this dissertation develops a unique framework for automatically identifying bands of frequencies exhibiting similar nonstationary behavior. This proposal provides a standardized, unifying approach to constructing customized frequency bands for different signals under study across different settings. A frequency-domain, iterative cumulative sum procedure is formulated to identify frequency bands that exhibit similar nonstationary patterns in the power spectrum through time. A formal hypothesis testing procedure is also developed to test which, if any, frequency bands remain stationary. This method is shown to consistently estimate the number of frequency bands and the location of the upper and lower bounds defining each frequency band. This method is used to estimate frequency bands useful in summarizing nonstationary behavior of full night heart rate variability data.
Temple University--Theses

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
PROGRAMA DE EXCELENCIA ACADEMICA
A previsão de séries temporais é um assunto de grande importância para diversas áreas, podendo servir como base para planejamento e controle, entre outros. As formas mais comuns de previsão são as pontuais. É arriscado, no entanto, planejadores tomarem decisões unicamente com base em previsões pontuais, pois séries reais são compostas por uma parte aleatória que não pode ser definida por modelagem matemática. Um modo de contornar este problema é realizando previsões intervalares. Estas fornecem informações sobre as incertezas das previsões pontuais, o que auxilia o planejador em suas decisões. Modelos de lógica fuzzy têm sido investigados na literatura de previsão devido a sua capacidade de modelar incertezas. Apesar disso, sistemas de lógica fuzzy Mamdani (MFLS) foram pouco investigados no tema, comparando-se a outros tipos de modelagens fuzzy. Ademais, entende-se que a literatura de previsão intervalar com modelos fuzzy é limitada. Neste contexto, este trabalho propõe um método para construção de previsões intervalares a partir das previsões pontuais do modelo MFLS de tipo-1 (T1 MFLS). O método proposto para construção de previsões intervalares do MFLS é baseado na reamostragem de erros in-sample. O modelo T1 MFLS é construído com uma heurística (para partição do universo de discurso das variáveis do modelo) e com a seleção da entrada do modelo. Previsões pontuais e intervalares são produzidas para séries horárias de carga de energia elétrica. A literatura de modelos fuzzy de previsão é revisada.
Time series forecasting is an important subject for many areas; it can serve as basis for planning and control, among others. The most common type of forecast is the point forecast. It is, nevertheless, risky to make decisions based on point forecasts, considering that real time series are composed by a random part that cannot be exactly defined by mathematical modeling. One way to by-pass this problem is by producing interval forecasts. These provide information about point forecasts reliability, what helps the planner make his decisions. Fuzzy logic models have been investigated in the forecasting literature due to their ability to model uncertainties. In spite of this, Mamdani fuzzy logic systems (MFLS) have been less investigated in this subject than other types of fuzzy modeling approaches. Furthermore, it is understood that the literature of interval forecasting with fuzzy models is very limited. In this context, this work proposes a method for creating interval prediction from point forecasts of a type-1 MFLS (T1 MFLS). The proposed method for interval forecast construction is based on the resampling of in-sample errors. The T1 MFLS model is constructed with a heuristic (that makes the partition of the universe of discourse of the model s variables) and with selection of the model s inputs. Point and interval forecasts are produced for hourly electricity load series. The literature of fuzzy models applied in forecasting is reviewed.

