Economic theory frequently predicts the existence of equilibria in which the involved processes converge, in the long run, to a constant value or maintain a constant growth rate. Deviations from these equilibria can only be temporary as the economic forces will push the series back to their equilibrium patterns. The existence of the predicted equilibria, and equivalently whether their originating theories hold, can be tested statistically with the so called “unit root tests”. The hypothesis of interest is whether a series is a “unit root” process or a “stationary” one. A unit root process does not exhibit reverting behaviour around a constant mean or trend because every shock has a permanent effect and makes it fluctuate unpredictably. On the contrary, a stationary process revolves around a mean or a trend, from which every deviation is temporary. The existence of an equilibrium and therefore the validity of an economic theory can be confirmed when the related series are statistically found to be stationary.
In this Nottingham School of Economics working paper Yiannis Karavias and Elias Tzavalis propose powerful tests of the unit root hypothesis for panel data with few time series observations. The new tests are general enough to accommodate many characteristics of economic data: multiple structural changes, spatial dependence between different units, non-linear trends, heteroscedasticity and correlation between the different time periods. The structural breaks can be at known or unknown dates. For the latter case, analytic probability density functions of the asymptotic distributions of the tests are provided based on a minimum order statistic. The tests allow for general forms of spatial dependence for which the spatial weights matrix does not have to be defined due to the utilization of a non-parametric estimator. A set of sufficient conditions which determines admissible deterministic trend functions is also provided. Finally, extensive Monte Carlo experiments show the usefulness of the new tests.
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Granger Centre for Time Series Econometrics 2014-03, “Testing for unit roots in panels with structural changes, spatial and temporal dependence when the time dimension is finite” by Yiannis Karavias and Elias Tzavalis, 2014
Yiannis Karavias and Elias Tzavalis
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Posted on Tuesday 1st July 2014