Many techniques have been developed to measure the difficulty of forecasting data from an observed time series. This paper introduces a measure which we call the "forecast entropy" designed to measure the predictability of a time series. We use attractors reconstructed from the time series and the distributions in the regular and tangent spaces of the data which comprise the attractor. We then consider these distributions on different scales. We present a formula for calculating the forecast entropy. To provide a standard of predictability, we define an idealized random system whose forecast entropy will be maximal; we then use this measure to rescale the forecast entropy to lie in the range [0,1]. The time series obtained from several chaotic systems as well as from a pseudorandom system are studied using this measure. We present evidence that the forecast entropy can be used as a tool for determining optimal delays and embedding dimensions used for reconstructing better attractors. We also show that the forecast entropy of a random system has completely different characteristics from that of a deterministic one.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.69.066121 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
A dual decomposition integration and error correction model for carbon price prediction.
J Environ Manage
January 2025
School of Management, Xi'an University of Architecture and Technology, Xi'an, 710055, China.
Accurately predicting carbon prices is crucial for effective government decision-making and maintenance the stable operation of carbon markets. However, the instability and nonlinearity of carbon prices, driven by the complex interaction between economic, environmental, and political factors, often result in inaccurate predictions. To confront this challenge, this paper proposed a carbon price prediction model that integrates dual decomposition integration and error correction.
View Article and Find Full Text PDFA scaling law to model the effectiveness of identification techniques.
Nat Commun
January 2025
Data Science Institute, Imperial College London, London, UK.
AI techniques are increasingly being used to identify individuals both offline and online. However, quantifying their effectiveness at scale and, by extension, the risks they pose remains a significant challenge. Here, we propose a two-parameter Bayesian model for exact matching techniques and derive an analytical expression for correctness (κ), the fraction of people accurately identified in a population.
View Article and Find Full Text PDFEntropy as a Tool for the Analysis of Stock Market Efficiency During Periods of Crisis.
Entropy (Basel)
December 2024
Department of Corporate Finance and Public Finance, Faculty of Economics and Finance, Wroclaw University of Economics and Business, 53-345 Wroclaw, Poland.
In the article, we analyse the problem of the efficiency market hypothesis using entropy in moments of transition from a normal economic situation to crises or slowdowns in European, Asian and US stock markets and the economy in the years 2007-2023 (2008-2009, U.S. financial sector crises; 2020-2021, Pandemic period; and the 2022-2023 period of Russia's attack on Ukraine).
View Article and Find Full Text PDFPredictive Complexity of Quantum Subsystems.
Entropy (Basel)
December 2024
Department of Physics, University of Maryland, College Park, MD 20742-4111, USA.
We define predictive states and predictive complexity for quantum systems composed of distinct subsystems. This complexity is a generalization of entanglement entropy. It is inspired by the statistical or forecasting complexity of predictive state analysis of stochastic and complex systems theory but is intrinsically quantum.
View Article and Find Full Text PDFAir Quality Prediction Based on Singular Spectrum Analysis and Artificial Neural Networks.
Entropy (Basel)
December 2024
Department of Statistics, Federal University of Bahia, Salvador 40170-110, Brazil.
Singular spectrum analysis is a powerful nonparametric technique used to decompose the original time series into a set of components that can be interpreted as trend, seasonal, and noise. For their part, neural networks are a family of information-processing techniques capable of approximating highly nonlinear functions. This study proposes to improve the precision in the prediction of air quality.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!