Mustafa R. Kılınç, Michael Massmann
arXiv 19 Apr 2024 · Econometrics · publishedJournal of Econometrics (2026)
arXiv:2404.12882 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we analyse the influence of estimating a constant term on the bias of the conditional sum-of-squares (CSS) estimator in a stationary or non-stationary type-II ARFIMA ($p_1$,$d$,$p_2$) model. We derive expressions for the estimator's bias and show that the leading term can be easily removed by a simple modification of the CSS objective function. We call this new estimator the modified conditional sum-of-squares (MCSS) estimator. We show theoretically and by means of Monte Carlo simulations that its performance relative to that of the CSS estimator is markedly improved even for small sample sizes. Finally, we revisit three classical short datasets that have in the past been described by ARFIMA($p_1$,$d$,$p_2$) models with constant term, namely the post-second World War real GNP data, the extended Nelson-Plosser data, and the Nile data.
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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 | Hualde, Javier and Nielsen, Morten Ø (2022) Truncated sum-of-squares estimation of fractional time series models with generalized power law trend | 1.000 | 7 | 3 | 100% |
| 2 | Lieberman, Offer and Phillips, Peter C B (2005) Expansions for approximate maximum likelihood estimators of the fractional difference parameter | 1.000 | 6 | 3 | 100% |
| 3 | Hualde, Javier and Robinson, Peter M (2011) Gaussian pseudo-maximum likelihood estimation of fractional time series models | 0.928 | 15 | 4 | 80% |
| 4 | Hassler, Uwe (2019) Time Series Analysis with Long Memory in View | 0.928 | 5 | 4 | 80% |
| 5 | Robinson, Peter M. and Velasco, Carlos (2015) Efficient inference on fractionally integrated panel data models with fixed effects | 0.928 | 4 | 4 | 100% |
| 6 | Hualde, Javier and Nielsen, Morten Ø (2020) Truncated sum of squares estimation of fractional time series models with deterministic trends | 0.913 | 25 | 5 | 76% |
| 7 | McCullagh, Peter and Tibshirani, Robert (1990) A simple method for the adjustment of profile likelihoods | 0.874 | 12 | 2 | 100% |
| 8 | Johansen, Søren and Nielsen, Morten Ø (2016) The role of initial values in conditional sum-of-squares estimation of nonstationary fractional time series models | 0.800 | 41 | 3 | 51% |
| 9 | Johansen, Søren (2008) A representation theory for a class of vector autoregressive models for fractional processes | 0.737 | 3 | 2 | 100% |
| 10 | Martellosio, Federico and Hillier, Grant (2020) Adjusted QMLE for the spatial autoregressive parameter | 0.737 | 3 | 2 | 100% |
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