Long Memory Processes: Forecasts, Estimates and Extreme Values.

Summary This work concerns the study of Long Memory processes (LM in the following). After having recalled the concept of LM, we present, in Chapter 1, the Gegenbauer type LM processes. Properties are recalled, as well as methods of estimation and forecasting of series using these processes. In Chapter 2, we focus on non-Gaussian LM processes. A method to construct these processes is developed and used for estimations and forecasts of time series. Chapter 3, we study different problems occurring when modeling series using Gegenbauer processes, such as under-modeling. Chapter 4, we study the extreme behavior of processes by applying the results of Chapter 2. After stating some properties concerning the extreme behavior of some independent and stationary processes, we give properties of the extreme index for these processes.