Haofeng Liao, Xing Wang
arXiv 4 Aug 2026 · Econometrics
arXiv:2608.03773 · PDF · Extracted main text
This paper develops an econometric framework for analysing smooth structural change in cointegrated systems following a known intervention time. We consider a vector error-correction model in which the cointegration rank and the pre-intervention cointegrating structure are identified from a stable pre-intervention subsample. After the intervention, both the adjustment coefficients and the cointegrating vectors are allowed to evolve smoothly as functions of rescaled time, which are estimated using kernel-weighted local reduced-rank methods. The analysis is formulated directly in a cointegrated VAR/VECM system, which preserves the treatment of long-run relations and short-run error-correction dynamics. By working with the decomposition $Π(δ)=α(δ)β(δ)'$, the method separates changes in the equilibrium relation from those in the speed of adjustment. We also provide two tests for the parameter consistency and the post-intervention parameter smoothness respectively. An empirical application to energy market, foreign-exchange, and gold-market index around the 24 February 2022 Russia's invasion of Ukraine illustrates how the proposed approach distinguishes between a discrete regime shift and smooth post-intervention evolution. The results suggest that cointegrating relation among the price of Brent crude oil, the spot exchange rate (USD/EUR), and the Credit Suisse NASDAQ Gold Price Index has smoothly changed after the outbreak of war, instead of a constant long-run conintegration system in the pre-intervention period.
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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 | Phillips, Peter CB and Li, Degui and Gao, Jiti (2017) Estimating smooth structural change in cointegration models | 1.000 | 7 | 4 | 100% |
| 2 | Seo, Byeongseon (1998) Tests for structural change in cointegrated systems | 1.000 | 6 | 3 | 100% |
| 3 | Bierens, Herman J and Martins, Luis F (2010) Time-varying cointegration | 0.843 | 3 | 3 | 100% |
| 4 | Gregory, Allan W and Hansen, Bruce E (1996) Residual-based tests for cointegration in models with regime shifts | 0.737 | 3 | 2 | 100% |
| 5 | Park, Joon Y and Hahn, Sang B (1999) Cointegrating regressions with time varying coefficients | 0.737 | 3 | 2 | 100% |
| 6 | Johansen, Søren (1988) Statistical analysis of cointegration vectors | 0.585 | 3 | 1 | 100% |
| 7 | Baur, Dirk G and McDermott, Thomas K (2010) Is gold a safe haven? International evidence | 0.511 | 2 | 1 | 100% |
| 8 | Li, Degui and Phillips, Peter C. B. and Gao, Jiti (2020) Kernel-based inference in time-varying coefficient cointegrating regression | 0.511 | 2 | 1 | 100% |
| 9 | Andrews, Donald WK (1993) Tests for parameter instability and structural change with unknown change point | 0.405 | 1 | 1 | 100% |
| 10 | Andrews, Donald WK (1994) Asymptotics for semiparametric econometric models via stochastic equicontinuity | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 38 scored citations.