Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors |
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Authors: | Nunzio Cappuccio Diego Lubian |
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Institution: | (1) Department of Economics, University of Padova, Padova, Italy;(2) Department of Economics, University of Verona, Verona, Italy |
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Abstract: | The purpose of this paper is to investigate the asymptotic null distribution of stationarity and nonstationarity tests when
the distribution of the error term belongs to the normal domain of attraction of a stable law in any finite sample but the
error term is an i.i.d. process with finite variance as . This local-to-finite variance setup is helpful to highlight the behavior of test statistics under the null hypothesis in
the borderline or near borderline cases between finite and infinite variance and to assess the robustness of these test statistics
to small departures from the standard finite variance context. From an empirical point of view, our analysis can be useful
in settings where the (non)-existence of the (second) moments is not clear-cut, such as, for example, in the analysis of financial
time series. A Monte Carlo simulation study is performed to improve our understanding of the practical implications of the
limi theory we develop. The main purpose of the simulation experiment is to assess the size distortion of the unit root and
stationarity tests under investigation. |
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Keywords: | Stable distributions Unit root tests Stationarity tests Asymptotic distributions Local-to-finite variance Size distortion |
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