| The dissertation considers the theoretical study of long memory series and their empirical applications to international finance and climatic change. A considerable amount of recent work has centered on estimation and testing for long memory, fractionally integrated processes that are associated with hyperbolically decaying autocorrelations and impulse response weights. Often several related series are observed, and it is important to model the short- and long-range behavior of the individual series, as well as possible interdependencies between them.; In Chapter 2, we describe the maximum likelihood estimation procedure for univariate fractionally integrated ARMA and trend stationary-fractional white noise models, and multivariate ARFIMA models. We provide asymptotic results for the MLE estimates and simulation evidence on their finite sample properties.; In an application of univariate and multivariate long memory models to several related series of annual temperature and tree rings and to squared returns in exchange rates, chapter 3 and chapter 4 use an approximate time-domain maximum likelihood approach to fit the theoretical model developed in Chapter 2. Another empirical analysis in chapter 4 tests whether a system of exchange rates is cointegrated and whether spot and forward rates are cointegrated. |
