In this work the techniques of chaotic time series analysis are applied to music. The audio stream from musical recordings are treated as representing experimental data from a dynamical system. Several performance of well-known classical pieces are analysed using recurrence analysis, stationarity measures, information metrics, and other time series based approaches. The benefits of such analysi...

Previous studies indicated that nonlinear properties of Gaussian distributed time series with long-range correlations, u(i), can be detected and quantified by studying the correlations in the magnitude series |u(i)|, the "volatility." However, the origin for this empirical observation still remains unclear and the exact relation between the correlations in u(i) and the correlations in |u(i)| is...

1 School of Information Science & Technology, East China Normal University, Shanghai 200241, China 2 Department of Mathematics, University of Rome “La Sapienza”, Piazzale Aldo Moro 2, 00185 Rome, Italy 3 Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy 4 Faculty of Engineering, Multimedia University, 63100 Cyberjaya, Selanger, Malaysia 5 College of ...

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of nonlinearity in a ge...

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments,...

Nonlinear time series analysis is a practical spinoff from complex dynamical systems theory and chaos theory. It allows one to characterize dynamical systems in which nonlinearities give rise to a complex temporal evolution. Importantly, this concept allows extracting information that cannot be resolved using classical linear techniques such as the power spectrum or spectral coherence. Applicat...

Time series modeling and analysis is central to most financial and econometric data modeling. With increased globalization in trade, commerce and finance, national variables like gross domestic productivity (GDP) and unemployment rate, market variables like indices and stock prices and global variables like commodity prices are more tightly coupled than ever before. This translates to the use o...

We propose a dynamic adaptive partitioning scheme for nonparametric analysis of stationary nonlinear time series. It yields estimates of the whole probability distribution of the underlying process. We use information from past values to construct adaptive partitioning in a dynamic fashion which is then diierent from the more common static schemes in the regression setup. The idea of dynamic pa...