Adjusted Empirical Likelihood Method For Long-range Dependent Process

In this thesis, we first review some background knowledge about the empirical likelihood method and briefly summarized some main applications. Many empirical likelihood results about independent and short-range dependent processes have been obtained. However, the previous approaches can fail in the presence of strong depen-dence. We introduce an adjusted empirical likelihood method on the basis of Nordman’s method. Dividing the process into blocks, including adjustment term, we construct the empirical likelihood ratio. By strictly proving, we show Wilks’ theorem is correct by choosing some reasonable block adjustment term.About numerical studies, FARIMA process, a typical process, is stimulated by the circulant embedding method. To deal with the FARIMA process, we use empirical likelihood method and adjusted empirical likelihood method. Both show a good ob-served coverage fraction, and the adjusted one is a little better. Meanwhile, an adjusted empirical likelihood method perform different results, according to different choices of adjustment coefficient. An optimal one remains unsolved and is expected to be solved in the future.