Qualitative identification of chaotic patterns in multidimensional time series
Mirko Dohnal, Jifri Lunacek, Tomáš Meluzín · 2010
Concepts of chaos have been introduced into time series theory relatively long time ago. However, multidimensional chaotic tasks are still prohibitively difficult to solve. Qualitative models are based on three values only - decreasing, constant, and increasing. A qualitative solution of a chaotic model gives a set of time scenarios. E.g. Lorenz model has 813 qualitative scenarios. There are 8222 transitions among the set of Lorenz scenarios. A qualitative interpretation of quantitative multidimensional time series is based on some quantitative smoothing algorithm followed by qualitative descriptions of the first and second derivatives. If a qualitative interpretation of a time series represents a path in the Lorenz oriented graph then the time series has the Lorenz chaotic patterns.