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A counter‐example from chaos theory is used to challenge the augmented Dickey‐Fuller (ADF) test and common prewhitening techniques. The ADF test is applied to data constructed from a fully deterministic nonlinear (chaotic) process. The null hypothesis, that a unit root is present, cannot be rejected; "stationarity" is achieved by prewhitening. The largest Lyapunov exponent and the correlation dimension are estimated for the original and conditioned series in efforts to detect the nonlinearity and ascertain information regarding its specification. This is repeated in the presence of additive white noise. In no case is the procedure successful, nor is misspecification avoided. Along the way, the tests for nonlinearity provide evidence in support of the results of Nelson and Plosser (1982), that the removal of deterministic trends from time series that appear to be unit root processes can lead to spurious results.

In this paper alternative approaches for testing the unit root hypothesis in panel data are considered. First, a robust version of the Dickey‐Fuller t‐statistic under contemporaneous correlated errors is suggested. Second, the GLS t‐statistic is considered, which is based on the t‐statistic of the transformed model. The asymptotic power of both tests is compared against a sequence of local alternatives. To adjust for short‐run serial correlation of the errors, we propose a pre‐whitening procedure that yields a test statistic with a standard normal limiting distribution as N and T tends to infinity. The test procedure is further generalized to accommodate individual specific intercepts or linear time trends. From our Monte Carlo simulations it turns out that the robust OLS t‐statistic performs well with respect to size and power, whereas the GLS t‐statistic may suffer from severe size distortions in small and moderate sample sizes. The tests are applied to test for a unit root in real exchange rates.

AbstractA fundamental challenge facing applied time‐series analysts is how to draw inferences about long‐run relationships (LRR) when we are uncertain whether the data contain unit roots. Unit root tests are notoriously unreliable and often leave analysts uncertain, but popular extant methods hinge on correct classification. Webb, Linn, and Lebo (WLL; 2019) develop a framework for inference based on critical value bounds for hypothesis tests on the long‐run multiplier (LRM) that eschews unit root tests and incorporates the uncertainty inherent in identifying the dynamic properties of the data into inferences about LRRs. We show how the WLL bounds procedure can be applied to any fully specified regression model to solve this fundamental challenge, extend the results of WLL by presenting a general set of critical value bounds to be used in applied work, and demonstrate the empirical relevance of the LRM bounds procedure in two applications.

The statistical properties and historical characteristics of British industrial production are examined. Since 1923 production appears to follow a segmented trend stationary process. Prior historical information and recursive searching are used to identify discontinuities in 1973 and 1979. The wartime shift to fuller employment was accompanied by a productivity crash, and trend industrial growth changed little. The major shift in production trend was at the time of the 1973 oil shock. Discontinuity around 1979 took the form of a crash, and accelerating productivity contributed to industrial employment collapsing to levels not experienced since the nineteenth century.