Diss. Stockholm : Handelshögskolan, 2002.

[pt] O objetivo desta dissertação é propor um mecanismo de testes para a avaliação dos resultados obtidos em uma modelagem TS-TARX.A principal motivação é encontrar uma solução para um problema comum na modelagem TS-TARX : os modelos espúrios que são gerados durante o processo de divisão do espaço das variáveis independentes.O modelo é uma heurística baseada em análise de árvore de regressão, como discutido por Brieman -3, 1984-. O modelo proposto para a análise de séries temporais é chamado TARX - Threshold Autoregressive with eXternal variables-. A idéia central é encontrar limiares que separem regimes que podem ser explicados através de modelos lineares. Este processo é um algoritmo que preserva o método de regressão por mínimos quadrados recursivo -MQR-. Combinando a árvore de decisão com a técnica de regressão -MQR-, o modelo se tornou o TS-TARX -Tree Structured - Threshold AutoRegression with external variables-.Será estendido aqui o trabalho iniciado por Aranha em -1, 2001-. Onde a partir de uma base de dados conhecida, um algoritmo eficiente gera uma árvore de decisão por meio de regras, e as equações de regressão estimadas para cada um dos regimes encontrados. Este procedimento pode gerar alguns modelos espúrios ou por construção,devido a divisão binária da árvore, ou pelo fato de não existir neste momento uma metodologia de comparação dos modelos resultantes.Será proposta uma metodologia através de sucessivos testes de Chow -5, 1960- que identificará modelos espúrios e reduzirá a quantidade de regimes encontrados, e consequentemente de parâmetros a estimar. A complexidade do modelo final gerado é reduzida a partir da identificação de redundâncias, sem perder o poder preditivo dos modelos TS-TARX .O trabalho conclui com exemplos ilustrativos e algumas aplicações em bases de dados sintéticas, e casos reais que auxiliarão o entendimento. / [en] The goal of this dissertation is to propose a test mechanism to evaluate the results obtained from the TS-TARX modeling procedure.The main motivation is to find a solution to a usual problem related to TS-TARX modeling: spurious models are generated in the process of dividing the space state of the independent variables.The model is a heuristics based on regression tree analysis, as discussed by Brieman -3, 1984-. The model used to estimate the parameters of the time series is a TARX -Threshold Autoregressive with eXternal variables-.The main idea is to find thresholds that split the independent variable space into regimes which can be described by a local linear model. In this process, the recursive least square regression model is preserved. From the combination of regression tree analysis and recursive least square regression techniques, the model becomes TS-TARX -Tree Structured - Threshold Autoregression with eXternal variables-.The works initiated by Aranha in -1, 2001- will be extended. In his works, from a given data base, one efficient algorithm generates a decision tree based on splitting rules, and the corresponding regression equations for each one of the regimes found.Spurious models may be generated either from its building procedure, or from the fact that a procedure to compare the resulting models had not been proposed.To fill this gap, a methodology will be proposed. In accordance with the statistical tests proposed by Chow in -5, 196-, a series of consecutive tests will be performed.The Chow tests will provide the tools to identify spurious models and to reduce the number of regimes found. The complexity of the final model, and the number of parameters to estimate are therefore reduced by the identification and elimination of redundancies, without bringing risks to the TS-TARX model predictive power.This work is concluded with illustrative examples and some applications to real data that will help the readers understanding.

