@@ -710,7 +710,7 @@ class DFGLS(UnitRootTest):
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appears to be a unit root.
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DFGLS differs from the ADF test in that an initial GLS detrending step
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- is used before a trend-less ADF regression is run [1]_ .
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+ is used before a trend-less ADF regression is run.
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Critical values and p-values when trend is 'c' are identical to
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the ADF. When trend is set to 'ct, they are from ...
@@ -737,8 +737,8 @@ class DFGLS(UnitRootTest):
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References
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----------
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- .. [1 ] Elliott, G. R., T. J. Rothenberg, and J. H. Stock. 1996. Efficient
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- bootstrap for an autoregressive unit root. Econometrica 64: 813-836
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+ .. [* ] Elliott, G. R., T. J. Rothenberg, and J. H. Stock. 1996. Efficient
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+ bootstrap for an autoregressive unit root. Econometrica 64: 813-836
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"""
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def __init__ (self , y , lags = None , trend = 'c' ,
@@ -873,17 +873,17 @@ class PhillipsPerron(UnitRootTest):
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Notes
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-----
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The null hypothesis of the Phillips-Perron (PP) test is that there is a
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- unit root, with the alternative that there is no unit root [1]_ . If the pvalue
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+ unit root, with the alternative that there is no unit root. If the pvalue
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is above a critical size, then the null cannot be rejected that there
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and the series appears to be a unit root.
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Unlike the ADF test, the regression estimated includes only one lag of
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the dependant variable, in addition to trend terms. Any serial
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correlation in the regression errors is accounted for using a long-run
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- variance estimator (currently Newey-West [2]_ ).
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+ variance estimator (currently Newey-West).
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The p-values are obtained through regression surface approximation from
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- MacKinnon (1994) using the updated 2010 tables ([3]_, [4]_) .
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+ MacKinnon (1994) using the updated 2010 tables.
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If the p-value is close to significant, then the critical values should be
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used to judge whether to reject the null.
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@@ -915,22 +915,22 @@ class PhillipsPerron(UnitRootTest):
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References
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----------
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.. [*] Hamilton, J. D. 1994. Time Series Analysis. Princeton: Princeton
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- University Press.
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+ University Press.
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- .. [2 ] Newey, W. K., and K. D. West. 1987. "A simple, positive
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- semidefinite, heteroskedasticity and autocorrelation consistent covariance
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- matrix". Econometrica 55, 703-708.
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+ .. [* ] Newey, W. K., and K. D. West. 1987. "A simple, positive
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+ semidefinite, heteroskedasticity and autocorrelation consistent covariance
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+ matrix". Econometrica 55, 703-708.
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- .. [1 ] Phillips, P. C. B., and P. Perron. 1988. "Testing for a unit root in
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- time series regression". Biometrika 75, 335-346.
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+ .. [* ] Phillips, P. C. B., and P. Perron. 1988. "Testing for a unit root in
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+ time series regression". Biometrika 75, 335-346.
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- .. [3 ] MacKinnon, J.G. 1994. "Approximate asymptotic distribution
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- functions for unit-root and cointegration bootstrap". Journal of
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- Business and Economic Statistics. 12, 167-76.
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+ .. [* ] MacKinnon, J.G. 1994. "Approximate asymptotic distribution
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+ functions for unit-root and cointegration bootstrap". Journal of
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+ Business and Economic Statistics. 12, 167-76.
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- .. [4 ] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests."
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- Queen's University, Dept of Economics, Working Papers. Available at
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- http://ideas.repec.org/p/qed/wpaper/1227.html
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+ .. [* ] MacKinnon, J.G. 2010. "Critical Values for Cointegration Tests."
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+ Queen's University, Dept of Economics, Working Papers. Available at
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+ http://ideas.repec.org/p/qed/wpaper/1227.html
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"""
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def __init__ (self , y , lags = None , trend = 'c' , test_type = 'tau' ):
@@ -1022,8 +1022,8 @@ class KPSS(UnitRootTest):
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lags : int, optional
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The number of lags to use in the Newey-West estimator of the long-run
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covariance. If omitted or None, the number of lags is calculated
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- with the data-dependent method of Hobijn et al. (1998) [2]_ . See also
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- Andrews (1991) [3]_ , Newey & West (1994) [4]_ , and Schwert (1989) [5]_ .
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+ with the data-dependent method of Hobijn et al. (1998). See also
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+ Andrews (1991), Newey & West (1994), and Schwert (1989).
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Set lags=-1 to use the old method that only depends on the sample
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size, 12 * (nobs/100) ** (1/4).
