A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test

Abstract

A class of stochastic unit-root bilinear processes, allowing for GARCH-type effects with asymmetries, is studied. Necessary and sufficient conditions for the strict and second-order stationarity of the error process are given. The strictly stationary solution is shown to be strongly mixing under mild additional assumptions. It follows that, in this model, the standard (non-stochastic) unit-root tests of Phillips-Perron and DickeyFuller are asymptotically valid to detect the presence of a (stochastic) unit-root. The finite sample properties of these tests are studied via Monte Carlo experiments. JEL classification: C22, C12, C52.

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Cite this paper

@inproceedings{Francq2017ACO, title={A class of stochastic unit-root bilinear processes: Mixing properties and unit-root test}, author={Christian Francq and Svetlana V Makarova and Jean-Michel Zak{\"{o}ıan and Takeshi Amemiya and A. Ronald Gallant and John Geweke and Cheng Hsiao and Peter M. W. Robinson and Arnold Zellner and Yacine A{\"{i}t-Sahalia and Badi H. Baltagi and Michael Brandt and Marcus J. Chambers and SONGNIAN CHEN and Manfred Deistler and Miguel Delgado and Jean-Marie Dufour and SYLVIA FRUHWIRTH and ERIC GHYSELS and John C. Ham and Javier Hidalgo and Han Hong and Yongmiao Hong and Bo E. Honor{\'e} and Maxwell L. King and Yuichi Kitamura and Naoto Kunitomo and Kajal Lahiri and Qi Li and Tong Li and Oliver Linton and James G. MacKinnon and Robert A McCulloch and Ingmar R. Prucha and Peter C. Reiss and {\'E}ric Renault and FRANK SCHORFHEIDE and Robin C. Sickles and Fallaw B. Sowell and Quang Hong Vuong and Edward J. Vytlacil and Tom J. Wansbeek and Andrew M. Weiss and Tao Zha and Jean-Michel Zako{\"{i}an}, year={2017} }