Transfer Entropy and Applications to Ecosystem Atmospheric Data

Abstract

This thesis studies methods for inferring time series influences on one another. Specifically transfer entropy is motivated, derived and explained through informa- tion theory and Markov chains. Issues and solutions for the calculation of transfer entropy in the context of discrete, coarse grained and continuous time series are covered. The equality of Granger causality and transfer entropy in the Gaussian case is explored. Software package TISEAN for nonlinear time series analysis is explored and its capabilities are explained. In this thesis nonlinear methods are applied to measurements from SMEAR II station which is located in Hyytiälä Forestry Field Station in Hyytiälä, Finland. The problems caused by nonstationarity of the data are discussed and a solution to these problems is attempted. The ecosystem exchange is found to be nonstationary and containing two dif- ferent strong periodic components implying that the underlying dynamical system changes its characteristics. This prevented obtaining a phase space embedding from the measured data within the scope of this thesis. Further work is needed to find out whether transfer entropy can give new in- sights into analyzing the ecosystem and its influences. Rudimentary ground work has been laid with this thesis and possible ways of mitigating the nonstationarity in the future are given. All the code for reproducing the analysis and plots are included in the appendix to help future work.