Forecasting for Nonlinear and Nonstationary Systems Using Intrinsic Functional Decomposition Models

The purpose of this study is to develop nonlinear and nonstationary time series forecasting methods to address modeling and prediction of real-world, complex systems. Particular emphasis has been placed on nonlinear and nonstationary time series forecasting in systems and processes that are of interest to IE researchers. Two new advanced prediction methods are developed using nonlinear decomposition techniques and a battery of advanced statistical methods. The research methodologies include empirical mode decomposition (EMD)-based prediction, structural relationship identification (SRI) methodology, and intrinsic time-scale decomposition (ITD)-based prediction. The advantages of using these prediction methods are local characteristic time scales and the use of an adaptive basis that does not require a parametric functional form (during the decomposition process). The utilization of SRI methodology in ITD-based prediction also provides a relationship identification advantage that can be used to capture the interrelationships of variables in the system for prediction application. The empirical results of using these new prediction methods have shown a significant improvement in the accuracy for customer willingness-to-pay and automobile demand prediction applications.Industrial Engineering & Managemen

Skewness and nonstationarity measures applied to reliable speech endpoint detection

In this paper we are addressed to the problem of speech presence and silences detection. Speech signals possess properties to which higher order statistics are sensitive. Bispectral-based statistics have been proved a good alternative [3] to energy-based statistics in a speech presence detector scheme, but at the cost of computations. Three alternative methods are proposed for a reliable and more computationally efficient detection. Two, lag-and frequency-domain, methods for the computation of the IT and the OT contribution to total skew while keeping the ability of the statistic in [3]. And a method based in the integrated polyspectrum (IP).Peer Reviewe

Distance-based analysis of dynamical systems and time series by optimal transport

The concept of distance is a fundamental notion that forms a basis for the orientation in space. It is related to the scientific measurement process: quantitative measurements result in numerical values, and these can be immediately translated into distances. Vice versa, a set of mutual distances defines an abstract Euclidean space. Each system is thereby represented as a point, whose Euclidean distances approximate the original distances as close as possible. If the original distance measures interesting properties, these can be found back as interesting patterns in this space. This idea is applied to complex systems: The act of breathing, the structure and activity of the brain, and dynamical systems and time series in general. In all these situations, optimal transportation distances are used; these measure how much work is needed to transform one probability distribution into another. The reconstructed Euclidean space then permits to apply multivariate statistical methods. In particular, canonical discriminant analysis makes it possible to distinguish between distinct classes of systems, e.g., between healthy and diseased lungs. This offers new diagnostic perspectives in the assessment of lung and brain diseases, and also offers a new approach to numerical bifurcation analysis and to quantify synchronization in dynamical systems.LEI Universiteit LeidenNWO Computational Life Sciences, grant no. 635.100.006Analyse en stochastie