Uni-variate Unit Root and Stationarity Tests – Arranged

Up till now there are many unit root tests and stationary tests being developed, some are popular and regularly used and some are unique in terms of its application. Following table of unit root tests which have been derived from this article arranged in terms of its major property. In the end references for all tests are also mentioned.

Unit root tests with Ho: Series have a Unit root against H1: Series is Stationary
Dickey – Fuller Test (1979): DF Test
Dickey – Fuller Test (1979, 1981): ADF Test
Phillips – Perron (1988): PP Test
Elliot et al. (1996); DF-GLS Test
Point Optimal Test: P Test
Ng-Perron (2001); MZdα , MZdt, MSBd and MPdT test
Stationarity tests with H0: Series is stationary against H1: Series has a Unit Root
Kwiatkowski at al. (1992): KPSS Test
Leybourne – McCabe (1994)
Unit Root tests which allow for structural break both in H0 and H1
Perron (1989) [Break dates are exogenously specified]
Perron – Vogelsang (1992) [Break dates are endogenously determined]
Clemente et al. (1998) [considered non-trending series only (an additive and innovation outlier models)]
Lee- Strazicich (2003) [checking two breaks in H1]
Lee- Strazicich (2003) [checking one break in H1]
Kim – Perron (2009)
Unit Root tests which allow for structural break in H1
Zivot – Andrews (1992): ZA Test [checking one break in H1]
Lumsdaine – Papell (1997); LP Test  [checking two breaks in trend in H1]
Perron(1997)
Stationarity tests with structural breaks
Lee- Strazicich (2001) [checking break in H0]
Carrion-i-Silvestre – Sanso (2007) [checking two breaks in H0]
Special Unit root tests
Kapetanios et al. (2003): KSS Test [series is global stationary in H1]
Elliot – Jansson (2003); EJ Test [tests uses stationary covariates]
Panel Unit root tests
Unit Root tests with H0: common unit root against H1: Common stationary
Levin – Lin (1993); LL Test
Levin – Lin – Chu(2002); LLC Test
Harris – Tzavalis (1999)
Breitung – Das (1995) [account cross sectional dependence, use SUR estimation framework]
Unit root tests with H0: all have unit root against H1: some are stationary
Im – Pesaran – Shin (2003); IPS Test
Maddala – Wu (1999); Fisher test
Chang (2002) [account cross sectional dependence]
Pesaran (2007) [account cross sectional dependence]
Phillips – Su (2003) [account cross sectional dependence]
Moon – Perron (2004) [account cross sectional dependence]
Choi (2006) [account cross sectional dependence]
Pesaran – Smith – Yamagata (2009) [account cross sectional dependence]
Taylor – Sarno (1998); MADF Test [account cross sectional dependence]
Stationary test with H0: all are stationary against H1: some have unit root
Choi (2001)
Hadri (2000)
Harris – Leybourne – McCabe (2004) [account cross sectional dependence]
Demetrescu – Hassler – Tarcolea (2010) [account cross sectional dependence]
Unit root test which allow for structural breaks
Lee – Im – Tieslau (2005) LIT Test [account cross sectional dependence, allow for shift in level]
Hadri – Rao (2008) [account cross sectional dependence, allow for shift in level and trend]
Im – Lee – Tieslau (2010) ILT Test [account cross sectional dependence, allow for shift in level and trend]
Special Panel Unit root tests
Taylor – Sarno (1998) JLR Test [account cross sectional dependence, Cointegration based]
Breuer – McNown – Wallace (2001) [account cross sectional dependence, it can divide the panel into stationary and non stationary cross sections]

References:

Breitung, J. – Das, S. (2005). Panel unit root tests under cross-sectional dependence. Statistica Neerlandica, 59(4), 414-33.

Breuer, J. B. – McNown, R. – Wallace, M. (2002). Series-specific Unit Root Tests with Panel Data. Oxford Bulletin of Economics and Statistics, 64(5), 527-546.

Carrion-i-Silvestre, J. L. – Sansó, A. (2007). The KPSS test with two structural breaks. Spanish Economic review, 9(2), 105-27.

Chang, Y. (2002). Nonlinear IV Unit Root Tests in Panels with Cross-Sectional Dependency, Journal of Econometrics, 110(2), 261-92.

Choi, I. (2001). Unit Root Tests for Panel Data, Journal of International Money and Finance, 20(2), 249-72.

Choi, I. (2006). Combination Unit Root Tests for Cross-sectionally Correlated Panels. In: Corbae, D. – Durlauf, S. – Hansen, B. (Eds.), Econometric Theory and Practice: Frontiers of Analysis and Applied Research, essays in honor of Peter C. B. Phillips. Cambridge: Cambridge University Press.

Clemente, J. – Montanes, A. – Reyes, M. (1998). Testing for a unit root in variables with a double change in the mean. Economics Letters, 59(2), 175-182.

Dickey, D. A. – Fuller, W. A. (1979). Distribution of the Estimators for Autoregressive Time Series With a Unit Root. Journal of the American Statistical Association, 74(366), 427-31.

