BOOTSTRAP INFERENCE ON THE BOUNDARY OF THE PARAMETER SPACE WITH APPLICATION TO CONDITIONAL VOLATILITY MODELS
Giuseppe Cavaliere (),
Heino Bohn Nielsen,
Rasmus Søndergaard Pedersen and
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Heino Bohn Nielsen: Department of Economics, University of Copenhagen, Denmark
Rasmus Søndergaard Pedersen: Department of Economics, University of Copenhagen, Denmark
Anders Rahbek: Department of Economics, University of Copenhagen, Denmark
No 18-10, Discussion Papers from University of Copenhagen. Department of Economics
It is a well-established fact that testing a null hypothesis on the boundary of the parameter space, with an unknown number of nuisance parameters at the boundary, is infeasible in practice in the sense that limiting distributions of standard test statistics are non-pivotal. In particular, likelihood ratio statistics have limiting distributions which can be characterized in terms of quadratic forms minimized over cones, where the shape of the cones depends on the unknown location of the (possibly mulitiple) model parameters not restricted by the null hypothesis. We propose to solve this inference problem by a novel bootstrap, which we show to be valid under general conditions, irrespective of the presence of (unknown) nuisance parameters on the boundary. That is, the new bootstrap replicates the unknown limiting distribution of the likelihood ratio statistic under the null hypothesis and is bounded (in probability) under the alternative. The new bootstrap approach, which is very simple to implement, is based on shrinkage of the parameter estimates used to generate the bootstrap sample toward the boundary of the parameter space at an appropriate rate. As an application of our general theory, we treat the problem of inference in ?nite-order ARCH models with coefficients subject to inequality constraints. Extensive Monte Carlo simulations illustrate that the proposed bootstrap has attractive ?nite sample properties both under the null and under the alternative hypothesis.
Keywords: Inference on the boundary; Nuisance parameters on the boundary; ARCH models; Bootstrap (search for similar items in EconPapers)
JEL-codes: C12 C22 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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