Several industrial, scientific and commercial processes produce open-ended sequences of observations which are referred to as data streams. We can understand the phenomena responsible for such streams by analyzing data in terms of their inherent recurrences and behavior changes. Recurrences support the inference of more stable models, which are deprecated by behavior changes though. External influences are regarded as the main agent actuacting on the underlying phenomena to produce such modifications along time, such as new investments and market polices impacting on stocks, the human intervention on climate, etc. In the context of Machine Learning, there is a vast research branch interested in investigating the detection of such behavior changes which are also referred to as concept drifts. By detecting drifts, one can indicate the best moments to update modeling, therefore improving prediction results, the understanding and eventually the controlling of other influences governing the data stream. There are two main concept drift detection paradigms: the first based on supervised, and the second on unsupervised learning algorithms. The former faces great issues due to the labeling infeasibility when streams are produced at high frequencies and large volumes. The latter lacks in terms of theoretical foundations to provide detection guarantees. In addition, both paradigms do not adequately represent temporal dependencies among data observations. In this context, we introduce a novel approach to detect concept drifts by tackling two deficiencies of both paradigms: i) the instability involved in data modeling, and ii) the lack of time dependency representation. Our unsupervised approach is motivated by Carlsson and Memolis theoretical framework which ensures a stability property for hierarchical clustering algorithms regarding to data permutation. To take full advantage of such framework, we employed Takens embedding theorem to make data statistically independent after being mapped to phase spaces. Independent data were then grouped using the Permutation-Invariant Single-Linkage Clustering Algorithm (PISL), an adapted version of the agglomerative algorithm Single-Linkage, respecting the stability property proposed by Carlsson and Memoli. Our algorithm outputs dendrograms (seen as data models), which are proven to be equivalent to ultrametric spaces, therefore the detection of concept drifts is possible by comparing consecutive ultrametric spaces using the Gromov-Hausdorff (GH) distance. As result, model divergences are indeed associated to data changes. We performed two main experiments to compare our approach to others from the literature, one considering abrupt and another with gradual changes. Results confirm our approach is capable of detecting concept drifts, both abrupt and gradual ones, however it is more adequate to operate on complicated scenarios. The main contributions of this thesis are: i) the usage of Takens embedding theorem as tool to provide statistical independence to data streams; ii) the implementation of PISL in conjunction with GH (called PISLGH); iii) a comparison of detection algorithms in different scenarios; and, finally, iv) an R package (called streamChaos) that provides tools for processing nonlinear data streams as well as other algorithms to detect concept drifts. / Diversos processos industriais, científicos e comerciais produzem sequências de observações continuamente, teoricamente infinitas, denominadas fluxos de dados. Pela análise das recorrências e das mudanças de comportamento desses fluxos, é possível obter informações sobre o fenômeno que os produziu. A inferência de modelos estáveis para tais fluxos é suportada pelo estudo das recorrências dos dados, enquanto é prejudicada pelas mudanças de comportamento. Essas mudanças são produzidas principalmente por influências externas ainda desconhecidas pelos modelos vigentes, tal como ocorre quando novas estratégias de investimento surgem na bolsa de valores, ou quando há intervenções humanas no clima, etc. No contexto de Aprendizado de Máquina (AM), várias pesquisas têm sido realizadas para investigar essas variações nos fluxos de dados, referidas como mudanças de conceito. Sua detecção permite que os modelos possam ser atualizados a fim de apurar a predição, a compreensão e, eventualmente, controlar as influências que governam o fluxo de dados em estudo. Nesse cenário, algoritmos supervisionados sofrem com a limitação para rotular os dados quando esses são gerados em alta frequência e grandes volumes, e algoritmos não supervisionados carecem de fundamentação teórica para prover garantias na detecção de mudanças. Além disso, algoritmos de ambos paradigmas não representam adequadamente as dependências temporais entre observações dos fluxos. Nesse contexto, esta tese de doutorado introduz uma nova metodologia para detectar mudanças de conceito, na qual duas deficiências de ambos paradigmas de AM são confrontados: i) a instabilidade envolvida na modelagem dos dados, e ii) a representação das dependências temporais. Essa metodologia é motivada pelo arcabouço teórico de Carlsson e Memoli, que provê uma propriedade de estabilidade para algoritmos de agrupamento hierárquico com relação à permutação dos dados. Para usufruir desse arcabouço, as observações são embutidas pelo teorema de imersão de Takens, transformando-as em independentes. Esses dados são então agrupados pelo algoritmo Single-Linkage Invariante à Permutação (PISL), o qual respeita a propriedade de estabilidade de Carlsson e Memoli. A partir dos dados de entrada, esse algoritmo gera dendrogramas (ou modelos), que são equivalentes a espaços ultramétricos. Modelos sucessivos são comparados pela distância de Gromov-Hausdorff a fim de detectar mudanças de conceito no fluxo. Como resultado, as divergências dos modelos são de fato associadas a mudanças nos dados. Experimentos foram realizados, um considerando mudanças abruptas e o outro mudanças graduais. Os resultados confirmam que a metodologia proposta é capaz de detectar mudanças de conceito, tanto abruptas quanto graduais, no entanto ela é mais adequada para cenários mais complicados. As contribuições principais desta tese são: i) o uso do teorema de imersão de Takens para transformar os dados de entrada em independentes; ii) a implementação do algoritmo PISL em combinação com a distância de Gromov-Hausdorff (chamado PISLGH); iii) a comparação da metodologia proposta com outras da literatura em diferentes cenários; e, finalmente, iv) a disponibilização de um pacote em R (chamado streamChaos) que provê tanto ferramentas para processar fluxos de dados não lineares quanto diversos algoritmos para detectar mudanças de conceito.

