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The Effect of Data Transformation on Common Cycle, Cointegration and Unit Root Tests: Monte Carlo Results and a Simple Test

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Author Info

  • Valentina Corradi

    ()
    (Queen Mary, University of London)

  • Norman R. Swanson

    ()
    (Rutgers University)

Abstract

In the conduct of empirical macroeconomic research, unit root, cointegration, common cycle, and related test statistics are often constructed using logged data, even though there is often no clear reason, at least from an empirical perspective, why logs should be used rather than levels. Unfortunately, it is also the case that standard data transformation tests, such as those based on Box-Cox transformation, cannot be shown to be consistent unless the assumption is made concerning whether the series being examined is I(0) or I(1), so that a sort of circular testing problem exists. In this paper, we discuss two quite different but related issues that arise in the context of data transformation. First, we address the circular testing problem that arises when choosing data transformation and order of integratedness. In particular, we propose a simple randomized procedure, coupled with simple conditioning, for choosing between levels and log-levels specifications in the presence of deterministic and/or stochastic trends. Second, we note that even if pre-testing is not undertaken to determine data transformation, it is important to be aware of the impact that incorrect data transformation has on tests frequently used in empirical works. For this reason, we carry out a series of Monte Carlo experiments illustrating the rather substantive effect that incorrect transformation can have on the finite sample performance of common feature and cointegration tests. These Monte Carlo findings underscore the importance of either using economic theory as a guide to data transformation and/or using econometric tests such as discussed in this paper as aids when choosing data transformation.

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Bibliographic Info

Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200322.

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Date of creation: 27 Oct 2003
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Handle: RePEc:rut:rutres:200322

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Keywords: common cycles; common trends; nonlinear transformation; non stationarity; randomised procedure;

