On the predictability of time series by metric entropy

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2006Includes bibliographical references (leaves: 48-49)Text in English; Abstract: Turkish and Englishxi, 55 leavesThe computation of the metric entropy, a measure of the loss of information along the attractor, from experimental time series is the main objective of this study. In this study, replacing the current warning systems (simple threshold based, on/off circuits), a new and promising prognosis system is tried to be achieved by the metric entropy, i.e. Kolmogorov . Sinai entropy, from chaotic time series. Additional to metric entropy, correlation dimension and time series statistical parameters were investigated.Condition monitoring of ball bearings and drill bits was achieved in the light of practical considerations of time series applications. Two different accelerated bearing run-to-failure test rigs were constructed and the prediction tests were performed.However, as a reason of shaft failure in both structures during the experiments, none of them is completed. Finally, drill bit breakage experiments were carried out. In the experiments, 10 small drill bits (1 mm ) were tested until they broke down, while vibration data were consecutively taken in equal time intervals. After the analysis, a consistent decrement in variation of metric entropy just before the breakage was observed. As a result of the experiment results, metric entropy variation could be proposed as an early warning system

Chaos in GDP

This paper presents an analysis of GDP and finds chaos in GDP. I tried to find a nonlinear lower-dimensional discrete dynamic macroeconomic model that would characterize GDP. This model is represented by a set of differential equations. I have used the Mathematica and MS Excel programs for the analysis

An analysis-forecast system for uncertainty modeling of wind speed: A case study of large-scale wind farms

© 2017 Elsevier Ltd The uncertainty analysis and modeling of wind speed, which has an essential influence on wind power systems, is consistently considered a challenging task. However, most investigations thus far were focused mainly on point forecasts, which in reality cannot facilitate quantitative characterization of the endogenous uncertainty involved. An analysis-forecast system that includes an analysis module and a forecast module and can provide appropriate scenarios for the dispatching and scheduling of a power system is devised in this study; this system superior to those presented in previous studies. In order to qualitatively and quantitatively investigate the uncertainty of wind speed, recurrence analysis techniques are effectively developed for application in the analysis module. Furthermore, in order to quantify the uncertainty accurately, a novel architecture aimed at uncertainty mining is devised for the forecast module, where a non-parametric model optimized by an improved multi-objective water cycle algorithm is considered a predictor for producing intervals for each mode component after feature selection. The results of extensive in-depth experiments show that the devised system is not only superior to the considered benchmark models, but also has good potential practical applications in wind power systems

Financial predictions using intelligent systems

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis presents a collection of practical techniques for analysing various market properties in order to design advanced self-evolving trading systems based on neural networks combined with a genetic algorithm optimisation approach. Nonlinear multivariate statistical models have gained increasing importance in financial time series analysis, as it is very hard to fmd statistically significant market inefficiencies using standard linear modes. Nonlinear models capture more of the underlying dynamics of these high dimensional noisy systems than traditional models, whilst at the same time making fewer restrictive assumptions about them. These adaptive trading systems can extract information about associated time varying processes that may not be readily captured by traditional models. In order to characterise the fmancial time series in terms of its dynamic nature, this research employs various methods such as fractal analysis, chaos theory and dynamical recurrence analysis. These techniques are used for evaluating whether markets are stochastic and deterministic or nonlinear and chaotic, and to discover regularities that are completely hidden in these time series and not detectable using conventional analysis. Particular emphasis is placed on examining the feasibility of prediction in fmancial time series and the analysis of extreme market events. The market's fractal structure and log-periodic oscillations, typical of periods before extreme events occur, are revealed through recurrence plots. Recurrence qualification analysis indicated a strong presence of structure, recurrence and determinism in the fmancial time series studied. Crucial fmancial time series transition periods were also detected. This research performs several tests on a large number of US and European stocks using methodologies inspired by both fundamental analysis and technical trading rules. Results from the tests show that profitable trading models utilising advanced nonlinear trading systems can be created after accounting for realistic transaction costs. The return achieved by applying the trading model to a portfolio of real price series differs significantly from that achieved by applying it to a randomly generated price series. In some cases, these models are compared against simpler alternative approaches to ensure that there is an added value in the use of these more complex models. The superior performance of multivariate nonlinear models is also demonstrated. The long-short trading strategies performed well in both bull and bear markets, as well as in a sideways market, showing a great degree of flexibility and adjustability to changing market conditions. Empirical evidence shows that information is not instantly incorporated into market pnces and supports the claim that the fmancial time series studied, for the periods analysed, are not entirely random. This research clearly shows that equity markets are partially inefficient and do not behave along lines dictated by the efficient market hypothesis

Synchronization and prediction of chaotic dynamics on networks of optoelectronic oscillators

The subject of this thesis is the exploration of chaotic synchronization for novel applications including time-series prediction and sensing. We begin by characterizing the nonlinear dynamics of an optoelectronic time-delayed feedback loop. We show that synchronization of an accurate numerical model to experimental measurements provides a way to assimilate data and forecast the future of deterministic chaotic behavior. Next, we implement an adaptive control method that maintains isochronal synchrony for a network of coupled feedback loops when the interaction strengths are unknown and time-varying. Control signals are used as real-time estimates of the variations present within the coupling paths. We analyze the stability of synchronous solutions for arbitrary coupling topologies via a modified master stability function that incorporates the adaptation response dynamics. Finally, we show that the master stability function, which is derived from a set of linearized equations, can also be experimentally measured using a two-node network, and it can be applied to predict the convergence behavior of large networks

Interdisciplinary application of nonlinear time series methods

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 general sense has to be inferred statistically. The paper reviews the relevant methods and discusses the implications for deterministic modeling. Most field measurements yield nonstationary time series, which poses a severe problem for their analysis. Recent progress in the detection and understanding of nonstationarity is reported. If a clear signature of approximate determinism is found, the notions of phase space, attractors, invariant manifolds etc. provide a convenient framework for time series analysis. Although the results have to be interpreted with great care, superior performance can be achieved for typical signal processing tasks. In particular, prediction and filtering of signals are discussed, as well as the classification of system states by means of time series recordings.Comment: 86 pages, 26 figure

Nonlinear and chaotic dynamics and its application to historical financial markets

Seit ungefähr 15 Jahren beschäftigt sich die ökonomische Forschung mit der Dynamik 'chaotischer' Systeme. Inzwischen hat die Chaosforschung bzw. -theorie einen festen Platz in der Wissenschaft, obgleich dem Enthusiasmus der ersten Phase vorsichtigere Überlegungen über die Leistungsfähigkeit dieses Ansatzes gewichen sind. Der vorliegende Beitrag versucht die Entwicklung knapp zu resümieren und entwickelt einige Ideen über mögliche Anwendungen der Chaos Theorie für die Wirtschaftsgeschichte bzw. deren Theorie. Ein Großteil der Chaosforschung hat sich mit der Analyse von Finanzmärkten beschäftigt. Der Autor gibt einen Überblick über diese Forschungsbemühungen. (ICE2)'For roughly 15 years, economic research has been involved with chaotic systems. During these years chaos theory took a firm place in science, although the enthusiasm of the first decade was followed by a more subdued kind of consideration. This might be the time to sum up some of the results and to develop some ideas concerning possible applications of chaos theory to economic history (and its theory). Since a good portion of the chaos research that has been done until now deals with financial markets, we consider that section of economics.' (author's abstract