Kung-Sik Chan, Simone Giannerini, Greta Goracci, Howell Tong
arXiv 23 Feb 2020 · Statistics — Methodology · publishedStatistica Sinica (2022) · 4 citations (OpenAlex)
arXiv:2002.09968 · PDF · DOI · OpenAlex · Extracted main text
Regulation is an important feature characterising many dynamical phenomena and can be tested within the threshold autoregressive setting, with the null hypothesis being a global non-stationary process. Nonetheless, this setting is debatable since data are often corrupted by measurement errors. Thus, it is more appropriate to consider a threshold autoregressive moving-average model as the general hypothesis. We implement this new setting with the integrated moving-average model of order one as the null hypothesis. We derive a Lagrange multiplier test which has an asymptotically similar null distribution and provide the first rigorous proof of tightness pertaining to testing for threshold nonlinearity against difference stationarity, which is of independent interest. Simulation studies show that the proposed approach enjoys less bias and higher power in detecting threshold regulation than existing tests when there are measurement errors. We apply the new approach to the daily real exchange rates of Eurozone countries. It lends support to the purchasing power parity hypothesis, via a nonlinear mean-reversion mechanism triggered upon crossing a threshold located in the extreme upper tail. Furthermore, we analyse the Eurozone series and propose a threshold autoregressive moving-average specification, which sheds new light on the purchasing power parity debate.
appendix boundary found by appendix_titled_section at “\Large Supplement for:\\ Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis.” · 47% of the source is main text. Read the extracted text to check this.
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 | F. Bec, M. Ben Salem, and M. Carrasco (2004) Tests for unit-root versus threshold specification with an application to the purchasing power parity relationship | 0.843 | 3 | 3 | 100% |
| 2 | G. Li and W.K. Li (2011) Testing a linear time series model against its threshold extension | 0.843 | 3 | 3 | 100% |
| 3 | K.-S. Chan and G. Goracci (2019) On the ergodicity of first-order threshold autoregressive moving-average processes self | 0.811 | 4 | 2 | 100% |
| 4 | T. Björk (2019) The Pedestrian’s Guide to Local Time, chapter Chapter 3, pages 43–67 | 0.644 | 2 | 2 | 100% |
| 5 | H.P. Boswijk and Y. Zu (2018) Adaptive Wild Bootstrap Tests for a Unit Root With Non‐Stationary Volatility | 0.644 | 2 | 2 | 100% |
| 6 | K.-S. Chan, S. Giannerini, G. Goracci, and H. Tong (2002) Unit-root test within a threshold ARMA framework self | 0.644 | 2 | 2 | 100% |
| 7 | K.-S. Chan (1886) Testing for threshold autoregression self | 0.644 | 2 | 2 | 100% |
| 8 | W. Enders and C.W.J. Granger (1998) Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates | 0.644 | 2 | 2 | 100% |
| 9 | G. Goracci, S. Giannerini, K.-S. Chan, and H. Tong (2020) Testing for threshold effects in the TARMA framework self | 0.644 | 2 | 2 | 100% |
| 10 | B.E. Hansen (1996) Inference when a nuisance parameter is not identified under the null hypothesis | 0.644 | 2 | 2 | 100% |
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