Nonlinear projective filtering I: Background in chaos theory

We derive a locally projective noise reduction scheme for nonlinear time series using concepts from deterministic dynamical systems, or chaos theory. We will demonstrate its effectiveness with an example with known deterministic dynamics and discuss methods for the verification of the results in the case of an unknown deterministic system.Comment: 4 pages, PS figures, needs nolta.st

Recurrence-based time series analysis by means of complex network methods

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.Comment: To be published in International Journal of Bifurcation and Chaos (2011

Dynamical systems theory for music dynamics

We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of {\it temporal dynamics} in music. (i) Phase space portraits are constructed from the time series wherefrom the dimensionality is evaluated as a measure of the {\pit global} dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra ($\sim f^{-\nu}$) close to {\pit red noise} ($\nu \sim 2$) in the low frequency range. (iii) We define an information entropy which provides a measure of the {\pit local} dynamics in the musical piece; the entropy can be interpreted as an evaluation of the degree of {\it complexity} in the music, but there is no evidence of an analytical relation between local and global dynamics. These findings are based on computations performed on eighty sequences sampled in the music literature from the 18th to the 20th century.Comment: To appear in CHAOS. Figures and Tables (not included) can be obtained from [email protected]

Time Series Analysis in Flight Flutter Testing at the Air Force Flight Test Center: Concepts and Results

The Air Force Flight Test Center (AFFTC) flight flutter facility is described. Concepts of using a minicomputer-based time series analyzer and a modal analysis software package for flight flutter testing are examined. The results of several evaluations of the software package are given. The reasons for employing a minimum phase concept in analyzing response only signals are discussed. The use of a Laplace algorithm is shown to be effective for the modal analysis of time histories in flutter testing. Sample results from models and flight tests are provided. The limitations inherent in time series analysis methods are discussed, and the need for effective noise reduction techniques is noted. The use of digital time series analysis techniques in flutter testing is shown to be fast, accurate, and cost effective

Development and Validation of a Rule-based Time Series Complexity Scoring Technique to Support Design of Adaptive Forecasting DSS

Evidence from forecasting research gives reason to believe that understanding time series complexity can enable design of adaptive forecasting decision support systems (FDSSs) to positively support forecasting behaviors and accuracy of outcomes. Yet, such FDSS design capabilities have not been formally explored because there exists no systematic approach to identifying series complexity. This study describes the development and validation of a rule-based complexity scoring technique (CST) that generates a complexity score for time series using 12 rules that rely on 14 features of series. The rule-based schema was developed on 74 series and validated on 52 holdback series using well-accepted forecasting methods as benchmarks. A supporting experimental validation was conducted with 14 participants who generated 336 structured judgmental forecasts for sets of series classified as simple or complex by the CST. Benchmark comparisons validated the CST by confirming, as hypothesized, that forecasting accuracy was lower for series scored by the technique as complex when compared to the accuracy of those scored as simple. The study concludes with a comprehensive framework for design of FDSS that can integrate the CST to adaptively support forecasters under varied conditions of series complexity. The framework is founded on the concepts of restrictiveness and guidance and offers specific recommendations on how these elements can be built in FDSS to support complexity

Petyarra and Moffatt: 'Looking from the sky'

Moffatt’s Up in the Sky series draws attention to the relation between sky and earth, through the content and camera angles of the images. Similarly, Kathleen Petyarre’s Central Desert acrylic dot painting evokes this relation representing country and Dreaming from a celestial perspective—as she says ‘looking from the sky’. Yet here any association between these artists seems to end with the urban artist refusing to engage Aboriginal tradition and the desert artist focused on Dreaming, country and heritage. However, a further connection between these disparate works may also be discerned as each, in differing ways, transforms our conventional perceptions of space and time. Reading these images in relation to Walter Benjamin’s concepts of the auratic and of messianic time, I suggest that each restructures dimension and duration putting in question the (post)modern calibrations of our space/time experience. This paper stages an engagement between these artists’ works and Benjamin’s concepts exploring the variations and modifications of the spatial and the temporal that hybrid cross-cultural exchanges require and facilitate

Copulas and time series with long-ranged dependences

We review ideas on temporal dependences and recurrences in discrete time series from several areas of natural and social sciences. We revisit existing studies and redefine the relevant observables in the language of copulas (joint laws of the ranks). We propose that copulas provide an appropriate mathematical framework to study non-linear time dependences and related concepts - like aftershocks, Omori law, recurrences, waiting times. We also critically argue using this global approach that previous phenomenological attempts involving only a long-ranged autocorrelation function lacked complexity in that they were essentially mono-scale.Comment: 11 pages, 8 figure