arXiv 20 Oct 2022 · Econometrics
arXiv:2210.11398 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we use the results in Andrews and Cheng (2012), extended to allow for parameters to be near or at the boundary of the parameter space, to derive the asymptotic distributions of the two test statistics that are used in the two-step (testing) procedure proposed by Pedersen and Rahbek (2019). The latter aims at testing the null hypothesis that a GARCH-X type model, with exogenous covariates (X), reduces to a standard GARCH type model, while allowing the "GARCH parameter" to be unidentified. We then provide a characterization result for the asymptotic size of any test for testing this null hypothesis before numerically establishing a lower bound on the asymptotic size of the two-step procedure at the 5% nominal level. This lower bound exceeds the nominal level, revealing that the two-step procedure does not control asymptotic size. In a simulation study, we show that this finding is relevant for finite samples, in that the two-step procedure can suffer from overrejection in finite samples. We also propose a new test that, by construction, controls asymptotic size and is found to be more powerful than the two-step procedure when the "ARCH parameter" is "very small" (in which case the two-step procedure underrejects).
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Andrews, D. W. K (2001) Testing When a Parameter Is on the Boundary of the Maintained Hypothesis | 0.721 | 8 | 3 | 38% |
| 2 | Andrews, D. W. K. and X. Cheng (2012) Estimation and Inference With Weak, Semi-Strong, and Strong Identification | 0.644 | 2 | 2 | 100% |
| 3 | Pedersen, R. S. and A. Rahbek (2019) Testing GARCH-X Type Models | 0.644 | 2 | 2 | 100% |
| 4 | Andrews, D. W. K. and P. Guggenberger (2010) Asymptotic Size and a Problem With Subsampling and With the m out of n Bootstrap | 0.405 | 1 | 1 | 100% |
| 5 | Andrews, D. W. K (1999) Estimation When a Parameter Is on a Boundary | 0.405 | 1 | 1 | 100% |
| 6 | Cox, G (2022) Weak Identification with Bounds in a Class of Minimum Distance Models | 0.405 | 1 | 1 | 100% |
| 7 | Ketz, P (2018) Subvector inference when the true parameter vector may be near or at the boundary self | 0.405 | 1 | 1 | 100% |
| 8 | Kopylev, L. and B. Sinha (2011) On the asymptotic distribution of likelihood ratio test when parameters lie on the boundary | 0.405 | 1 | 1 | 100% |
| 9 | Leeb, H. and B. M. Pötscher (2005) Model selection and inference: Facts and fiction | 0.405 | 1 | 1 | 100% |
| 10 | Leeb, H. and B. M. Pötscher (2008) Can one estimate the unconditional distribution of post-model-selection estimators? | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 12 scored citations.