How Can We Define The Concept of Long Memory? An Econometric Survey

In this paper we discuss different aspects of long mzmory behavior and specify what kinds of parametric models follow them. We discuss the confusion which can arise when empirical autocorrelation function of a short memory process decreases in an hyperbolic way.Long-memory, Switching, Estimation theory, Spectral

Statistical modelling approaches with Bayesian tensor factorisations

We propose a flexible nonparametric Bayesian modelling of univariate and multivariate time series of count data based on conditional tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with non-linear serial dependence or, with an introduction of appropriate latent variables, as a Bayesian hierarchical model with conditionally independent Poisson distributed observations. Inference about the important lags and their complex interactions is achieved via Markov chain Monte Carlo. When the observed counts are large, we deal with the resulting computational complexity of the model by performing an initial analysis in a training set of the data that is not used further in the inference and prediction. Our methodology is illustrated using simulation experiments and real-world data. Our Bayesian tensor factorisations model can have a good performance in inference and prediction on time series of count data that tends to be non-linear, and in the meanwhile, can deal with Markov chains of linear or log-linear count data. Moreover, our Bayesian tensor factorisations model can capture higher-order interactions among the lags and then, maximal orders, in time series where the actual order of Markov chain of count data and serial dependence are unknown

Ensaios em análise técnica e cadeias de Markov

Doutoramento em EconomiaA hipótese do mercado eficiente (Fama, 1970) tem sido um dos mais fundamentais pilares da teoria financeira moderna. De acordo com a forma fraca da hipótese, os preços dos ativos financeiros devem refletir todas as informações disponíveis. Consequentemente, não é possível obter consistentemente retornos superiores à média do mercado com qualquer estratégia de investimento destinada a prever oscilações dos preços das ações com base em dados históricos (Fama, 1965; e Fama & Miller, 1972). No entanto, nas últimas décadas, estudos empíricos têm fornecido indícios de que os modelos utilizados para a previsão do mercado de ações com base em informações históricas, como a análise técnica (AT), podem conduzir a uma rentabilidade sustentável. Efetivamente, a metodologia da AT, uma das ferramentas de previsão de mercado financeiro mais ampla- mente utilizada, tem vindo a ser classificada como um método de alta performance, capaz de prever os mercados de ações. A AT é uma metodologia de previsão de preços e “timing“ de mercado que se baseia nas premissas de que os mercados oscilam por tendências, e de que essas tendências persistem, sugerindo algum tipo de dependência em série com base no seu comportamento passado. No jargão da AT, o mercado desconta tudo. Nesta dissertação, estudamos empiricamente a capacidade de previsão de indicadores de análise técnica e propomos um novo quadro teórico, baseado numa metodologia estatística e matemática bem definida. Neste sentido, apresentamos uma nova metodologia de AT, com base em cadeias de Markov multivariadas. Utilizando como fonte o modelo MTD- Probit proposto por Nicolau (2014), exploramos o uso da cadeia de Markov para explicar o desvio em relação à propriedade de Martingale quando o ”data-snooping” é estatisticamente controlado.The efficient market hypothesis (Fama, 1970) has been one of the most fundamen- tal pillars of modern financial theory. According to the weak-form of the efficient market hypothesis, prices should reflect all available information. Consequently, it should not be possible to earn excess returns consistently from any investment strategy that attempts to predict asset price movements based on historical data (Fama, 1965; and Fama & Miler,1972). Nevertheless, in recent decades, empirical studies have provided evidence that models used for forecasting stock markets, such as technical analysis (TA), which are based on past stock price and volume, can lead to sustainable profitability. Indeed, the TA methodology, which is one of the most widely-used financial market forecasting tools, has been classified as a high-performing method, capable of predicting the stock market. TA is classified as a price forecasting and market timing methodology, based on the assumptions that markets move in trends, and that these trends persist, suggesting some sort of serial dependency of the behavior of past prices series. In the TA jargon, market action discounts everything. In this dissertation, we empirically study the predictive power of technical analysis indicators and propose a new theoretical framework, based on a well-defined statistical and mathematical platform. Accordingly, we introduce a new TA methodology, based on multivariate Markov chains. Using as a source the MTD-Probit model proposed by Nicolau (2014), we explore the use of the Markov chain to explain the departure from the martingale property when data snooping is statistically controlled.N/

Informed Segmentation Approaches for Studying Time-Varying Functional Connectivity in Resting State fMRI

The brain is a complex dynamical system that is never truly “at rest”. Even in the absence of explicit task demands, the brain still manifests a stream of conscious thought, varying levels of vigilance and arousal, as well as a number of postulated ongoing “under the hood” functions such as memory consolidation. Over the past decade, the field of time-varying functional connectivity (TVFC) has emerged as a means of detecting dynamic reconfigurations of the network structure in the resting brain, as well as uncovering the relevance of these changing connectivity patterns with respect to cognition, behavior, and psychopathology. Since the nature and timescales of the underlying resting dynamics are unknown, methodologies that can detect changing temporal patterns in connectivity without imposing arbitrary timescales are required. Moreover, as the study of TVFC is still in its infancy, rigorous evaluation of new and existing methodologies is critical to better understand their behavior when applied in resting data, which lacks ground truth temporal landmarks against which accuracy can be assessed. In this dissertation, I contribute to the methodological component of the TVFC discourse. I propose two distinct, yet related, approaches for identifying TVFC using an informed segmentation framework. This data-driven framework bridges instantaneous and windowed approaches for studying TVFC, in an attempt to mitigate the limitations of each while simultaneously leveraging the advantages of both. I also present a comprehensive, head-to-head comparative analysis of several of the most promising TVFC methodologies proposed to date, which does not exist in the current body of literature.PHDBioinformaticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/170046/1/marlenad_1.pd