Ce manuscrit propose de nouvelles méthodes d’estimation robustes pour les fonctions matricielles d’autocovariance et d’autocorrélation de séries chronologiques multivariées stationnaires pouvant présenter des valeurs aberrantes aléatoires additives. Ces fonctions jouent un rôle important dans l’identification et l’estimation des paramètres de modèles de séries chronologiques multivariées stationnaires. Nous proposons tout d'abord de nouveaux estimateurs des fonctions matricielles d’autocovariance et d’autocorrélation construits en utilisant une approche spectrale à l'aide du périodogramme matriciel. Comme dans le cas des estimateurs classiques des fonctions d’autocovariance et d’autocorrélation matricielles, ces estimateurs sont affectés par des observations aberrantes. Ainsi, toute procédure d'identification ou d'estimation les utilisant est directement affectée, ce qui entraîne des conclusions erronées. Pour atténuer ce problème, nous proposons l’utilisation de techniques statistiques robustes pour créer des estimateurs résistants aux observations aléatoires aberrantes. Dans un premier temps, nous proposons de nouveaux estimateurs des fonctions d’autocorvariance et d’autocorrélation de séries chronologiques univariées. Les domaines temporel et fréquentiel sont liés par la relation existant entre la fonction d’autocovariance et la densité spectrale. Le périodogramme étant sensible aux données aberrantes, nous obtenons un estimateur robuste en le remplaçant parle $M$-périodogramme. Les propriétés asymptotiques des estimateurs sont établies. Leurs performances sont étudiées au moyen de simulations numériques pour différentes tailles d’échantillons et différents scénarios de contamination. Les résultats empiriques indiquent que les méthodes proposées fournissent des valeurs proches de celles obtenues par la fonction d'autocorrélation classique quand les données ne sont pas contaminées et resistent à différents cénarios de contamination. Ainsi, les estimateurs proposés dans cette thèse sont des méthodes alternatives utilisables pour des séries chronologiques présentant ou non des valeurs aberrantes. Les estimateurs obtenus pour des séries chronologiques univariées sont ensuite étendus au cas de séries multivariées. Cette extension est simplifiée par le fait que le calcul du périodogramme croisé ne fait intervenir que les coefficients de Fourier de chaque composante de la série. Le $M$-périodogramme matriciel apparaît alors comme une alternative robuste au périodogramme matriciel pour construire des estimateurs robustes des fonctions matricielles d’autocovariance et d’autocorrélation. Les propriétés asymptotiques sont étudiées et des expériences numériques sont réalisées. Comme exemple d'application avec des données réelles, nous utilisons les fonctions proposées pour ajuster un modèle autoregressif par la méthode de Yule-Walker à des données de pollution collectées dans la région de Vitória au Brésil.Enfin, l'estimation robuste du nombre de facteurs dans les modèles factoriels de grande dimension est considérée afin de réduire la dimensionnalité. En présence de valeurs aberrantes, les critères d’information proposés par Bai & Ng (2002) tendent à surestimer le nombre de facteurs. Pour atténuer ce problème, nous proposons de remplacer la matrice de covariance standard par la matrice de covariance robuste proposée dans ce manuscrit. Nos simulations montrent qu'en l'absence de contamination, les méthodes standards et robustes sont équivalentes. En présence d'observations aberrantes, le nombre de facteurs estimés augmente avec les méthodes non robustes alors qu'il reste le même en utilisant les méthodes robustes. À titre d'application avec des données réelles, nous étudions des concentrations de polluant PM$_{10}$ mesurées dans la région de l'Île-de-France en France
This manuscript proposes new robust estimation methods for the autocovariance and autocorrelation matrices functions of stationary multivariates time series that may have random additives outliers. These functions play an important role in the identification and estimation of time series model parameters. We first propose new estimators of the autocovariance and of autocorrelation matrices functions constructed using a spectral approach considering the periodogram matrix periodogram which is the natural estimator of the spectral density matrix. As in the case of the classic autocovariance and autocorrelation matrices functions estimators, these estimators are affected by aberrant observations. Thus, any identification or estimation procedure using them is directly affected, which leads to erroneous conclusions. To mitigate this problem, we propose the use of robust statistical techniques to create estimators resistant to aberrant random observations.As a first step, we propose new estimators of autocovariance and autocorrelation functions of univariate time series. The time and frequency domains are linked by the relationship between the autocovariance function and the spectral density. As the periodogram is sensitive to aberrant data, we get a robust estimator by replacing it with the $M$-periodogram. The $M$-periodogram is obtained by replacing the Fourier coefficients related to periodogram calculated by the standard least squares regression with the ones calculated by the $M$-robust regression. The asymptotic properties of estimators are established. Their performances are studied by means of numerical simulations for different sample sizes and different scenarios of contamination. The empirical results indicate that the proposed methods provide close values of those obtained by the classical autocorrelation function when the data is not contaminated and it is resistant to different contamination scenarios. Thus, the estimators proposed in this thesis are alternative methods that