Likelihood inference in processes of Ornstein-Uhlenbeck type

In this thesis, the extension of the Ornstein-Uhlenbeck process is studied by first driving this model not by a classical Brownian motion but a more general Lévy process. This process, to which we will call a process of Ornstein-Uhlenbeck type, is then generalized to a fractionally integrated Ornstein-Uhlenbeck Lévy (FIOUL) process with the purpose to encompass a long range dependence. Our main goal is to develop a likelihood or quasi-likelihood statistical methodology to estimate the parameters of these processes. After studying some topics that are necessary for the sequel, we present in Chapter 3 a novel maximum likelihood estimation methodology to deal with a one-dimensional process of Ornstein-Uhlenbeck type. Chapter 4 extends this methodology to the multidimensional case. In Chapter 5 we propose a quasi-likelihood estimator for the FIOUL process. While the estimations in Chapters 3 and 4 are based on Fourier inversion techniques, the estimations in Chapter 5 are based on spectral techniques and more precisely on the Whittle minimum contrast estimator. Some particular stationary models are treated and a comprehensive simulation study is conducted to demonstrate the goodness of our approach.Chapter 1 Lévy processes Chapter 2 Processes of Ornstein-Uhlenbeck type Chapter 3 Maximum likelihood estimation in univariate processes of Ornstein-Uhlenbeck type Chapter 4 Maximum likelihood estimation in multivariate processes of Ornstein-Uhlenbeck type Chapter 5 Fractionally integrated processes of Ornstein-Uhlenbeck typestatus: publishe