Essays in time series econometrics: Methods for improved finite-sample inference in nonstationary, noninvertible and nonlinear models

The first essay proposes a bootstrap method for constructing two-sided confidence intervals for the moving average parameter in nearly noninvertible models. The confidence intervals are obtained by inverting the acceptance region of the likelihood ratio (LR) test. The LR statistic reflects the asymmetry of the likelihood function that arises from the pile-up property of the maximum likelihood estimator near the noninvertibility boundary. Since the limiting distribution of the LR test is nonpivotal, its quantiles are parameterized as a function of the moving average parameter and approximated by grid bootstrap. The proposed method is used to investigate the parameter instability in inflation and time variability of risk premium in interest rates.; The second essay considers the construction of median unbiased forecasts for near-integrated autoregressive (AR) processes. It derives the appropriately scaled limiting distribution of the deviation of the point forecast from the true conditional mean. The dependence of the limiting distribution on a nuisance parameter precludes the use of the standard asymptotic and bootstrap methods for bias correction. For this purpose, we develop a method that generates bootstrap samples backward in time and approximates the median function of the predictive distribution on a grid of values of the nuisance parameter. The numerical results demonstrate the excellent properties of the bootstrap-based forecasts. The proposed procedure can be easily adapted to approximate any quantile of the conditional predictive distribution.; The third essay addresses some empirical problems in the term structure of interest rates using a nonlinear framework. It shows the potential of the threshold models to capture some important regularities in the data. We suggest some asymptotic and bootstrap approximations that ensure the validity of the statistical inference for nonlinearity in the presence of high persistence and conditional heteroskedasticity documented in the empirical studies of interest rates. The size and the power properties of these approximations are evaluated by simulation. The empirical results indicate a presence of nonlinearities in the conditional mean of the short rate and forecasting improvements of the threshold models with conditional heteroskedasticity over the traditional methods.