مقایسهٔ روش‌ها

	آزمون ریشه واحد بیزی ADF	مدل تصحیح خطای برداری بیزی (Bayesian VECM)
حوزه	اقتصادسنجی	اقتصادسنجی
خانواده	Regression model	Regression model
سال پیدایش	1991–1992	2002–2005
پدیدآور	Sims & Uhlig (1991); Koop, Osiewalski & Steel (1992)	Kleibergen & Paap; Villani
نوع	Bayesian hypothesis test	Bayesian multivariate time series model
منبع بنیادین	Sims, C. A., & Uhlig, H. (1991). Understanding unit rooters: A helicopter tour. Econometrica, 59(6), 1591–1599.	Kleibergen, F., & Paap, R. (2002). Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration. Journal of Econometrics, 111(2), 223–249.
نام‌های دیگر	Bayesian ADF test, Bayesian unit root test, Bayesian Dickey-Fuller, BADF	Bayesian VECM, B-VECM, Bayesian cointegrated VAR, Bayesian vector error correction
مرتبط	6	5
خلاصه	The Bayesian Augmented Dickey-Fuller (BADF) unit root test re-frames the classical ADF test within a Bayesian framework. Rather than computing a frequentist p-value, it quantifies evidence for or against a unit root by comparing posterior probabilities or Bayes factors under the null (unit root) and alternative (stationarity) hypotheses, incorporating prior beliefs about the autoregressive parameter.	The Bayesian VECM combines the classical Vector Error Correction Model — which captures both short-run dynamics and long-run cointegrating relationships among non-stationary multivariate time series — with Bayesian prior distributions over the cointegrating rank and coefficient matrices. This allows principled uncertainty quantification, incorporation of economic theory as priors, and coherent inference even in small samples.