My dissertation develops a nonlinear cointegration method and a threshold unit root test, and applies them to the long-run money demand function estimation and the purchasing power parity, respectively.
In the first essay “A New Nonlinear Cointegration Method” I develop a new nonlinear cointegration method that can be used for the logarithmic function of an I(1) process in a more general time series setting. I propose a new estimator, and establish its asymptotic properties, such as consistency and asymptotic normality. Also for the statistical inference, I propose a fully-modified type technique.
My second essay “Money Demand Function Estimation by Nonlinear Cointegration” is an empirical application of the newly developed nonlinear cointegration method. I estimate three different functional forms of the long-run money demand. Two of them are nonlinear functions of the nominal interest rate that allow for the liquidity trap. Nonlinear cointegration method allows us to estimate different functional forms under the one assumption that the nominal interest rate is an I(1) process. For US, the new nonlinear cointegration method produces superior out-of-sample prediction performance than linear cointegration methods. Among the different functional forms, nonlinear functional forms outperform the linear functional form. For Japan, the nonlinear functional forms outperform the linear one in terms of out-of-sample prediction performance, however there is no significant difference among different estimation methods.
In the final essay of my dissertation "Correlation Robust Threshold Unit Root Tests" I proposes a new three-regime threshold unit root test that is robust against serial correlation in error terms. I use the similar bandwidth-type sequence to eliminate the consequence from discontinuity of the indicator function and general dependence structure in error terms. Since threshold parameters are not identified under the unit root null hypothesis, I consider a test statistic that is obtained by optimizing the t-statistic over the unidentified threshold parameters. I apply the new test to the purchasing power parity. I find that the new test can reject the unit root null hypothesis more often than the conventional unit root tests, such as ADF and PP tests.