can be used for time series with or without outliers.The estimators obtained for univariate time series are then extended to the case of multivariate series. This extension is simplified by the fact that the calculation of the cross-periodogram only involves the Fourier coefficients of each component from the univariate series. Thus, the $M$-periodogram matrix is a robust periodogram matrix alternative to build robust estimators of the autocovariance and autocorrelation matrices functions. The asymptotic properties are studied and numerical experiments are performed. As an example of an application with real data, we use the proposed functions to adjust an autoregressive model by the Yule-Walker method to Pollution data collected in the Vitória region Brazil.Finally, the robust estimation of the number of factors in large factorial models is considered in order to reduce the dimensionality. It is well known that the values random additive outliers affect the covariance and correlation matrices and the techniques that depend on the calculation of their eigenvalues and eigenvectors, such as the analysis principal components and the factor analysis, are affected. Thus, in the presence of outliers, the information criteria proposed by Bai & Ng (2002) tend to overestimate the number of factors. To alleviate this problem, we propose to replace the standard covariance matrix with the robust covariance matrix proposed in this manuscript. Our Monte Carlo simulations show that, in the absence of contamination, the standard and robust methods are equivalent. In the presence of outliers, the number of estimated factors increases with the non-robust methods while it remains the same using robust methods. As an application with real data, we study pollutant concentrations PM$_{10}$ measured in the Île-de-France region of France
Este manuscrito é centrado em propor novos métodos de estimaçao das funçoes de autocovariancia e autocorrelaçao matriciais de séries temporais multivariadas com e sem presença de observaçoes discrepantes aleatorias. As funçoes de autocovariancia e autocorrelaçao matriciais desempenham um papel importante na analise e na estimaçao dos parametros de modelos de série temporal multivariadas. Primeiramente, nos propomos novos estimadores dessas funçoes matriciais construıdas, considerando a abordagem do dominio da frequencia por meio do periodograma matricial, um estimador natural da matriz de densidade espectral. Como no caso dos estimadores tradicionais das funçoes de autocovariancia e autocorrelaçao matriciais, os nossos estimadores tambem sao afetados pelas observaçoes discrepantes. Assim, qualquer analise subsequente que os utilize é diretamente afetada causando conclusoes equivocadas. Para mitigar esse problema, nos propomos a utilizaçao de técnicas de estatistica robusta para a criaçao de estimadores resistentes as observaçoes discrepantes aleatorias. Inicialmente, nos propomos novos estimadores das funçoes de autocovariancia e autocorrelaçao de séries temporais univariadas considerando a conexao entre o dominio do tempo e da frequencia por meio da relaçao entre a funçao de autocovariancia e a densidade espectral, do qual o periodograma tradicional é o estimador natural. Esse estimador é sensivel as observaçoes discrepantes. Assim, a robustez é atingida considerando a utilizaçao do Mperiodograma. O M-periodograma é obtido substituindo a regressao por minimos quadrados com a M-regressao no calculo das estimativas dos coeficientes de Fourier relacionados ao periodograma. As propriedades assintoticas dos estimadores sao estabelecidas. Para diferentes tamanhos de amostras e cenarios de contaminaçao, a performance dos estimadores é investigada. Os resultados empiricos indicam que os métodos propostos provem resultados acurados. Isto é, os métodos propostos obtêm valores proximos aos da funçao de autocorrelaçao tradicional no contexto de nao contaminaçao dos dados. Quando ha contaminaçao, os M-estimadores permanecem inalterados. Deste modo, as funçoes de M-autocovariancia e de M-autocorrelaçao propostas nesta tese sao alternativas vi aveis para séries temporais com e sem observaçoes discrepantes. A boa performance dos estimadores para o cenario de séries temporais univariadas motivou a extensao para o contexto de séries temporais multivariadas. Essa extensao é direta, haja vista que somente os coeficientes de Fourier relativos à cada uma das séries univariadas sao necessarios para o calculo do periodograma cruzado. Novamente, a relaçao de dualidade entre o dominio da frequência e do tempo é explorada por meio da conexao entre a funçao matricial de autocovariancia e a matriz de densidade espectral de séries temporais multivariadas. É neste sentido que, o presente artigo propoe a matriz M-periodograma como um substituto robusto à matriz periodograma tradicional na criaçao de estimadores das funçoes matriciais de autocovariancia e autocorrelaçao. As propriedades assintoticas sao estudas e experimentos numéricos sao realizados. Como exemplo de aplicaçao à dados reais, nos aplicamos as funçoes propostas no artigo na estimaçao dos parâmetros do modelo de série temporal multivariada pelo método de Yule-Walker para a modelagem dos dados MP10 da regiao de Vitoria/Brasil. Finalmente, a estimaçao robusta dos numeros de fatores em modelos fatoriais aproximados de alta dimensao é considerada com o objetivo de reduzir a dimensionalidade. Ésabido que dados discrepantes afetam as matrizes de covariancia e correlaçao. Em adiçao, técnicas que dependem do calculo dos autovalores e autovetores dessas matrizes, como a analise de componentes principais e a analise fatorial, sao completamente afetadas. Assim, na presença de observaçoes discrepantes, o critério de informaçao proposto por Bai & Ng (2002) tende a superestimar o numero de fatores. [...]