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trend : {'c', 'ct'}, optional
@@ -1047,7 +1047,7 @@ class KPSS(UnitRootTest):
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Notes
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-----
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The null hypothesis of the KPSS test is that the series is weakly
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- stationary and the alternative is that it is non-stationary [1]_ .
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+ stationary and the alternative is that it is non-stationary.
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If the p-value is above a critical size, then the null cannot be
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rejected that there and the series appears stationary.
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@@ -1075,22 +1075,22 @@ class KPSS(UnitRootTest):
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References
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----------
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- .. [3 ] Andrews, D.W.K. (1991). "Heteroskedasticity and autocorrelation
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- consistent covariance matrix estimation". Econometrica, 59: 817-858.
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+ .. [* ] Andrews, D.W.K. (1991). "Heteroskedasticity and autocorrelation
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+ consistent covariance matrix estimation". Econometrica, 59: 817-858.
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- .. [2 ] Hobijn, B., Frances, B.H., & Ooms, M. (2004). Generalizations
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- of the KPSS-test for stationarity. Statistica Neerlandica, 52: 483-502.
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+ .. [* ] Hobijn, B., Frances, B.H., & Ooms, M. (2004). Generalizations
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+ of the KPSS-test for stationarity. Statistica Neerlandica, 52: 483-502.
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- .. [1 ] Kwiatkowski, D.; Phillips, P. C. B.; Schmidt, P.; Shin, Y. (1992).
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- "Testing the null hypothesis of stationarity against the alternative of
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- a unit root". Journal of Econometrics 54 (1-3), 159-178
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+ .. [* ] Kwiatkowski, D.; Phillips, P. C. B.; Schmidt, P.; Shin, Y. (1992).
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+ "Testing the null hypothesis of stationarity against the alternative of
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+ a unit root". Journal of Econometrics 54 (1-3), 159-178
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- .. [4 ] Newey, W.K., & West, K.D. (1994). "Automatic lag selection in
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- covariance matrix estimation". Review of Economic Studies, 61: 631-653.
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+ .. [* ] Newey, W.K., & West, K.D. (1994). "Automatic lag selection in
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+ covariance matrix estimation". Review of Economic Studies, 61: 631-653.
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- .. [5 ] Schwert, G. W. (1989). "Tests for unit roots: A Monte Carlo
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- investigation". Journal of Business and Economic Statistics, 7 (2):
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- 147-159.
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+ .. [* ] Schwert, G. W. (1989). "Tests for unit roots: A Monte Carlo
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+ investigation". Journal of Business and Economic Statistics, 7 (2):
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+ 147-159.
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"""
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def __init__ (self , y , lags = None , trend = 'c' ):
@@ -1206,8 +1206,8 @@ class ZivotAndrews(UnitRootTest):
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-----
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H0 = unit root with a single structural break
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- Algorithm follows Baum (2004/2015) [1]_ approximation to original
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- Zivot-Andrews [2]_ method. Rather than performing an autolag regression at
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+ Algorithm follows Baum (2004/2015) approximation to original
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+ Zivot-Andrews method. Rather than performing an autolag regression at
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each candidate break period (as per the original paper), a single
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autolag regression is run up-front on the base model (constant + trend
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with no dummies) to determine the best lag length. This lag length is
@@ -1219,17 +1219,17 @@ class ZivotAndrews(UnitRootTest):
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References
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----------
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- .. [1 ] Baum, C.F. (2004). ZANDREWS: Stata module to calculate Zivot-Andrews
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- unit root test in presence of structural break," Statistical Software
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- Components S437301, Boston College Department of Economics, revised
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- 2015.
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+ .. [* ] Baum, C.F. (2004). ZANDREWS: Stata module to calculate Zivot-Andrews
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+ unit root test in presence of structural break," Statistical Software
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+ Components S437301, Boston College Department of Economics, revised
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+ 2015.
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.. [*] Schwert, G.W. (1989). Tests for unit roots: A Monte Carlo
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- investigation. Journal of Business & Economic Statistics, 7: 147-159.
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+ investigation. Journal of Business & Economic Statistics, 7: 147-159.
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- .. [2 ] Zivot, E., and Andrews, D.W.K. (1992). Further evidence on the great
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- crash, the oil-price shock, and the unit-root hypothesis. Journal of
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- Business & Economic Studies, 10: 251-270.
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+ .. [* ] Zivot, E., and Andrews, D.W.K. (1992). Further evidence on the great
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+ crash, the oil-price shock, and the unit-root hypothesis. Journal of
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+ Business & Economic Studies, 10: 251-270.
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"""
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def __init__ (self , y , lags = None , trend = 'c' , trim = 0.15 , max_lags = None , method = 'AIC' ):
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super (ZivotAndrews , self ).__init__ (y , lags , trend , ('c' , 't' , 'ct' ))
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