Estimation and testing of persistence in nonlinear and cyclical time series
Throughout this thesis, we are concerned with filling some of the gaps in the literature concerning parametric and semiparametric Whittle estimation of long-run and/or cyclical persistence in economic time series. In Chapter 2, we consider local Whittle estimation, and without relying on the assumption of a linear model, we establish sufficient conditions for consistency and provide expansions and rate of convergence for the estimator. In Chapter 3, we apply the results of Chapter 2 to examine the local Whittle estimator for the signal plus noise model and some special cases of it: structural model, nonlinear transformations of a Gaussian process, and long memory stochastic volatility model. Under these specifications, we establish the asymptotic properties of the estimator, and raise several issues concerning its rate of convergence and finite sample bias. In Chapter 4, we employ Monte-Carlo simulations to investigate the finite sample properties of the local Whittle estimator under the linear and nonlinear specifications of Chapters 2 and 3. Furthermore, we apply local Whittle estimation to expected and realized inflation rates, nominal and real interest rates, and transformations of foreign exchange rate returns, in order to assess their long-run persistence and address several issues that have appeared in the empirical literature. Finally, Chapter 5 presents two testing procedures, based on the parametric Whittle method, for the null hypothesis of no persistent component in the data. We derive the asymptotic properties of our test statistics, and moreover introduce and validate a bootstrap scheme for calculating their critical values. A Monte-Carlo study of the finite sample performance of our testing procedures, and an empirical application on the growth rate of industrial production and unemployment rate are also included.