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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.

This thesis is a collection of four essays with main focus on testing for a unit root under structural change, and on the behaviour of power-enhancing unit root tests that have recently emerged as a solution to the well-known power deficiency of traditional such tests. New tests and variants of commonly applied ones are introduced in response to the need for reliable statistical techniques in modelling economic series over time. The first essay explores the possibility that a time series may change structure from trend-stationarity to difference-stationarity, or vice versa as has been recognised by economists for several years. Taking difference-stationarity as the null hypothesis, tests are developed for this possibility, where neither the location nor direction of any possible change under the alternative hypothesis need be specified. Application of these tests to series on consumer price inflation in the G7 countries reveals evidence of a change from trend-stationarity to difference-stationarity in the majority of these countries. In the second essay we apply two elaboration principles of standard unit root tests in the more flexible setting of testing for a unit root against the alternative of stationarity around a smooth transition in linear trend. In comparison to the standard case, the modified tests within this context generate only moderate additional power, a phenomenon which appears to be related to the elaborate nature of the trend function under the alternative. An empirical application of the modified smooth transition tests to common macroeconomic time series in the US economy leads to stronger evidence in favour of the smooth transition alternative than do the unmodified tests. In the third essay we show that more powerful variants of commonly applied unit root tests to panel data, seeking mean or trend reversion, are readily available. Moreover, power gains persist when the modifications are applied to bootstrap procedures that may be employed when cross-correlation of a rather general sort among individual panel members is suspected. That such an approach can strongly influence inference is demonstrated through an application to a panel of real exchange rates against the US dollar. The final essay explores the behaviour of the power-enhancing unit root test most widely applied in the empirical literature. The principle issue is that such a test can have very low power for certain parameter configurations and sample sizes relative to conventional unit root tests. A theoretical attempt is made to identify these unsatisfactory cases relying on local to unity asymptotics, through investigation of the relative efficiencies in the case of an unknown mean. Extensive Monte Carlo results highlight the shortcomings of such a test under higher order autoregressive processes and indicate preference for its existing rivals.