Nonparametric tests for unit roots and cointegration

Following Bierens (1997a,b) and Vogelsang (1998a,b), unit root tests can be constructed which are asymptotically invariant to parameters involved by the short run dynamics of the process. Such an approach is called nonparametric by Bierens (1997b) and can be used to test a wide range of nonlinear models. We consider three different versions of such a test. However, simulation results suggest that only the variance ratio statistic is able to compete with the traditional augmented Dickey-Fuller test. A straightforward generalization of the variance ratio statistic is suggested, which can be used to test the cointegration rank in the spirit of Johansen (1988).

[1]  N. Herrndorf.  A Functional Central Limit Theorem for Weakly Dependent Sequences of Random Variables , 1984 .

[2]  Serena Ng,et al.  Useful Modifications to some Unit Root Tests with Dependent Errors and their Local Asymptotic Properties , 1996 .

[3]  H. Bierens.  Nonparametric cointegration analysis , 1997 .

[4]  Fallaw Sowell,et al.  The Fractional Unit Root Distribution , 1990 .

[5]  C. Praagman,et al.  System Dynamics in Economic and Financial Models , 1997 .

[6]  Hiro Y. Toda.  Finite Sample Properties of Likelihood Ratio Tests for Cointegrating Ranks when Linear Trends are Present , 1994 .

[7]  D. Dickey,et al.  Testing for unit roots in autoregressive-moving average models of unknown order , 1984 .

[8]  S. Johansen.  STATISTICAL ANALYSIS OF COINTEGRATION VECTORS , 1988 .

[9]  D. Harris.  Principal Components Analysis of Cointegrated Time Series , 1997, Econometric Theory.

[10]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[11]  Herman J. Bierens,et al.  Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate☆ , 1997 .

[12]  C. Granger,et al.  An introduction to bilinear time series models , 1979 .

[13]  Katsuto Tanaka.  Testing for a Moving Average Unit Root , 1990, Econometric Theory.

[14]  S. Johansen,et al.  The role of the constant and linear terms in cointegration analysis of nonstationary variables , 1994 .

[15]  W. Fuller,et al.  Distribution of the Estimators for Autoregressive Time Series with a Unit Root , 1979 .

[16]  T. W. Anderson,et al.  Statistical analysis of time series , 1972 .

[17]  Peter C. B. Phillips,et al.  Towards a Unified Asymptotic Theory for Autoregression , 1987 .

[18]  Victor Solo,et al.  Asymptotics for Linear Processes , 1992 .

[19]  C. Z. Wei,et al.  Limiting Distributions of Least Squares Estimates of Unstable Autoregressive Processes , 1988 .

[20]  H. White,et al.  A Unified Theory of Estimation and Inference for Nonlinear Dynamic Models , 1988 .

[21]  Timothy J. Vogelsang,et al.  Trend Function Hypothesis Testing in the Presence of Serial Correlation , 1998 .

[22]  J. Breitung.  Rank Tests for Nonlinear Cointegration , 2001 .

[23]  James Davidson,et al.  Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes , 2002 .

[24]  P. Phillips.  Testing for a Unit Root in Time Series Regression , 1988 .

[25]  J. Stock,et al.  Efficient Tests for an Autoregressive Unit Root , 1992 .

[26]  P. Phillips,et al.  Statistical Inference in Regressions with Integrated Processes: Part 1 , 1988, Econometric Theory.

[27]  C. Gouriéroux,et al.  Rank tests for unit roots , 1997 .

[28]  Carmela Quintos.  Fully Modified Vector Autoregressive Inference in Partially Nonstationary Models , 1998 .

[29]  Timothy J. Vogelsang,et al.  Testing for a Shift in Mean Without Having to Estimate Serial-Correlation Parameters , 1998 .

[30]  S. Johansen.  Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models , 1991 .

[31]  G. Schwert,et al.  Tests for Unit Roots: a Monte Carlo Investigation , 1988 .

[32]  Norman R. Swanson,et al.  An introduction to stochastic unit-root processes , 1997 .

[33]  Mark P. Taylor,et al.  Nonlinear permanent – temporary decompositions in macroeconomics and finance* , 2002 .