Unit-Root tests in high-dimensional panels

The four chapters of this PhD thesis all concern panel unit-root tests, i.e., tests for the stationarity properties of a large number of time-series. The first chapter analyzes the testing problem in case stationary alternatives offset explosives ones. While the panel units are assumed to be independent in the first chapter, the subsequent chapters consider ‘second-generation’ panel unit-root tests which allow the different time series to be correlated through a factor structure. Chapter 2 considers two common approaches of modeling this dependence and shows that the associated unit-root testing problems are asymptotically equivalent. Using Le Cam’s theory of statistical experiments, an optimal test is derived jointly in both setups. Chapter 3 studies unit-root tests for the underlying common factors rather than the idiosyncratic parts. It is demonstrated that unit root tests can be applied to a number of different factor estimates as if the factor was observed. A similar result is obtained for the case in which the factors have non-zero mean innovations. The final Chapter 4 revisits the testing problem for the unobserved common factors but exploits additional observed covariates that are known to be stationary to obtain higher powers.