The classical Fourier analysis of time series data can be used to detect periodic trends that are of sinusoidal shape. However, this analysis can be misleading when time series trends are not sinusoidal. When the time series process of interest is binary or categorical-valued data, it might be more reasonable that the time process be represented by a square or rectangular form of functions instead of sinusoidal functions. The WalshFourier analysis takes this approach using a square form of functions. The Walsh-Fourier analysis is based on the Walsh functions. The Walsh functions are a square form of functions that take on only two values + 1 and -1. But, unlike sinusoidals, the Walsh functions are not periodic. Harmuth (1969) introduced the term sequency to describe generalized frequency to identify functions that are not periodic, such as Walsh functions. The term sequency is interpreted as the nun1ber of zero crossings or sign changes per unit time. While the Walsh-Fourier analysis is reasonable in theory for binary or categorical-valued time series data, the interpretation of sequency is often difficult. In this dissertation, using a sequence of periodic functions, we develop the theory and method that can be applied to binary or categorical-valued data where patterns more naturally follow a rectangular shape. The theory parallels the Fourier theory and leads to a "Fourier-like" data transform that is specifically suited to the identification of rectangular trends.
Ph. D.

Thesis (DrPH)--University of North Carolina at Chapel Hill, 2009.
Title from electronic title page (viewed Jun. 4, 2010). "... in partial fulfillment of the requirement for the degree of Doctor of Public Health in the Department of Biostatistics, Gillings School of Global Public Health." Discipline: Biostatistics; Department/School: Public Health.

