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Title: Model-free tests for the null hypothesis of stochastic trendless Authors:  Julio Angel Afonso-Rodriguez - University of the Balearic Islands (Spain) [presenting]
Abstract: There exists large evidence indicating that many macroeconomic and financial time series can be well characterized as containing a stochastic trend component, but exhibiting some periods of exuberance or high instability. Among some existing alternatives, this departure from the pure I(1) behaviour, or even from the local-level model, could be explained by the inclusion of an additional component allowing to capture these periods of excessive variability. The resulting generating mechanism is called stochastically integrated, and nests both conventional integration and stationarity, and the so-called case of heteroskedastic integration (HI). We study the theoretical properties of some commonly used testing procedures for the null hypothesis of conventional integration and stationarity under stochastic integration, and found that their outcomes can lead to wrong spurious evidence of stationarity or integration, respectively. Given these results, we adapt two existing statistics in the context of stochastic cointegration to test for the null of a stochastically trendless (ST) process against the alternative of I(1) and to test for the null of standard stationarity against the alternative of ST. Finally, we also consider the possibility of using modified versions of these procedures to test for the null of I(1) against the alternative of HI.