Academic and applied researchers in economics have, in the last 10 years, become increasingly interested in the topic of chaotic dynamics. In this paper we undertake non-linear dynamical analysis of one representative time series taken from financial markets, namely the Standard and Poor's (S&P) Composite Price Index. The data is based upon (adjusted) daily data from 1928 to 1987 comprising 16 ...

One of the phenomena that can be observed when using neural networks for time series prediction is that the quality of forecasts is correlated to the dimensionality of data. Higher data dimensionality leads in most cases to higher prediction errors. This phenomenon is connected by some authors to the decrease of the variance of the distance between data points which occurs when the length of pr...

This paper investigates dynamics of a local search trajectory generated by running the Or-opt heuristic on the traveling salesman problem. This study evaluates the dynamics of the local search heuristic by estimating the correlation dimension for the search trajectory, and finds that the local heuristic search process exhibits the transition from high-dimensional stochastic to low-dimensional c...

The wheelset bearing play an important role in train running safety. In this paper, we introduce the nonlinear dynamical method to study the wheelset bearing vibration signal. Based on the comparative studies of the phase graph and the correlation dimension of the vibration signals under normal condition, outer peeling fault condition and rolling element electric erosion fault condition, the fo...

Three hundred patients were randomly selected as the research object, of which 150 were on Chinese medical treatment; rehabilitation of 150 people was recorded for each patient before and after treatment by the three outcome measures Fugle-Meyer baseline, NHISS baseline, and baseline BI , coupled with the treatment process spent in a variety of costs mainly medicine costs, medicine,laboratory t...

Ž . Temporal complexity of early ventricular fibrillation VF is re-assessed through measuring the correlation dimension Ž . D , entropy K and high-dimensional component s from electrocardiogram ECG recordings using the Gaussian kernel 2 2 algorithm. Seven representative ECG traces of induced VF among 53 pig subjects are selected for analysis. VF is found to have 80–90% low-dimensional determini...

Phase space reconstruction of financial time series has become an effective approach for financial system analysis. Since the phase space obtained by the traditional method had the large embedding dimension and was susceptible to noise, this paper proposed a novel phase space reconstruction approach based on manifold learning, called manifold learning-based phase space reconstruction (MLPSR), w...

Understanding the dynamics of the various components (and the mechanisms involved) in a river system and establishing precise relationships between them are important for an accurate description of the sediment transport phenomenon. Despite the significant progress achieved in the last century with the development of a variety of approaches, there is no generally accepted simple relationship be...

The aim of this paper is to study the (clinical) time-series data of three diseases with complex dynamics: Parkinson’s disease, Huntington’s disease and Amyotrophic Lateral Sclerosis. For this purpose, first all of the time series data are embedded in a vector space of suitable dimension and then the correlation dimension of the above mentioned diseases is estimated. The results are also compar...