So sánh phương pháp

	Kiểm định Fourier KPSS về tính dừng với các điểm đứt gãy cấu trúc trơn tru	Kiểm định tính dừng KPSS	Kiểm định nghiệm đơn vị Zivot-Andrews với một điểm đứt gãy cấu trúc
Lĩnh vực	Kinh tế lượng	Kinh tế lượng	Kinh tế lượng
Họ	Regression model	Regression model	Hypothesis test
Năm ra đời	2006	1992	1992
Người khởi xướng	Becker, Enders, and Lee	Kwiatkowski, Phillips, Schmidt & Shin	Eric Zivot & Donald Andrews
Loại	Stationarity test	Stationarity test (reverse of unit-root tests)	Sequential unit-root test with endogenous break-point selection
Công trình gốc	Becker, R., Enders, W., & Lee, J. (2006). A stationarity test in the presence of an unknown number of smooth breaks. Journal of Time Series Analysis, 27(3), 381-409.	Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178.	Zivot, E., & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis. Journal of Business & Economic Statistics, 10(3), 251–270.
Tên gọi khác	Fourier KPSS, flexible Fourier stationarity test, F-KPSS, KPSS with Fourier approximation	Kwiatkowski-Phillips-Schmidt-Shin test, stationarity test, KPSS durağanlık testi	ZA Test, Zivot-Andrews Break Test, Endogenous Break Unit-Root Test, Zivot-Andrews Birim Kök Testi
Liên quan	3	4	3
Tóm tắt	The Fourier KPSS test extends the standard KPSS stationarity test by embedding a flexible Fourier series in the deterministic component of the model. This approach captures smooth, gradual structural breaks in the level or trend of a time series without requiring the researcher to specify the number or timing of those breaks, yielding more reliable inference under structural change.	The KPSS test, introduced by Kwiatkowski, Phillips, Schmidt and Shin in 1992, tests the null hypothesis that a series is stationary against the alternative that it contains a unit root — the reverse of the ADF and Phillips-Perron tests. By flipping the burden of proof, it is designed to be used alongside unit-root tests so that the two can confirm one another and expose ambiguous, borderline cases.	The Zivot-Andrews (ZA) test, introduced by Eric Zivot and Donald Andrews in 1992, is a sequential unit-root test that allows for a single structural break at an unknown date. It extends the augmented Dickey-Fuller framework by endogenously selecting the break point that provides the strongest evidence against the unit-root null hypothesis, making it particularly useful for macroeconomic and financial time series that may have been disrupted by events such as policy changes, financial crises, or supply shocks.