Greta Goracci, Simone Giannerini, Kung-Sik Chan, Howell Tong
arXiv 25 Mar 2021 · Statistics — Methodology · publishedStatistica Sinica (2021) · 1 citations (OpenAlex)
arXiv:2103.13977 · PDF · DOI · OpenAlex · Extracted main text
We present supremum Lagrange Multiplier tests to compare a linear ARMA specification against its threshold ARMA extension. We derive the asymptotic distribution of the test statistics both under the null hypothesis and contiguous local alternatives. Moreover, we prove the consistency of the tests. The Monte Carlo study shows that the tests enjoy good finite-sample properties, are robust against model mis-specification and their performance is not affected if the order of the model is unknown. The tests present a low computational burden and do not suffer from some of the drawbacks that affect the quasi-likelihood ratio setting. Lastly, we apply our tests to a time series of standardized tree-ring growth indexes and this can lead to new research in climate studies.
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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 | Ling, S. and Tong, H (2005) Testing for a linear MA model against threshold MA models self | 0.956 | 8 | 5 | 88% |
| 2 | Chan, K.-S (1990) Testing for threshold autoregression self | 0.928 | 4 | 3 | 100% |
| 3 | Li, G. and Li, W (2011) Testing a linear time series model against its threshold extension | 0.843 | 10 | 5 | 60% |
| 4 | Chan, K. S (1991) Percentage points of likelihood ratio tests for threshold autoregression self | 0.737 | 3 | 2 | 100% |
| 5 | Andrews, D (2003) Tests for parameter instability and structural change with unknown change point: A corrigendum | 0.644 | 2 | 2 | 100% |
| 6 | Chan, K.-S. and Goracci, G (2019) On the ergodicity of first-order threshold autoregressive moving-average processes self | 0.644 | 2 | 2 | 100% |
| 7 | Chan, K.-S., Giannerini, S., Goracci, G., and Tong, H (2020) Unit-root test within a threshold ARMA framework self | 0.644 | 2 | 2 | 100% |
| 8 | Goracci, G., Giannerini, S., Chan, K.-S., and Tong, H (2021) Supplement to: Testing for threshold effects in arma models self | 0.644 | 2 | 2 | 100% |
| 9 | Tong, H (2011) Threshold models in time series analysis–30 years on self | 0.511 | 2 | 1 | 100% |
| 10 | Billingsley, P (1968) Convergence of probability measure | 0.405 | 1 | 1 | 100% |
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