Testing for Unit Roots with Prediction Errors

Testing for Seasonal Unit Roots

This paper examines, both theoretically and through Monte Carlo analysis, the implications of applying the HEGY seasonal root tests to a process that is periodically integrated. As an important special case, the random walk process is also considered. In the context of the HEGY regression, the asymptotic distribution of the zero frequency test statistic is dependent on the coefficients of the p...

Testing for unit roots in time series with level shifts

Tests for unit roots in univariate time series with level shifts are proposed and investigated The level shift is assumed to occur at a known time It may be a simple one time shift which can be captured by a dummy variable or it may have a more general form which can be modeled by some general nonlinear transition function There may also be more than one shift point and there may be other deter...

Testing for unit roots in autoregressions with multiple level shifts ∗

The asymptotic distributions of Augmented-Dickey-Fuller (ADF) unit root tests for autoregressive processes with a unit or near-unit root are discussed in the presence of multiple stochastic level shifts of large size occurring independently in time. The distributions depend on a Brownian motion and a Poisson-type jump process. Due to the latter, tests based on standard critical values experienc...

Testing for Unit Roots: What Should Students Be Taught?

Unit-root testing strategies are unnecessarily complicated because they do not exploit prior knowledge of the growth status of the time series, they worry about unrealistic outcomes, and they doubleor triple-test for unit roots. The authors provide a testing strategy that cuts through these complications and so facilitates teaching this dimension of the unit-root phenomenon. F tests are used as...

Testing for Seasonal Unit Roots in Periodic Integrated Autoregressive Processes