The purpose of this study is to investigate the asymptotics of a first order auto regressive unit root process, AR(1). The goal is to determine which tests could be used to test for the presence of a unit root in a first order auto regressive process. A unit root is present when the root of the characteristic equation of this process equals unity. In order to test for the presence of a unit roo...

In this paper the asymptotic properties of ARMA processes with complex-conjugate unit roots in the AR lag polynomial are studied. These processes behave quite di¤erently from regular unit root processes (with a single root equal to 1). In particular, the asymptotic properties of a standardized version of the periodogram for such processes are analyzed, and a nonparametric test of the complex un...

This paper presents the nonlinear IV methodology as an effective inferential basis for nonstationary panels. The nonlinear IV method resolves the inferential difficulties in testing for unit roots arising from the intrinsic heterogeneities and cross-dependencies of panel models. Individual units are allowed to be dependent through correlations among innovations, interrelatedness of short-run dy...

It is generally believed that for the power of unit root tests, only the time span and not the observation frequency matters. In this paper we show that the observation frequency does matter when the high-frequency data display fat tails and volatility clustering, as is typically the case for nancial time series such as exchange rate returns. Our claim builds on recent work on unit root and coi...

The contribution of this paper is three-fold. Firstly, a characterisation theorem of the sub-hypotheses comprising the seasonal unit root hypothesis is presented which provides a precise formulation of the alternative hypotheses against which regression-based seasonal unit root tests test. Secondly, it proposes regressionbased tests for the seasonal unit root hypothesis which allow a general se...

In this paper, several seasonal unit root tests are analysed in the context of structural breaks at known time and a new break corrected test is suggested. We show that the widely used HEGY test as well as an LM variant thereof are asymptotically robust to seasonal mean shifts of finite magnitude. In finite samples, however, experiments reveal that such tests suffer from severe size distortions...

We consider the bootstrap method for the covariates augmented DickeyFuller (CADF) unit root test suggested in Hansen (1995) which uses related variables to improve the power of univariate unit root tests. It is shown that there are substantial power gains from including correlated covariates. The limit distribution of the CADF test, however, depends on the nuisance parameter that represents the...

We propose a multiple imputation estimator for parameter estimation in a quantile regression model when some covariates are missing at random. The estimation procedure fully utilizes the entire dataset to achieve increased efficiency, and the resulting coefficient estimators are root-n consistent and asymptotically normal. To protect against possible model misspecification, we further propose a...

This paper uses a new non-parametric, unconditional, hyperbolic order-α quantile estimator to construct a hyperbolic version of the Malmquist index. Unlike traditional non-parametric efficiency estimators, the new estimator is both robust to data outliers and has a root-n convergence rate. We use this estimator to examine changes in the efficiency and productivity of U.S. banks between 1985 and...

This paper makes two main contributions to inference for conditional quantiles. First, we construct a generic confidence interval for a conditional quantile from any given estimator of the conditional quantile via the direct approach. Our generic confidence interval makes use of two estimates of the conditional quantile function evaluated at two appropriately chosen quantile levels. In contrast...