Topological data analysis has been shown to provide novel insight in many natural sciences. To our knowledge, the area is however relatively unstudied on financial data. This thesis explores the use of topological data analysis on one dimensional financial time series. Takens embedding theorem is used to transform a one dimensional time series to an $m$-dimensional point cloud, where $m$ is the embedding dimension. The point cloud of the time series represents the states of the dynamical system of the one dimensional time series. To see how the topology of the states differs in different partitions of the time series, sliding window technique is used. The point cloud of the partitions is then reduced to three dimensions by PCA to allow for computationally feasible persistent homology calculation. Synthetic examples are shown to illustrate the process. Lastly, persistence landscapes are used to allow for statistical analysis of the topological features. The topological properties of financial data are compared with quantum noise data to see if the properties differ from noise. Complexity calculations are performed on both datasets to further investigate the differences between high-frequency FX data and noise. The results suggest that high-frequency FX data differs from the quantum noise data and that there might be some property other than mutual information of financial data which topological data analysis uncovers.
Topologisk dataanalys har visat sig kunna ge ny insikt i många naturvetenskapliga discipliner. Till vår kännedom är tillämpningar av metoden på finansiell data relativt ostuderad. Uppsatsen utforskar topologisk dataanalys på en endimensionell finanstidsserie. Takens inbäddningsteorem används för att transformera en endimensionell tidsserie till ett $m$-dimensionellt punktmoln, där $m$ är inbäddningsdimensionen. Tidsseriens punktmoln representerar tillstånd hos det dynamiska systemet som associeras med den endimensionella tidsserien. För att undersöka hur topologiska tillstånd varierar inom tidsserien används fönsterbaserad teknik för att segmentera den endimensionella tidsserien. Segmentens punktmoln reduceras till 3D med PCA för att göra ihållande homologi beräkningsmässigt möjligt. Syntetiska exempel används för att illustrera processen. En jämförelse mellan topologiska egenskaper hos finansiell tidseries och kvantbrus utförs för att se skillnader mellan dessa. Även komplexitetsberäkningar utförs på dessa data set för att vidare utforska skillnaderna mellan kvantbrus och högfrekventa FX-data. Resultatet visar på att högfrekvent FX-data skiljer sig från kvantbrus och att det finns egenskaper förutom gemensam information hos finansiella tidsserier som topologisk dataanalys visar på.

This thesis is composed of three chapters which propose some novel approaches to model and forecast financial time series. The first chapter focuses on high frequency financial returns and proposes a quantile regression approach to model their intraday seasonality and dynamics. The second chapter deals with the problem of forecasting the yield curve including large datasets of macroeconomics information. While the last chapter addresses the issue of modelling the term structure of interest rates.

The first chapter investigates the distribution of high frequency financial returns, with special emphasis on the intraday seasonality. Using quantile regression, I show the expansions and shrinks of the probability law through the day for three years of 15 minutes sampled stock returns. Returns are more dispersed and less concentrated around the median at the hours near the opening and closing. I provide intraday value at risk assessments and I show how it adapts to changes of dispersion over the day. The tests performed on the out-of-sample forecasts of the value at risk show that the model is able to provide good risk assessments and to outperform standard Gaussian and Student’s t GARCH models.

The second chapter shows that macroeconomic indicators are helpful in forecasting the yield curve. I incorporate a large number of macroeconomic predictors within the Nelson and Siegel (1987) model for the yield curve, which can be cast in a common factor model representation. Rather than including macroeconomic variables as additional factors, I use them to extract the Nelson and Siegel factors. Estimation is performed by EM algorithm and Kalman filter using a data set composed by 17 yields and 118 macro variables. Results show that incorporating large macroeconomic information improves the accuracy of out-of-sample yield forecasts at medium and long horizons.

The third chapter statistically tests whether the Nelson and Siegel (1987) yield curve model is arbitrage-free. Theoretically, the Nelson-Siegel model does not ensure the absence of arbitrage opportunities. Still, central banks and public wealth managers rely heavily on it. Using a non-parametric resampling technique and zero-coupon yield curve data from the US market, I find that the no-arbitrage parameters are not statistically different from those obtained from the Nelson and Siegel model, at a 95 percent confidence level. I therefore conclude that the Nelson and Siegel yield curve model is compatible with arbitrage-freeness.

Doctorat en Sciences économiques et de gestion
info:eu-repo/semantics/nonPublished

Inverse Synthetic Aperture Radar coherently processes the return signal from the target in order to construct the image of the target. The conventional methodology used for obtaining the image is the Fourier transform which is not capable of suppressing the Doppler change in the return signal. As a result, Range-Doppler image is degraded. A proper time-frequency transform suppresses the degradation due to time varying Doppler shift. In this thesis, high resolution joint-time frequency transformations that can be used in place of the conventional method are evaluated. Wigner-Ville Distribution, Adaptive Gabor Representation with Coarse-to-Fine search algorithm, and Time-Frequency Distribution Series are examined for the target imaging system. The techniques applied to sample signals compared with each other. The computational and memorial complexity of the methods are evaluated and compared to each other and possible improvements are discussed. The application of these techniques in the target imaging system is also performed and resulting images compared to each other.

