Complexity and time series analyses of natural and synthetic time series

In this thesis, two methods have been proposed to literature for analy- sing natural complex systems which have non equally sampled time series and recurrence plot analyses of paleoclimate records have been done to detect ext- reme climate events at past by using these methods. By using metric distance aproach which is explained in the first part of the thesis, recurrence plot analyses of oxygen isotope rate time series which are obtained from Secret Cave at China have been done. Results of the analyses show that the known events in the literature are statistically detected and some new events are suggested. Transformation Cost Time Series method which is explained at the se- cond part of the thesis, transform a non-equally sampled time series to equ- ally sampled time series by using the interval dynamics of system. By using this method, recurrence plot analyses of the oxygen isotope rate time series obtained from Secret Cave in Indonesia have been done. The recurrence plot analyses resulted in the statistically detection of events existed in the literature and new events were predicted statistically. At another study, same analyses has been applied to two time series for same case obtained from KNI-51 Cave in Australia and Dongge Cave in China. The %90 of events in the literature have been reproduced by using this method. Therefore, we analysed thecar- bon isotope rate data related with solar activity in the Northern Hemisphere using determinism in time series, then we compared this result with the re- sults obtained from KNI- 51 and Dongge caves. The correlation of these events revealed that there is an anti-phase monsoon regime between two regions and this situation is related with position of Sun