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Title: Bootstrap tests for integer-valued GARCH models with covariates Authors:  Adriana Cornea-Madeira - University of York (United Kingdom) [presenting]
Andreea Halunga - University of Bath (United Kingdom)
Abstract: Estimation and testing on the boundary of the parameter space is nontrivial, particularly if the variable of interest is discrete. We derive the asymptotic distribution of the QMLE and Wald test for the integer-valued GARCH model with covariates, INGARCH-X, when parameters are on the boundary. The asymptotic distribution of the Wald test is non-standard and, in general, non-pivotal. As a consequence of this, coupled with the poor finite sample properties of the Wald test, we propose an asymptotically valid parametric bootstrap procedure for testing the statistical significance of parameters in an INGARCH-X model. The Monte Carlo study reveals that the bootstrap procedure performs really well. We apply these results to test for temporal clustering in extra-tropical cyclones.