Abstract
The thesis contains the four chapters: Testing parameter constancy in unit root autoregressive models against continuous change; Dickey-Fuller type of tests against nonlinear dynamic models; Inference for unit roots in a panel smooth transition autoregressive model where the time dimension is fixed; Testing unit roots in nonlinear dynamic heterogeneous panels. In Chapter 1 we derive tests for parameter constancy when the data generating process is non-stationary against the hypothesis that the parameters of the model change smoothly over time. To obtain the asymptotic distributions of the tests we generalize many theoretical results, as well as new are introduced, in the area of unit roots . The results are derived under the assumption that the error term is a strong mixing. Small sample properties of the tests are investigated, and in particular, the power performances are satisfactory. In Chapter 2 we introduce several test statistics of testing the null hypotheses of a random walk (with or without drift) against models that accommodate a smooth nonlinear shift in the level, the dynamic structure, and the trend. We derive analytical limiting distributions for all tests. Finite sample properties are examined. The performance of the tests is compared to that of the classical unit root tests by Dickey-Fuller and Phillips and Perron, and is found to be superior in terms of power. In Chapter 3 we derive a unit root test against a Panel Logistic Smooth Transition Autoregressive (PLSTAR). The analysis is concentrated on the case where the time dimension is fixed and the cross section dimension tends to infinity. Under the null hypothesis of a unit root, we show that the LSDV estimator of the autoregressive parameter in the linear component of the model is inconsistent due to the inclusion of fixed effects. The test statistic, adjusted for the inconsistency, has an asymptotic normal distribution whose first two moments are calculated analytically. To complete the analysis, finite sample properties of the test are examined. We highlight scenarios under which the traditional panel unit root tests by Harris and Tzavalis have inferior or reasonable power compared to our test. In Chapter 4 we present a unit root test against a non-linear dynamic heterogeneous panel with each country modelled as an LSTAR model. All parameters are viewed as country specific. We allow for serially correlated residuals over time and heterogeneous variance among countries. The test is derived under three special cases: (i) the number of countries and observations over time are fixed, (ii) observations over time are fixed and the number of countries tend to infinity, and (iii) first letting the number of observations over time tend to infinity and thereafter the number of countries. Small sample properties of the test show modest size distortions and satisfactory power being superior to the Im, Pesaran and Shin t-type of test. We also show clear improvements in power compared to a univariate unit root test allowing for non-linearities under the alternative hypothesis.