Mustafa R. Kılınç, Michael Massmann, Maximilian Ambros
arXiv 14 Oct 2024 · Econometrics
arXiv:2410.10749 · PDF · DOI · OpenAlex · Extracted main text
This note proposes semi-parametric tests for investigating whether a stochastic process is fractionally integrated of order $\delta$, where $|\delta| < 1/2$, when smooth trends are present in the model. We combine the semi-parametric approach by Iacone, Nielsen & Taylor (2022) to model the short range dependence with the use of Chebyshev polynomials by Cuestas & Gil-Alana to describe smooth trends. Our proposed statistics have standard limiting null distributions and match the asymptotic local power of infeasible tests based on unobserved errors. We also establish the conditions under which an information criterion can consistently estimate the order of the Chebyshev polynomial. The finite sample performance is evaluated using simulations, and an empirical application is given for the UK Great Ratios.
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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 | Lavielle, Marc and Moulines, Eric (2000) Least-squares estimation of an unknown number of shifts in a time series | 1.000 | 10 | 4 | 100% |
| 2 | Cuestas, Juan Carlos and Gil-Alaña, Luis Alberiko (2016) Testing for long memory in the presence of non-linear deterministic trends with Chebyshev polynomials | 1.000 | 6 | 3 | 100% |
| 3 | Iacone, Fabrizio and Nielsen, Morten Ørregaard and Taylor, AM Robert (2022) Semiparametric tests for the order of integration in the possible presence of level breaks | 0.913 | 21 | 4 | 76% |
| 4 | Kapetanios, George and Millard, Stephen and Petrova, Katerina and Pr… (2020) Time-varying cointegration with an application to the UK Great Ratios | 0.874 | 8 | 2 | 100% |
| 5 | Lobato, Ignacio N and Robinson, Peter M (1998) A nonparametric test for I(0) | 0.874 | 7 | 2 | 100% |
| 6 | Bierens, Herman J (1997) Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and… | 0.874 | 5 | 2 | 100% |
| 7 | Hall, Alastair R and Osborn, Denise R and Sakkas, Nikolaos (2013) Inference on structural breaks using information criteria | 0.874 | 5 | 2 | 100% |
| 8 | Shao, Xiaofeng and Wu, Wei Biao (2007) Local asymptotic powers of nonparametric and semiparametric tests for fractional integration | 0.836 | 12 | 4 | 58% |
| 9 | Shao, Xiaofeng and Wu, Wei Biao (2007) Local Whittle estimation of fractional integration for nonlinear processes | 0.725 | 7 | 2 | 57% |
| 10 | Bierens, Herman J and Martins, Luis F (2010) Time-varying cointegration | 0.644 | 2 | 2 | 100% |
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