DChaos: An R Package for Chaotic Time Series Analysis
Identificadores
URI: http://hdl.handle.net/20.500.12020/1240DOI: https://doi.org/10.32614/RJ-2021-036
Fecha
2021Tipo de documento
articleÁrea/s de conocimiento
Matemáticas y FísicaResumen
Chaos theory has been hailed as a revolution of thoughts and attracting ever-increasing
attention of many scientists from diverse disciplines. Chaotic systems are non-linear deterministic
dynamic systems which can behave like an erratic and apparently random motion. A relevant field
inside chaos theory is the detection of chaotic behavior from empirical time-series data. One of the
main features of chaos is the well-known initial-value sensitivity property. Methods and techniques
related to testing the hypothesis of chaos try to quantify the initial-value sensitive property estimating
the so-called Lyapunov exponents. This paper describes the main estimation methods of the Lyapunov
exponent from time series data. At the same time, we present the DChaos library. R users may
compute the delayed-coordinate embedding vector from time series data, estimates the best-fitted
neural net model from the delayed-coordinate embedding vectors, calculates analytically the partial
derivatives from the chosen neural nets model. They can also obtain the neural net estimator of the
Lyapunov exponent from the partial derivatives computed previously by two different procedures
and four ways of subsampling by blocks. To sum up, the DChaos package allows the R users to test
robustly the hypothesis of chaos in order to know if the data-generating process behind time series
behaves chaotically or not. The package’s functionality is illustrated by examples.