Linganisha mbinu

	Kipimo cha Mizizi ya Kitengo cha ADF cha Kuvunja Muundo	Uchanganuzi wa Ugaidi wa Granger wa Vunja Muundo
Nyanja	Ekonometriki	Ekonometriki
Familia	Regression model	Regression model
Mwaka wa asili	1989-1992	1995-2010
Mwanzilishi	Perron (1989); Zivot and Andrews (1992)	Granger (1969) causality framework extended by Toda & Yamamoto (1995) and Balcilar et al. (2010)
Aina	Unit root test with structural break	Hypothesis test / time-series model
Chanzo asilia	Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica, 57(6), 1361-1401.	Toda, H. Y., & Yamamoto, T. (1995). Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics, 66(1-2), 225-250.
Majina mbadala	ADF with structural break, Perron unit root test, break-augmented ADF, unit root test with structural change	break-robust Granger causality, Granger causality under regime change, time-varying Granger causality, structural change Granger test
Zinazohusiana	6	3
Muhtasari	The structural break ADF unit root test extends the standard Augmented Dickey-Fuller test to allow for one or more discrete shifts in the level or trend of a time series. Because ignoring a structural break inflates the apparent persistence of a series, this test prevents false acceptance of the unit root null when the series is actually stationary around a shifting mean or trend.	Structural break Granger causality extends the classic Granger causality framework to accommodate regime shifts and parameter instability in time series. By detecting break points and testing causality within sub-samples or via rolling/recursive windows, it reveals whether a predictive relationship between variables switches on, switches off, or changes direction over time.