Juraj Bodík Abstract This thesis is dealing with the following problem: Let us have two stationary time series with heavy- tailed marginal distributions. We want to detect whether they have a causal relation, i.e. if a change in one of them causes a change in the other. The question of distinguishing between causality and correlation is essential in many different science fields. Usual methods for causality detection are not well suited if the causal mechanisms only manifest themselves in extremes. In this thesis, we propose a new method that can help us in such a nontraditional case distinguish between correlation and causality. We define the so-called causal tail coefficient for time series, which, under some assumptions, correctly detects the asymmetrical causal relations between different time series. We will rigorously prove this claim, and we also propose a method on how to statistically estimate the causal tail coefficient from a finite number of data. The advantage is that this method works even if nonlinear relations and common ancestors are present. Moreover, we will mention how our method can help detect a time delay between the two time series. We will show how our method performs on some simulations. Finally, we will show on a real dataset how this method works, discussing a cause of...

In this study, we present two new frequency domain tests for testing the Gaussianity and linearity of a sixth-order stationary univariate time series. Both are two-stage tests. The first stage is a test for the Gaussianity of the series. Under Gaussianity, the estimated normalized bispectrum has an asymptotic chi-square distribution with two degrees of freedom. If Gaussianity is rejected, the test proceeds to the second stage, which tests for linearity. Under linearity, with non-Gaussian errors, the estimated normalized bispectrum has an asymptotic non-central chi-square distribution with two degrees of freedom and constant noncentrality parameter. If the process is nonlinear, the noncentrality parameter is nonconstant. At each stage, empirical distribution function (EDF) goodness-ofit (GOF) techniques are applied to the estimated normalized bispectrum by comparing the empirical CDF with the appropriate null asymptotic distribution. The two specific methods investigated are the Anderson-Darling and Cramer-von Mises tests. Under Gaussianity, the distribution is completely specified, and application is straight forward. However, if Gaussianity is rejected, the proposed application of the EDF tests involves a transformation to normality. The performance of the tests and a comparison of the EDF tests to existing time and frequency domain tests are investigated under a variety of circumstances through simulation. For illustration, the tests are applied to a number of data sets popular in the time series literature.

