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STATIONARITY TESTING WITH COVARIATES

Published online by Cambridge University Press:  05 March 2004

Michael Jansson
Michael Jansson
Affiliation:
University of California, Berkeley
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Abstract

Two new stationarity tests are proposed. Both tests can be viewed as generalizations of existing stationarity tests and dominate these in terms of local asymptotic power. Improvements are achieved by accommodating stationary covariates. A Monte Carlo investigation of the small sample properties of the tests is conducted, and an empirical illustration from international finance is provided.This paper has benefited from the comments of Pentti Saikkonen (the co-editor), two anonymous referees, and seminar participants at University of Aarhus, Indiana University, Purdue University, Stanford University, UC Riverside, the 2001 Nordic Econometric Meeting, and the 2001 NBER Summer Institute. A MATLAB program that implements the tests proposed in this paper is available at http://elsa.Berkeley.EDU/users/mjansson.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 1 , February 2004 , pp. 56 - 94
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817–858.Google Scholar
Andrews, D.W.K. & J.C. Monahan (1992) An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica 60, 953–966.Google Scholar
Basawa, I.V. & D.J. Scott (1983) Asymptotic Optimal Inference for Non-Ergodic Models. Springer-Verlag.
Billingsley, P. (1999) Convergence of Probability Measures, 2nd ed. Wiley.
Choi, I. (1994) Residual-based tests for the null of stationarity with application to U.S. macroeconomic time series. Econometric Theory 10, 720–746.Google Scholar
Choi, I. & B.C. Ahn (1995) Testing for cointegration in a system of equations. Econometric Theory 11, 952–983.Google Scholar
Culver, S.E. & D.H. Papell (1999) Long-run purchasing power parity with short-run data: Evidence with Journal of International Money and Finance 18, 751–768.Google Scholar
Davies, R.B. (1969) Beta-optimal tests and an application to the summary evaluation of experiments. Journal of the Royal Statistical Society, Series B 31, 524–538.Google Scholar
Elliott, G. & M. Jansson (2003) Testing for unit roots with stationary covariates. Journal of Econometrics 115, 75–89.Google Scholar
Engel, C. (2000) Long-run PPP may not hold after all. Journal of International Economics 57, 243–273.Google Scholar
Froot, K.A. & K. Rogoff (1995) Perspectives on PPP and long-run real exchange rates. In G. Grossman & K. Rogoff (eds.), Handbook of International Economics, vol. 3, pp. 1647–1688. North-Holland.
Hansen, B.E. (1992) Convergence to stochastic integrals for dependent heterogeneous processes. Econometric Theory 8, 489–500.Google Scholar
Hansen, B.E. (1995) Rethinking the univariate approach to unit root testing: Using covariates to increase power. Econometric Theory 11, 1148–1171.Google Scholar
Horvath, M.T.K. & M.W. Watson (1995) Testing for cointegration when some of the cointegrating vectors are prespecified. Econometric Theory 11, 984–1014.Google Scholar
Jansson, M. (2002) Consistent covariance matrix estimation for linear processes. Econometric Theory 18, 1449–1459.Google Scholar
Jansson, M. (2003) Point Optimal Tests of the Null Hypothesis of Cointegration. Working paper, UC Berkeley.
Jansson, M. & N. Haldrup (2002) Regression theory for nearly cointegrated time series. Econometric Theory 18, 1309–1335.Google Scholar
Kuo, B.-S. & A. Mikkola (1999) Re-examining long-run purchasing power parity. Journal of International Money and Finance 18, 251–266.Google Scholar
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, & Y. Shin (1992) 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? Journal of Econometrics 54, 159–178.Google Scholar
LaMotte, L.R. & A. McWorther (1978) An exact test for the presence of random walk coefficients in a linear regression model. Journal of the American Statistical Association 73, 816–820.Google Scholar
Leybourne, S.J. & B.P.M. McCabe (1994) A consistent test for a unit root. Journal of Business and Economic Statistics 12, 157–166.Google Scholar
Nabeya, S. & K. Tanaka (1988) Asymptotic theory of a test for the constancy of regression coefficients against the random walk alternative. Annals of Statistics 16, 218–235.Google Scholar
Nyblom, J. (1986) Testing for deterministic linear trend in time series. Journal of the American Statistical Association 81, 545–549.Google Scholar
Nyblom, J. & A. Harvey (2000) Tests of common stochastic trends. Econometric Theory 16, 176–199.Google Scholar
Nyblom, J. & T. Mäkeläinen (1983) Comparisons of tests for the presence of random walk coefficients in a simple linear model. Journal of the American Statistical Association 78, 856–864.Google Scholar
Obstfeld, M. & K. Rogoff (1996) Foundations of International Macroeconomics. MIT Press.
Park, J.Y. (1992) Canonical cointegrating regressions. Econometrica 60, 119–143.Google Scholar
Phillips, P.C.B. (1988) Weak convergence of sample covariance matrices to stochastic integrals via martingale approximations. Econometric Theory 4, 528–533.Google Scholar
Phillips, P.C.B. (1991) Optimal inference in cointegrated systems. Econometrica 59, 283–306.Google Scholar
Phillips, P.C.B. & B.E. Hansen (1990) Statistical inference in instrumental variables regression with I(1) variables. Review of Economic Studies 57, 99–125.Google Scholar
Phillips, P.C.B. & V. Solo (1992) Asymptotics for linear processes. Annals of Statistics 20, 971–1001.Google Scholar
Saikkonen, P. (1991) Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21.Google Scholar
Saikkonen, P. (1992) Estimation and testing of cointegrated systems by an autoregressive approximation. Econometric Theory 8, 1–27.Google Scholar
Saikkonen, P. & R. Luukkonen (1993a) Point optimal tests for testing the order of differencing in ARIMA models. Econometric Theory 9, 343–362.Google Scholar
Saikkonen, P. & R. Luukkonen (1993b) Testing for a moving average unit root in autoregressive integrated moving average models. Journal of the American Statistical Association 88, 596–601.Google Scholar
Shin, Y. (1994) A residual-based test of the null of cointegration against the alternative of no cointegration. Econometric Theory 10, 91–115.Google Scholar
Stock, J.H. (1994) Unit roots, structural breaks and trends. In R.F. Engle & D.L. McFadden (eds.), Handbook of Econometrics, vol. 4, pp. 2739–2841. North-Holland.
Stock, J.H. & M.W. Watson (1993) A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783–820.Google Scholar
Tanaka, K. (1990) Testing for a moving average unit root. Econometric Theory 6, 433–444.Google Scholar
van Garderen, K.J. (2000) An alternative comparison of classical tests: Assessing the effects of curvature. In P. Marriott & M. Salmon (eds.), Applications of Differential Geometry to Econometrics, pp. 230–280. Cambridge University Press.
Zivot, E. (2000) The power of single equation tests for cointegration when the cointegrating vector is prespecified. Econometric Theory 16, 407–439.Google Scholar