Asymptotic and bootstrap tests for unit root and threshold cointegration

The first two essays of my dissertation provide comprehensive testing strategies for the presence of cointegration within threshold cointegration framework. In the first essay, I specify the dynamics of adjustment to the long-run equilibrium in a band type threshold vector error correction model. Since the threshold parameters are not identified under the null of no cointegration, the conventional sup-Wald type statistic is adopted. An asymptotic theory is developed to handle the nonstationary threshold variable. I propose a model-based bootstrap procedure in which the residuals are resampled independently with replacement. I show that the bootstrap is at least first-order correct. Monte Carlo simulations show that the bootstrap has reasonable size and attains better power than the conventional cointegration tests if threshold effects are present in the adjustment process.;In the second essay, I examine stationarity of the equilibrium error in a threshold autoregressive model, where the threshold variable is the lagged level of the equilibrium error. I extend the asymptotic theory developed in the first essay to the case of a mixing type innovation process and propose a residual-based block bootstrap to encompass the general dependent structure of the innovation. The asymptotic validity is established for this bootstrap, and Monte Carlo simulations are performed to find similar results as above. The proposed methods are applied to examine the law of one price hypothesis using the price indexes of used car markets from twenty nine different locations in the US.;In the third essay, I propose a modification of the ADF test to achieve reasonable size when the error exhibits a negative MA root. It is well known that many economic time series have a large negative moving average component. I justify my approach within a local asymptotic framework in which the MA root is local to negative one. A set of simulations shows that my test improves the finite sample size performance dramatically without losing substantial power. My method is illustrated using the inflation rate series from G7 countries.