Der technologische Fortschritt hat in jüngster Zeit zu einer großen Zahl von Zeitreihenmessdaten über komplexe dynamische Systeme wie das Klimasystem, das Gehirn oder das globale ökonomische System geführt. Beispielsweise treten im Klimasystem Prozesse wie El Nino-Southern Oscillation (ENSO) mit dem indischen Monsun auf komplexe Art und Weise durch Telekonnektionen und Rückkopplungen in Wechselwirkung miteinander. Die Analyse der Messdaten zur Rekonstruktion der diesen Wechselwirkungen zugrunde liegenden kausalen Mechanismen ist eine Möglichkeit komplexe Systeme zu verstehen, insbesondere angesichts der unendlich-dimensionalen Komplexität der physikalischen Prozesse. Diese Dissertation verfolgt zwei Hauptfragen: (i) Wie können, ausgehend von multivariaten Zeitreihen, kausale Wechselwirkungen praktisch detektiert werden? (ii) Wie kann die Stärke kausaler Wechselwirkungen zwischen mehreren Prozessen in klar interpretierbarer Weise quantifiziert werden? Im ersten Teil der Arbeit werden die Theorie zur Detektion und Quantifikation nichtlinearer kausaler Wechselwirkungen (weiter-)entwickelt und wichtige Aspekte der Schätztheorie untersucht. Zur Quantifikation kausaler Wechselwirkungen wird ein physikalisch motivierter, informationstheoretischer Ansatz vorgeschlagen, umfangreich numerisch untersucht und durch analytische Resultate untermauert. Im zweiten Teil der Arbeit werden die entwickelten Methoden angewandt, um Hypothesen über kausale Wechselwirkungen in Klimadaten der vergangenen hundert Jahre zu testen und zu generieren. In einem zweiten, eher explorativen Schritt wird ein globaler Luftdruck-Datensatz analysiert, um wichtige treibende Prozesse in der Atmosphäre zu identifizieren. Abschließend wird aufgezeigt, wie die Quantifizierung von Wechselwirkungen Aufschluss über mögliche qualitative Veränderungen in der Klimadynamik (Kipppunkte) geben kann und wie kausal treibende Prozesse zur optimalen Vorhersage von Zeitreihen genutzt werden können. / Today''s scientific world produces a vastly growing and technology-driven abundance of time series data of such complex dynamical systems as the Earth''s climate, the brain, or the global economy. In the climate system multiple processes (e.g., El Nino-Southern Oscillation (ENSO) or the Indian Monsoon) interact in a complex, intertwined way involving teleconnections and feedback loops. Using the data to reconstruct the causal mechanisms underlying these interactions is one way to better understand such complex systems, especially given the infinite-dimensional complexity of the underlying physical equations. In this thesis, two main research questions are addressed: (i) How can general causal interactions be practically detected from multivariate time series? (ii) How can the strength of causal interactions between multiple processes be quantified in a well-interpretable way? In the first part of this thesis, the theory of detecting and quantifying general (linear and nonlinear) causal interactions is developed alongside with the important practical issues of estimation. To quantify causal interactions, a physically motivated, information-theoretic formalism is introduced. The formalism is extensively tested numerically and substantiated by rigorous mathematical results. In the second part of this thesis, the novel methods are applied to test and generate hypotheses on causal interactions in climate time series covering the 20th century up to the present. The results yield insights on an understanding of the Walker circulation and teleconnections of the ENSO system, for example with the Indian Monsoon. Further, in an exploratory way, a global surface pressure dataset is analyzed to identify key processes that drive and govern interactions in the global atmosphere. Finally, it is shown how quantifying interactions can be used to determine possible structural changes, termed tipping points, and as optimal predictors, here applied to the prediction of ENSO.

Abstract In time series analysis, we often find the trend of dynamic data changing with time. Using the traditional model fitting can't get a good explanation for dynamic data. Therefore, many scholars developed various methods for model construction. The major drawback with most of the methods is that personal viewpoint and experience in model selection are usually influenced in them. Therefore, this paper presents a new approach on genetic-based modeling for the nonlinear time series. The research is based on the concepts of evolution theory as well as natural selection. In order to find a leading model from the nonlinear time series, we make use of the evolution rule: survival of the fittest. Through the process of genetic evolution, the AIC (Akaike information criteria) is used as the adjust function, and the membership function of the best-fitted models are calculated as performance index of chromosome. Empirical example shows that the genetic model can give an efficient explanation in analyzing Taiwan exchange rates, especially when the structure change occurs.

