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| Kipimo cha Fourier Johansen Cointegration× | Kielelezo cha Usahihishaji wa Hitilafu wa Kielekezi (VECM)× | |
|---|---|---|
| Nyanja | Ekonometriki | Ekonometriki |
| Familia | Regression model | Regression model |
| Mwaka wa asili≠ | 2012 (Fourier extension); 1988 (Johansen original) | 1987 |
| Mwanzilishi≠ | Enders & Lee (Fourier extension); Johansen (original trace/max-eigenvalue test) | Robert F. Engle and Clive W. J. Granger |
| Aina≠ | Cointegration test with smooth structural breaks | Multivariate time-series model |
| Chanzo asilia≠ | Enders, W., & Lee, J. (2012). A unit root test using a Fourier series to approximate smooth breaks. Oxford Bulletin of Economics and Statistics, 74(4), 574–599. DOI ↗ | Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55(2), 251–276. DOI ↗ |
| Majina mbadala | Fourier Johansen test, Fourier-Johansen trace test, smooth-break Johansen cointegration, FJ cointegration | VECM, error correction VAR, cointegrated VAR, vector equilibrium correction model |
| Zinazohusiana | 5 | 5 |
| Muhtasari≠ | The Fourier Johansen cointegration test extends the classical Johansen trace and maximum-eigenvalue tests by embedding low-frequency Fourier terms in the deterministic component of the VECM. This allows the test to remain valid when cointegrating relationships experience gradual, smooth regime shifts that standard Johansen critical values do not accommodate. | The Vector Error Correction Model extends the Vector Autoregression (VAR) framework to a system of variables that share one or more long-run equilibrium relationships. It jointly models short-run dynamics and the speed at which each variable corrects back toward equilibrium after a shock, making it the standard tool for analysing cointegrated multivariate time series. |
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