Nonlinear data modeling methods for multidimensional signal analysis

In this dissertation, various novel stochastic and deterministic nonlinear data models are proposed for the analysis of the discrete signals that are defined in multidimensional spaces. The purpose of choosing the multidimensional space is to analyze the data according to multiparameters at the same time. The reason of analysing nonlinear methods is their compatibility with chaotic and nonlinear behaviour of the data which are measured for natural events and in this thesis natural events are taken as case study. The comparison of stochastic and deterministic methods gives the opportunity to choose the most suitable model for the data of handled problem. As stochastic models, one and multidimensional versions of Mycielski method and different versions of Markov Chain Models are proposed. As determinsitic models, multidimensional polynoms, multidimensional splines, multidimensional Empirical Mode Decomposition and Wavelets are chosen. In addition a Markovian error tuning model is designed as an infrastructure to test these models, which is inspired from time varying and time invariant versions of the Hidden Markov Model. These comparative works try to reveals the phenomenon underlies the natural events as wind speed, solar radiation, temperature which are taken as case study in this work.