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References

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  1. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, October.
  2. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-60, Oct.-Dec..
  3. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
  4. Hecq, Alain & Palm, Franz C & Urbain, Jean-Pierre, 2000. " Permanent-Transitory Decomposition in VAR Models with Cointegration and Common Cycles," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 62(4), pages 511-32, September.
  5. Diebold & Senhadji, . "Deterministic vs. Stochastic Trend in U.S. GNP, Yet Again," Home Pages _054, University of Pennsylvania.
  6. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
  7. Corradi, V. & Swanson, N. & White, H., 1996. "Testing for Stationarity-Ergodicity and for Comovements Between Nonlinear Discrete Time Markov Processes," Papers 4-96-6, Pennsylvania State - Department of Economics.
  8. Joon Y. Park & Peter C. B. Phillips, 1999. "Nonlinear Regressions with Integrated Time Series," Working Paper Series no6, Institute of Economic Research, Seoul National University.
  9. Dufour, Jean-Marie & Kiviet, Jan F., 1996. "Exact tests for structural change in first-order dynamic models," Journal of Econometrics, Elsevier, vol. 70(1), pages 39-68, January.
  10. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : II. New directions," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 309-341.
  11. Vahid, Farshid & Issler, João Victor, 2001. "The Importance of Common Cyclical Features in VAR Analysis: A Monte-Carlo Study," Economics Working Papers (Ensaios Economicos da EPGE) 417, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  12. Michael P. Clements & David F. Hendry, 1999. "On winning forecasting competitions in economics," Spanish Economic Review, Springer, vol. 1(2), pages 123-160.
  13. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  14. Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
  15. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
  16. Stock, James H. & Watson, Mark W., 1989. "Interpreting the evidence on money-income causality," Journal of Econometrics, Elsevier, vol. 40(1), pages 161-181, January.
  17. Kobayashi, Masahito & McAleer, Michael, 1999. "Analytical Power Comparisons Of Nested And Nonnested Tests For Linear And Loglinear Regression Models," Econometric Theory, Cambridge University Press, vol. 15(01), pages 99-113, February.
  18. Inoue, Atsushi, 2001. "Testing For Distributional Change In Time Series," Econometric Theory, Cambridge University Press, vol. 17(01), pages 156-187, February.
  19. Proietti, Tommaso, 1997. "Short-Run Dynamics in Cointegrated Systems," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(3), pages 405-22, August.
  20. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
  21. van Dijk, D.J.C. & Franses, Ph.H.B.F. & Lucas, A., 1996. "Testing for ARCH in the Presence of Additive Outliers," Econometric Institute Research Papers EI 9659-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  22. Lutkepohl, Helmut & Burda, Maike M., 1997. "Modified Wald tests under nonregular conditions," Journal of Econometrics, Elsevier, vol. 78(2), pages 315-332, June.
  23. Franses, Philip Hans & Koop, Gary, 1998. "On the sensitivity of unit root inference to nonlinear data transformations," Economics Letters, Elsevier, vol. 59(1), pages 7-15, April.
  24. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  25. van Dijk, D.J.C. & Franses, Ph.H.B.F. & Lucas, A., 1996. "Testing for Smooth Transition Nonlinearity in the Presence of Outliers," Econometric Institute Research Papers EI 9622-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  26. Engle, Robert F. & Issler, Joao Victor, 1995. "Estimating common sectoral cycles," Journal of Monetary Economics, Elsevier, vol. 35(1), pages 83-113, February.
  27. Krämer, Walter & Davies, Laurie, 2000. "Testing for unit roots in the context of misspecified logarithmic random walks," Technical Reports 2000,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  28. James H. Stock & Mark W. Watson, 1987. "Interpreting Evidence on Money-Income Causality," NBER Working Papers 2228, National Bureau of Economic Research, Inc.
  29. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  30. Robert F. Engle & Sharon Kozicki, 1990. "Testing For Common Features," NBER Technical Working Papers 0091, National Bureau of Economic Research, Inc.
  31. Issler, Joao Victor & Vahid, Farshid, 2001. "Common cycles and the importance of transitory shocks to macroeconomic aggregates," Journal of Monetary Economics, Elsevier, vol. 47(3), pages 449-475, June.
  32. Kobayashi, Masahito, 1994. "Power of Tests for Nonlinear Transformation in Regression Analysis," Econometric Theory, Cambridge University Press, vol. 10(02), pages 357-371, June.
  33. Robert F. Engle & João Victor Issler, 1993. "Common trends and common cycles in Latin America," Revista Brasileira de Economia, FGV/EPGE Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 47(2), pages 149-176, April.
  34. Cubadda, Gianluca, 1999. "Common Cycles in Seasonal Non-stationary Time Series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 273-91, May-June.
  35. Corradi, V. & Swanson, N.R., 2000. "A Consistent Test for Nonlinear Out of Sample Predictive Accuracy," Discussion Papers 0012, Exeter University, Department of Economics.
  36. Swanson, Norman R., 1998. "Money and output viewed through a rolling window," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 455-474, May.
  37. Robert G. King & Charles I. Plosser & James H. Stock & Mark W. Watson, 1987. "Stochastic Trends and Economic Fluctuations," NBER Working Papers 2229, National Bureau of Economic Research, Inc.
  38. Anderson, Heather M. & Vahid, Farshid, 1998. "Testing multiple equation systems for common nonlinear components," Journal of Econometrics, Elsevier, vol. 84(1), pages 1-36, May.
  39. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-95, October.
  40. Anderson, Heather M, 1997. "Transaction Costs and Non-linear Adjustment towards Equilibrium in the US Treasury Bill Market," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 59(4), pages 465-84, November.
  41. Paul De Bruin & Philip Hans Franses, 1999. "Forecasting power-transformed time series data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(7), pages 807-815.
  42. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February.
  43. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February.
  44. repec:cup:etheor:v:10:y:1994:i:2:p:257-71 is not listed on IDEAS
  45. John C. Chao & Valentina Corradi & Norman R. Swanson, 2001. "Data Transformation and Forecasting in Models with Unit Roots and Cointegration," Annals of Economics and Finance, Society for AEF, vol. 2(1), pages 59-76, May.
  46. Cubadda, Gianluca & Hecq, Alain, 2001. "On non-contemporaneous short-run co-movements," Economics Letters, Elsevier, vol. 73(3), pages 389-397, December.
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Cited by:
  1. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
  2. Helmut Luetkepohl & Fang Xu, 2009. "The Role of the Log Transformation in Forecasting Economic Variables," CESifo Working Paper Series 2591, CESifo Group Munich.
  3. Greene, Clinton A., 2010. "Smooth-adjustment econometrics and inventory-theoretic money management," Journal of Economic Dynamics and Control, Elsevier, vol. 34(6), pages 1031-1047, June.

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