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The Impact of Persistent Cycles on Zero Frequency Unit Root Tests

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  • Tomás del Barrio Castro
  • Paulo M.M. Rodrigues
  • A. M. Robert Taylor

Abstract

In this paper we investigate the impact of non-stationary cycles on the asymptotic and finite sample properties of standard unit root tests. Results are presented for the augmented Dickey-Fuller normalised bias and t-ratio-based tests (Dickey and Fuller, 1979, and Said and Dickey, 1984), the variance ratio unit root test of Breitung (2002) and the M class of unit-root tests introduced by Stock (1999) and Perron and Ng (1996). The limiting distributions of these statistics are derived in the presence of non-stationary cycles. We show that while the ADF statistics remain pivotal (provided the test regression is properly augmented), this is not the case for the other statistics considered and show numerically that the size properties of the tests based on these statistics are too unreliable to be used in practice. We also show that the t-ratios associated with lags of the dependent variable of order greater than two in the ADF regression are asymptotically normally distributed. This is an important result as it implies that extant sequential methods (see Hall, 1994 and Ng and Perron, 1995) used to determine the order of augmentation in the ADF regression remain valid in the presence of non-stationary cycles.

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Paper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w201124.

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Date of creation: 2011
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Handle: RePEc:ptu:wpaper:w201124

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  1. Graham Elliott & Thomas J. Rothenberg & James H. Stock, 1992. "Efficient Tests for an Autoregressive Unit Root," NBER Technical Working Papers 0130, National Bureau of Economic Research, Inc.
  2. Gregoir, St phane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part I," Econometric Theory, Cambridge University Press, vol. 15(04), pages 435-468, August.
  3. Nielsen, Bent, 2001. "The Asymptotic Distribution of Unit Root Tests of Unstable Autoregressive Processes," Econometrica, Econometric Society, Econometric Society, vol. 69(1), pages 211-19, January.
  4. Bierens, Herman J., 2001. "Complex Unit Roots And Business Cycles: Are They Real?," Econometric Theory, Cambridge University Press, vol. 17(05), pages 962-983, October.
  5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 277-301, March.
  6. Gregoir, Stephane, 2006. "Efficient tests for the presence of a pair of complex conjugate unit roots in real time series," Journal of Econometrics, Elsevier, Elsevier, vol. 130(1), pages 45-100, January.
  7. Paul Conway & David Frame, 2000. "A spectral analysis of New Zealand output gaps using Fourier and wavelet techniques," Reserve Bank of New Zealand Discussion Paper Series DP2000/06, Reserve Bank of New Zealand.
  8. Kenneth D. West & Whitney K. Newey, 1995. "Automatic Lag Selection in Covariance Matrix Estimation," NBER Technical Working Papers 0144, National Bureau of Economic Research, Inc.
  9. Katsuyuki Shibayama, 2008. "On the Periodicity of Inventories," Studies in Economics, Department of Economics, University of Kent 0806, Department of Economics, University of Kent.
  10. Hall, Alastair R, 1994. "Testing for a Unit Root in Time Series with Pretest Data-Based Model Selection," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 12(4), pages 461-70, October.
  11. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
  12. Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198296836, October.
  13. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 21(4), pages 431-447.
  14. Jeganathan, P., 1991. "On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle," Econometric Theory, Cambridge University Press, vol. 7(03), pages 269-306, September.
  15. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1449-1459, December.
  16. Ulrich K. M¸ller & Graham Elliott, 2003. "Tests for Unit Roots and the Initial Condition," Econometrica, Econometric Society, Econometric Society, vol. 71(4), pages 1269-1286, 07.
  17. Ionel Birgean & Lutz Kilian, 2002. "Data-Driven Nonparametric Spectral Density Estimators For Economic Time Series: A Monte Carlo Study," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 21(4), pages 449-476.
  18. Serena Ng & Pierre Perron, 1997. "Lag Length Selection and the Construction of Unit Root Tests with Good Size and Power," Boston College Working Papers in Economics 369, Boston College Department of Economics, revised 01 Sep 2000.
  19. Faust, Jon, 1996. "Near Observational Equivalence and Theoretical size Problems with Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 12(04), pages 724-731, October.
  20. Ghysels, Eric & Lee, Hahn S. & Noh, Jaesum, 1994. "Testing for unit roots in seasonal time series : Some theoretical extensions and a Monte Carlo investigation," Journal of Econometrics, Elsevier, Elsevier, vol. 62(2), pages 415-442, June.
  21. Pagan, Adrian, 1999. "Some uses of simulation in econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, Elsevier, vol. 48(4), pages 341-349.
  22. Nyarko, Yaw, 1990. "Learning In Mis-Specified Models And The Possibility Of Cycles," Working Papers, C.V. Starr Center for Applied Economics, New York University 90-03, C.V. Starr Center for Applied Economics, New York University.
  23. Canova, Fabio, 1996. "Three tests for the existence of cycles in time series," Ricerche Economiche, Elsevier, Elsevier, vol. 50(2), pages 135-162, June.
  24. MÜller, Ulrich K., 2008. "The Impossibility Of Consistent Discrimination Between I(0) And I(1) Processes," Econometric Theory, Cambridge University Press, vol. 24(03), pages 616-630, June.
  25. Taylor, A M Robert, 2003. "Robust Stationarity Tests in Seasonal Time Series Processes," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 21(1), pages 156-63, January.
  26. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, Elsevier, vol. 108(2), pages 343-363, June.
  27. Choi, In, 1993. "Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications," Econometric Theory, Cambridge University Press, vol. 9(02), pages 263-282, April.
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