arXiv 13 May 2023 · Econometrics · publishedJournal of Econometrics (2024)
arXiv:2305.08880 · PDF · DOI · OpenAlex · Extracted main text
This paper aims to address the issue of semiparametric efficiency for cointegration rank testing in finite-order vector autoregressive models, where the innovation distribution is considered an infinite-dimensional nuisance parameter. Our asymptotic analysis relies on Le Cam's theory of limit experiment, which in this context takes the form of Locally Asymptotically Brownian Functional (LABF). By leveraging the structural version of LABF, an Ornstein-Uhlenbeck experiment, we develop the asymptotic power envelopes of asymptotically invariant tests for both cases with and without a time trend. We propose feasible tests based on a nonparametrically estimated density and demonstrate that their power can achieve the semiparametric power envelopes, making them semiparametrically optimal. We validate the theoretical results through large-sample simulations and illustrate satisfactory size control and excellent power performance of our tests under small samples. In both cases with and without time trend, we show that a remarkable amount of additional power can be obtained from non-Gaussian distributions.
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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 | Boswijk, H. P., Jansson, M., and Nielsen, M (2015) Improved likelihood ratio tests for cointegration rank in the VAR model | 1.000 | 7 | 5 | 100% |
| 2 | van der Vaart, A (2000) Asymptotic Statistics | 1.000 | 6 | 3 | 100% |
| 3 | Lütkepohl, H. and Saikkonen, P (2000) Testing for the cointegrating rank of a VAR process with a time trend | 1.000 | 5 | 4 | 100% |
| 4 | Hallin, M., van den Akker, R., and Werker, B. J (2016) Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointe… | 1.000 | 5 | 3 | 100% |
| 5 | Elliott, G., Rothenberg, T. J., and Stock, J. H (1996) Efficient Tests for an Autoregressive Unit Root | 0.928 | 4 | 3 | 100% |
| 6 | Saikkonen, P. and Lutkepohl, H (2000) Trend adjustment prior to testing for the cointegrating rank of a vector autoregressive process | 0.843 | 3 | 3 | 100% |
| 7 | Zhou, B., Van den Akker, R., and Werker, B. J (2019) Semiparametrically point-optimal hybrid rank tests for unit roots self | 0.843 | 3 | 3 | 100% |
| 8 | Jansson, M (2008) Semiparametric power envelopes for tests of the unit root hypothesis | 0.811 | 4 | 2 | 100% |
| 9 | Jeganathan, P (1995) Some aspects of asymptotic theory with applications to time series models | 0.737 | 3 | 2 | 100% |
| 10 | Bickel, P. J (1982) On adaptive estimation | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 45 scored citations.