Long range dependence in time series

Title: Long range dependence in time series Author: Alexander Till Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michaela Prokešová, Ph.D. Abstract: The diploma thesis demonstrates the necessity of a study of long range dependence, introduces fractional Gaussian noise and discusses possi- ble definitions of long memory. It is done by notions of ergodic theory and by second moment characteristics and spectral density. These definitions are confronted with the model of fractional Gaussian noise and with intuitive un- derstanding of long range memory. Relations and connections between these criteria are studied as well. The work is restricted to the study of discrete time processes. Method for Hurst index estimation for fractional Gaussian noise and it's application on logarithmic returns of shares of selected produ- cers of beer are included in this work.