This paper investigates the finite sample distribution of the least squares estimator of the autoregressive parameter in a first-order autoregressive model. Uniform asymptotic expansion for the distribution applicable to both stationary and nonstationary cases is obtained. Accuracy of the...

This study addresses the issue of the presence of a unit root on the growth rate estimation by the least-squares approach. We argue that when the log of a variable contains a unit root, i.e., it is not stationary then the growth rate estimate from the log-linear trend model is not a valid...

This paper considers the problem of testing for structural changes in the trend function of a univariate time series without any prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. We propose a new approach that builds on the work of Perron...

This paper investigates GLS detrending procedures for unit root tests against nonlinear stationary alternative hypotheses where deterministic components are assumed present in the series under investigation. It is found that the proposed procedures have considerable power gains in a majority of...

In this paper we propose tests based on GLS-detrending for testing the null hypothesis of deterministic seasonality. Unlike existing tests for deterministic seasonality, our tests do not suff er from asymptotic size distortions under near integration. We also investigate the behavior of the...

This study examines nonlinear adjustment effects in the purchasing power parity (PPP) between South Africa and her main currency trading partners; namely, the US, the UK, the Euro area, China and Japan. We use monthly data of the nominal exchange rates and domestic price level data collected...

Indices of financial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that...

In this paper two simple tests to distinguish between unit root processes and stationary nonlinear processes are proposed. New limit distribution results are provided, together with two F type test statistics for the joint unit root and linearity hypothesis against a specific nonlinear...

In ESTAR models it is usually difficult to determine parameter estimates, as it can be observed in the literature. We show that the phenomena of getting strongly biased estimators is a consequence of the so-called identification problem, the problem of properly distinguishing the transition...

This paper discusses model-based inference in an autoregressive model for fractional processes which allows the process to be fractional of order d or d-b. Fractional differencing involves infinitely many past values and because we are interested in nonstationary processes we model the data...