近幾年來，非線性時間數列轉折點的研究愈來愈受到重視，學者們也提出許多關於轉折點的偵測及檢定方法。若考慮實際資料走勢轉變的情形，“轉折區間”的概念更可以解釋結構改變的現象。但文獻中對於如何找尋時間數列結構改變之轉折區間的研究並不多。本文擬以時間數列統計模式及模糊學理論的角度來研究，並結合遺傳演算的規則而提出主導模式的概念，來架構出時間數列遺傳模式，再藉由轉折區間決策法則來找出數列的轉折區間。其中，我們以統計模式為遺傳演化過程中的染色體，而以候選模式之隸屬度函數為衡量染色體適應能力的指標。最後，我們舉出臺灣股價收盤指數之實例，分別以我們所提出的方法及其他方法找出數列的轉折區間及轉折點，並做比較。 / For recent years, the research of change point in nonlinear time series has been considered to be more and more important. Scholars have proposed a lot of detecting and testing methods about change points.If considering the trend of real situation, the concept of change period will show the phenomena of structure change.But there are not many researches about how to find change period in time series.My paper is based on the points of time series models and fuzzy theory.Besides,it combines the rules of genetic algorithm and provides the concepts of leading model to construct time seriep genetic model and to find out change period by decision rule.ln this paper, we use time series statistical models as chromosome in procedure of genetic evolution, and we also use membership function of selected models as pereformance: index of chromosome.Finally, the empirical application about change periods and change points detecting by our method and other's for Taiwan stock closing prices is demonstrated and make a comparision with these results.

近幾年來，非線性時間數列分析有快速的發展。其中的門檻自迴歸模式(SETAR)，以具有許多線性ARIMA模式所不能配適的特性而受到重視。但是，自1978年Tong建立SETAR模式以來，門檻參數估計的問題一直是SETAR模式在發展應用上的一個瓶頸。本文將探討以實數編碼遺傳演算法，結合統計學上的模式選取準則，建構SETAR模式門檻與延遲參數估計程序的可行性。並從這個基礎上，進一步地研究較精確的門檻參數估計法。 / Non-linear time series analysis has rapidly developed in recent years. Self-exciting threshold autoregression(SETAR) model of non-linear time series models is attentive, because it has some characters which linear ARIMA model fail to fit. But, It has not yet been applied widely because the question of estimation of threshold parameter limits its development and application since Tong proposed SETAR model in 1978. In this paper, we will study the feasibility which constructs a procedure of estimation of SETAR's threshod and delay parameters with real-coded genetic algorithm and statistical criterion of model selection, and develop a more precise estimation of threshold parameter in the basis.

依時間順序出現之一連串觀測值，通常會呈現某一型態，而根據所產生的 型態可以作為判斷事件發生的基礎。例如，震波形成原因的判斷﹔追查環 境污染源﹔以及在醫學方面，辨識一個正常人心電圖的型態與患有心臟病 的病人其心電圖的型態…等。對於這些問題，傳統之辨識方法常因前提假 設的限制而失去其準確性。在本文中，我們應用神經網路中的逆向傳播演 算法則來訓練網路，並利用此受過訓練的網路來辨別線性時間數列ARIMA 及非線性時間數列 BL(1,0,1,1)。結果發現，網路對於模擬資料中雙線性 係數介於0.2至$0.8$之間的資料有高達$80\%$以上的辨識能力。而在實例 研究中，我們訓練網路來判斷震波形成的原因，其正確率亦高達80\%以上 。同時，我們也將神經網路應用在環境保護方面，訓練網路來判斷二地區 空氣品質的型態。 / A series of observations indexed in time often produces a pattern that may form a basis for discriminatingetween different classes of events. For instance, in theeology, what are the causes of seismic waves? a earthquakesr the nuclear explosions ?in the eathenics, we can use theethod to inquire the source which pollutes the air in somelace, and in the medicine, to distinguish the difference oflectrocardiograms between a health person and an a patient..ect. In this paper, we utilize the back-propagation to trainnetwork and use of the trained networks to judge the linearRIMA(1,0,0) model between the nonlinear BIL(1,0,1,1) model,e can find that the trained network has a good recognitionhose accurate rate is above 80\% for the coefficient of the bilinear model being equal to 0.5 or 0.8. In a living example, we have trained a network to decidehich is the cause of seismic wave, and the trained networkhose accurate rate is larger than 80\%. At the same time, e also applied neural network in environmental protection.