Dickey, D. A. – Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49(4), 1057-72.

Elliott, G. – Jansson, M. (2003). Testing for unit roots with stationary covariates. Journal of Econometrics, 115(1), 75-89.

Elliott, G. – Rothenberg, T. J. – Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64(4), 813-36.

Hadri, K. – Rao, Y. (2008). Panel stationarity test with structural break. Oxford Bulletin of Economics and Statistics, 70(2), 245-69.

Hadri, K. (2000). Testing for stationarity in heterogeneous panels. The Econometrics Journal, 3(2), 148-61.

Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.

Harris, D. – Leybourne, S. – McCabe, B. (2005). Panel Stationarity Tests for Purchasing Power Parity with Cross-Sectional Dependence. Journal of Busienss and Economic Statistics, 23(4), 395-409.

Harris, R. D. F. – Tzavalis, E. (1999). Inference for unit roots in dynamic panels where the time dimension is fixed. Journal of Econometrics, 91(2), 201-26. 25

Im, K. – Pesaran, M. – Shin, Y. (2003). Testing for Unit Roots in Heterogeneous Panels. Journal of Econometrics, 115(1), 53–74.

Im. S. K. – Lee, J. – Tieslau, M. (2010). Stationarity of Inflation: Evidence from Panel Unit Root Tests with Trend Shifts. 20th Annual Meetings of the Midwest Econometrics Group, Oct 1-2, 2010.

Kapetanios, G. – Shin, Y. – Snell, A. (2003). Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112(2), 359-379.

Kim, D. – Perron, P. (2009). Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses, Journal of Econometrics, 148(1), 1-13.

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, 159- 78.

Lee, J. – Strazicich, M. (2001). Testing the null of stationarity in the presence of a structural break. Applied Economics Letters, 8(6), 377-82.

Lee, J. – Strazicich, M. (2003). Minimum lagrange multiplier unit root test with two structural breaks. The Review of Economics and Statistics, 85(4), 1082-89.

Lee, J. – Strazicich, M. (2004). Minimum LM Unit Root Test with One Structural Break, Department of Economics, Appalachian State University, 04-16.

Lee, Junsoo, Kyung S. Im, and Margie Tieslau (2005), Panel LM unit root tests with level shifts, Oxford Bulletin of Economics and Statistics, 67(3), 393-419.

Levin, A. – Lin, C.F. – Chu, C.S. (2002). Unit Root Tests in Panel Data: Asymptotic and Finite Sample Properties. Journal of Econometrics, 108(1), 1–24.

Levin, A. – Lin, C.F. (1993). Unit Root Test in Panel Data: New Results, Discussion Paper, 93-56, Department of Economics, University of California at San Diego.

Leybourne, S. J. – McCabe, B. P. M. (1994). A consistent test for a Unit Root. Journal of Business & Economic Statistics, 12(2), 157-66.

Lumsdaine, R. L. – Papell, D. H. (1997). Multiple Trend Breaks and the Unit-Root Hypothesis, The Review of Economics and Statistics, 79(02), 212-218.

Maddala, G. – Wu, S. (1999). A Comparative Study of Unit Root Tests and a New Simple Test, Oxford Bulletin of Economics and Statistics, 61(0), 631-52.

Moon, H. – Perron, B. (2004). Testing for a Unit Root in Panels with Dynamic Factors. Journal of Econometrics, 122(1), 8–126..

Ng, S. – Perron, P. (1995). Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag. Journal of the American Statistical Association, 90(419), 268-81.

Ng, S. – Perron, P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica, 69(6), 1519-54.

Perron, P. – Vogelsang, T. J. (1992). Nonstationarity and level shifts with an application to purchasing power parity. Journal of Business & Economic Statistics, 10(3), 301-20.

Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica, 57(6), 1361-401.

Perron, P. (1997). Further evidence on breaking trend functions in macroeconomic variables. Journal of Econometrics, 80(2), 355-85.

Pesaran, M.H. – Smith, L.V. – Yamagata, T. (2009). A Panel Unit Root Test in the Presence of a Multifactor Error Structure. Working paper, Cambridge University. 28

Pesaran, M.H. (2007). A Simple Panel Unit Root Test In The Presence Of Cross Section Dependence, Journal of Applied Econometrics, 22(2), 265-312.

Phillips, P. C. B. – Perron, P. (1988). Testing for a unit root in time series regression. Biometrica, 75(2), 335-46.

Taylor, M. P. – Sarno, L. (1998). The behavior of real exchange rates during the post-Bretton Woods period. Journal of International Economics, 46(2), 281-312.

Zivot, E – Andrews, D. W. K. (1992). Further Evidence on the Great Crash, the Oil-Price Shock, ant the Unit-Root Hypothesis. Journal of Business & Economic Statistics, 10(03), 251- 270.

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2 thoughts on “Uni-variate Unit Root and Stationarity Tests – Arranged

  1. gashaw says:

    please can you do a unit root test of Lee, J. – Strazicich, M. i wanted to test the persistance of givernment policy on gross domestc saving.

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