James A. Duffy, Sophocles Mavroeidis, Sam Wycherley
arXiv 17 Nov 2022 · Econometrics · publishedJournal of Econometrics (2025) · 3 citations (OpenAlex)
arXiv:2211.09604 · PDF · DOI · OpenAlex · Extracted main text
In the literature on nonlinear cointegration, a long-standing open problem relates to how a (nonlinear) vector autoregression, which provides a unified description of the short- and long-run dynamics of a vector of time series, can generate 'nonlinear cointegration' in the profound sense of those series sharing common nonlinear stochastic trends. We consider this problem in the setting of the censored and kinked structural VAR (CKSVAR), which provides a flexible yet tractable framework within which to model time series that are subject to threshold-type nonlinearities, such as those arising due to occasionally binding constraints, of which the zero lower bound (ZLB) on short-term nominal interest rates provides a leading example. We provide a complete characterisation of how common linear and nonlinear stochastic trends may be generated in this model, via unit roots and appropriate generalisations of the usual rank conditions, providing the first extension to date of the Granger-Johansen representation theorem to a nonlinearly cointegrated setting, and thereby giving the first successful treatment of the open problem. The limiting common trend processes include regulated, censored and kinked Brownian motions, none of which have previously appeared in the literature on cointegrated VARs. Our results and running examples illustrate that the CKSVAR is capable of supporting a far richer variety of long-run behaviour than is a linear VAR, in ways that may be particularly useful for the identification of structural parameters.
appendix boundary found by appendix_command · 56% 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 | Bykhovskaya, A. and J. A. Duffy (2024) The local to unity dynamic Tobit model self | 0.956 | 8 | 6 | 88% |
| 2 | Duffy, J. A., S. Mavroeidis, and S. Wycherley (2023) Stationarity with Occasionally Binding Constraints, arXiv:2307.06190 self | 0.928 | 5 | 4 | 80% |
| 3 | Johansen, S (1995) Likelihood-based Inference in Cointegrated Vector Autoregressive Models | 0.928 | 4 | 3 | 100% |
| 4 | Saikkonen, P (2008) Stability of regime switching error correction models under linear cointegration | 0.874 | 5 | 2 | 100% |
| 5 | Aruoba, S. B., M. Mlikota, F. Schorfheide, and S. Villalvazo (2022) SVARs with occasionally-binding constraints | 0.811 | 4 | 2 | 100% |
| 6 | Mavroeidis, S (2021) Identification at the zero lower bound self | 0.811 | 4 | 2 | 100% |
| 7 | Gonzalo, J. and J.-Y. Pitarakis (2006) Threshold effects in cointegrating relationships | 0.737 | 3 | 2 | 100% |
| 8 | Ascari, G., P. Bonomolo, and Q. Haque (2023) The long-run Phillips curve is a curve, De Nederlansche Bank Working Paper No.\ 789 | 0.644 | 2 | 2 | 100% |
| 9 | Cogley, T. and A. M. Sbordone (2008) Trend inflation, indexation, and inflation persistence in the New Keynesian Phillips curve | 0.644 | 2 | 2 | 100% |
| 10 | Cavaliere, G (2005) Limited time series with a unit root | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 71 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Inference on Common Trends in a Cointegrated Nonlinear SVAR | 0.963 | 169 | 7 |
| 2 | Structural Analysis of Vector Autoregressive Models | 0.405 | 1 | 1 |
| 3 | Estimation of a Dynamic Tobit Model with a Unit Root | 0.405 | 1 | 1 |