Specification and efficiency in econometrics

This dissertation explores the importance of efficiency and specification in unit root tests. The main contribution of this dissertation is the introduction of an adaptive estimator of the parameters of interest which is efficient even when the innovations of the data generating process are non-Gaussian. Consequently the unit root test based on the adaptive estimator has greater power than existing tests.;The first chapter introduces the adaptive estimator of the Dickey-Fuller model and establishes its efficiency when the density of the innovations has finite information. The asymptotic distribution of the unit root test is a convex combination of the Dickey-Fuller distribution and a mixture of normals where the weight is determined by the information of the density of the innovations. Under the alternative hypothesis, the unit root test based on the adaptive estimator has greater power than existing tests. The superior power of the unit root test is confirmed in a monte carlo study.;The second chapter analyses the size and power of an LM test of parameter stability of the GARCH(1, 1) model of conditional heteroskedasticity. The test has good size and power properties in comparison to existing tests. In an empirical study we find that the parameters of the GARCH(1, 1) model of the conditional variance of three stock price indices are unstable over time. Thus we can conclude that the GARCH(1, 1) model may not be adequate for modelling conditional heteroskedasticity.;In the third chapter we introduce the unit root test based on the adaptive estimator of both the conditional mean and variance. The Dickey-Fuller model is used as the specification of the conditional mean and the GARCH(1, 1) process is used to model the conditional variance. The asymptotic distribution of the unit root test is a convex combination of the Dickey-Fuller distribution and a mixture of normals where the weight is determined by the information of the density of the innovations and the parameters of the GARCH process. When there is no conditional heteroskedasticity present in the innovations, the asymptotic distribution collapses to the distribution in the first chapter. Under the alternative hypothesis, the unit root test has greater power than existing tests, including the test developed in the first chapter, i.e. improving the specification increases efficiency and power.