Heteroscedasticity (or time-dependent volatility) in economic and financial time series has been recognized for decades. Still, heteroscedasticity is surprisingly often neglected by practitioners and researchers. This may lead to inefficient procedures. Much of the work in this thesis is about finding more effective ways to deal with heteroscedasticity in economic and financial data. Paper I suggest a filter that, unlike the Box-Cox transformation, does not assume that the heteroscedasticity is a power of the expected level of the series. This is achieved by dividing the time series by a moving average of its standard deviations smoothed by a Hodrick-Prescott filter. It is shown that the filter does not colour white noise. An appropriate removal of heteroscedasticity allows more effective analyses of heteroscedastic time series. A few examples are presented in Paper II, III and IV of this thesis. Removing the heteroscedasticity using the proposed filter enables efficient estimation of the underlying probability distribution of economic growth. It is shown that the mixed Normal - Asymmetric Laplace (NAL) distributional fit is superior to the alternatives. This distribution represents a Schumpeterian model of growth, the driving mechanism of which is Poisson (Aghion and Howitt, 1992) distributed innovations. This distribution is flexible and has not been used before in this context. Another way of circumventing strong heteroscedasticity in the Dow Jones stock index is to divide the data into volatility groups using the procedure described in Paper III. For each such group, the most accurate probability distribution is searched for and is used in density forecasting. Interestingly, the NAL distribution fits best also here. This could hint at a new analogy between the financial sphere and the real economy, further investigated in Paper IV. These series are typically heteroscedastic, making standard detrending procedures, such as Hodrick-Prescott or Baxter-King, inadequate. Prior to this comovement study, the univariate and bivariate frequency domain results from these filters are compared to the filter proposed in Paper I. The effect of often neglected heteroscedasticity may thus be studied.

Water trees are a major form of degradation in solid organic electrical insulation subject to high AC voltages and water. The work is aimed at developing a more rigorous approach to analysing water tree data from ageing experiments on practical insulation geometries. Such data is in the form of tree length distributions and time-increasing tree number densities. Tree inception statistics are directly accessible from the data, but the effects of growth are convolved with those of inception. An approach is developed for analysing the data to quantify aspects of both inception and growth. In particular, mean growth rates and distributions of growth times can be estimated. The distribution of inception times seems to be close to exponential. Analysis shows that the effects of varying the field on the dynamics of inception depend upon whether the voltage or the insulation thickness is being varied. Increasing the frequency or decreasing thickness increases the number of possible water tree sites but decreases the inception rate from an average site. Frequency accelerates inception in a non-linear manner. Increasing the voltage both increases the number of sites and the inception rates. At frequencies close to 1 kHz, the mean length of a tree increases with the square root of growth time. Initial tree growth rates increase in a way that is consistent with a linear dependence on frequency. It is concluded that the approach developed can be applied to real data and is useful. It is expected that application of the approach to more extensive data sets would give rise to considerable advances in the empirical knowledge of the dependence of water treeing on various physical parameters which it is not possible to obtain using existing techniques.

Wetlands are nominally characterized by, vegetation, presence of saturated soils and/or period and depth of standing water (inundation). Wetland hydroperiod, traditionally defined by the period or duration of inundation, is considered to control the ecological function and resultant plant community. This study seeks to redefine "hydroperiod" to incorporate both surface and subsurface water-level fluctuations, to identify predominant hydroperiod of different wetland types, and to find the range of the water-level fluctuations during the predominant hydroperiod durations. The motivation being that wetland ecological condition is controlled not just by the period of inundation but also by the proximity and depth to water-table and period of water-level fluctuation. To accomplish this, a frequency distribution analysis of water-table and stage levels in wetlands is performed. The conclusions of this study suggest a need to rethink current definitions and methodologies in determining hydroperiod. Redefining wetland hydroperiod taking into consideration depth to water-table, namely water-level periods and depths below ground surface, may also aid in the understanding of how fluctuations in water-levels in a wetland affect plant ecology.