Fuzzy clustering of univariate and multivariate time series by genetic multiobjective optimization

COMISEF Working Papers Series WPS-028 08/02/2010 URL: http://comisef.eu/files/wps028.pd

Evaluating dynamic covariance matrix forecasting and portfolio optimization

In this thesis we have evaluated the covariance forecasting ability of the simple moving average, the exponential moving average and the dynamic conditional correlation models. Overall we found that a dynamic portfolio can gain significant improvements by implementing a multivariate GARCH forecast. We further divided the global investment universe into sectors and regions in order to investigate the relative portfolio performance of several asset allocation strategies with both variance and conditional value at risk as a risk measure. We found that the choice of risk measure does not seem to heavily impact the asset allocation. As comparison to the dynamic portfolios we added regional/sector portfolios which where rebalanced after a 3% threshold rule. The regional portfolio was constructed to mimic the current strategy of the Norwegian Pension Fund Global. The max Sharpe portfolio for regions had the highest risk adjusted return, but suffered from a very high turnover. After being modified however, this strategy turned out to be superior even after transaction costs were imposed

On the identification of non-stationary factor models and their application to atmospherical data analysis

A numerical framework for data-based identification of nonstationary linear factor models is presented. The approach is based on the extension of the recently developed method for identification of persistent dynamical phases in multidimensional time series, permitting the identification of discontinuous temporal changes in underlying model parameters. The finite element method (FEM) discretization of the resulting variational functional is applied to reduce the dimensionality of the resulting problem and to construct the numerical iterative algorithm. The presented method results in the sparse sequential linear minimization problem with linear constrains. The performance of the framework is demonstrated for the following two application examples: (i) in the context of subgrid-scale parameterization for the Lorenz model with external forcing and (ii) in an analysis of climate impact factors acting on the blocking events in the upper troposphere. The importance of accounting for the nonstationarity issue is demonstrated in the second application example: modeling the 40-yr ECMWF Re-Analysis (ERA-40) geopotential time series via a single best stochastic model with time-independent coefficients leads to the conclusion that all of the considered external factors are found to be statistically insignificant, whereas considering the nonstationary model (which is demonstrated to be more appropriate in the sense of information theory) identified by the methodology presented in the paper results in identification of statistically significant external impact factor influences

Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping

The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series is determining their pairwise similarity, i.e., the degree to which a given time series resembles another. Traditional distance measures such as the Euclidean are not well-suited due to the time-dependent nature of the data. Elastic metrics such as dynamic time warping (DTW) offer a promising approach, but are limited by their computational complexity, non-differentiability and sensitivity to noise and outliers. This thesis proposes novel elastic alignment methods that use parametric \& diffeomorphic warping transformations as a means of overcoming the shortcomings of DTW-based metrics. The proposed method is differentiable \& invertible, well-suited for deep learning architectures, robust to noise and outliers, computationally efficient, and is expressive and flexible enough to capture complex patterns. Furthermore, a closed-form solution was developed for the gradient of these diffeomorphic transformations, which allows an efficient search in the parameter space, leading to better solutions at convergence. Leveraging the benefits of these closed-form diffeomorphic transformations, this thesis proposes a suite of advancements that include: (a) an enhanced temporal transformer network for time series alignment and averaging, (b) a deep-learning based time series classification model to simultaneously align and classify signals with high accuracy, (c) an incremental time series clustering algorithm that is warping-invariant, scalable and can operate under limited computational and time resources, and finally, (d) a normalizing flow model that enhances the flexibility of affine transformations in coupling and autoregressive layers.Comment: PhD Thesis, defended at the University of Navarra on July 17, 2023. 277 pages, 8 chapters, 1 appendi

HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ‘traditional’ set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality. This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified-easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox. Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis

Untangling hotel industry’s inefficiency: An SFA approach applied to a renowned Portuguese hotel chain

The present paper explores the technical efficiency of four hotels from Teixeira Duarte Group - a renowned Portuguese hotel chain. An efficiency ranking is established from these four hotel units located in Portugal using Stochastic Frontier Analysis. This methodology allows to discriminate between measurement error and systematic inefficiencies in the estimation process enabling to investigate the main inefficiency causes. Several suggestions concerning efficiency improvement are undertaken for each hotel studied.info:eu-repo/semantics/publishedVersio

Clustering and Classification of Multivariate Stochastic Time Series in the Time and Frequency Domains

The dissertation primarily investigates the characterization and discrimination of stochastic time series with an application to pattern recognition and fault detection. These techniques supplement traditional methodologies that make overly restrictive assumptions about the nature of a signal by accommodating stochastic behavior. The assumption that the signal under investigation is either deterministic or a deterministic signal polluted with white noise excludes an entire class of signals -- stochastic time series. The research is concerned with this class of signals almost exclusively. The investigation considers signals in both the time and the frequency domains and makes use of both model-based and model-free techniques. A comparison of two multivariate statistical discrimination techniques, one based on a traditional covariance statistic and one based on a more recently proposed periodogram based statistic, is carried out through simulation study. This investigation validates the utility of the periodogram based statistic over the covariance based statistic. The periodogram based statistic proves more useful in identifying statistical dissimilarities in multidimensional time series than the more traditional statistic. Attention is then focused on using the periodogram based statistic as a distance measure for clustering and classifying time series, which is motivated by the periodogram method\u27s increased discrimination capability. The test statistic is used in both clustering and classification algorithms, and the performance is evaluated though a simulation study. This measure proves capable of grouping like series together while simultaneously separating dissimilar series from one another. Finally, the techniques are adapted to the time-domain where they are used to cluster multidimensional, non-stationary, climatological data. The non-stationary model accounts for seasonal means, seasonal standard deviations, and stochastic components. The statistical approach results in the development of a level-α test for assessing signal equality. This improves upon typical dendrogram techniques by defining a level under which the distance should be considered zero. Climatological time series from the west coast, Gulf of Mexico, and east coast are analyzed using the aforementioned techniques. To complement the time series analysis work, some effort (Appendix A) is focused on improving the bachelor of science in the department of mechanical engineering via the undergraduate laboratories. This is accomplished by identifying desired outcomes and implementing specific improvements in the undergraduate laboratory courses over a period of four years. The effects of these improvements are quantified with survey results. Overall, the improvements are very well received and result in significant increases in student satisfaction