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Testing for Unit Roots and Non‐linear Transformations

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  • Philip Hans Franses
  • Michael McAleer

Abstract

It is well known that the augmented Dickey–Fuller (ADF) test of unit roots in univariate time series is sensitive to non‐linear transformations: a common example is when variables expressed in logarithms are found to be stationary, whereas the same variables in levels are found to be non‐stationary. In this paper, the effects of non‐linear transformations on the ADF auxiliary regression are investigated within the class of the Box–Cox model, and a test of non‐linear transformation is developed to assess the adequacy of the ADF regression. The proposed test is computationally simple and is calculated as thet ratio of an added variable in the ADF regression. Cointegration among series which are subject to non‐linear transformations is also analysed, and a simple procedure is developed to test the non‐linear transformation used in cointegration analysis. Several empirical examples taken from the Nelson–Plosser data set illustrate the practical relevance of the proposed test for univariate series, and a second empirical example is used to illustrate the test of non‐linear transformation for cointegrated series

Suggested Citation

  • Philip Hans Franses & Michael McAleer, 1998. "Testing for Unit Roots and Non‐linear Transformations," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(2), pages 147-164, March.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:2:p:147-164
    DOI: 10.1111/1467-9892.00083
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    Cited by:

    1. Mark J. Holmes, 2005. "New evidence on long-run output convergence among Latin American countries," Journal of Applied Economics, Universidad del CEMA, vol. 8, pages 299-319, November.
    2. Franses, Philip Hans & de Bruin, Paul, 2002. "On data transformations and evidence of nonlinearity," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 621-632, September.
    3. Kramer, Walter & Davies, Laurie, 2002. "Testing for unit roots in the context of misspecified logarithmic random walks," Economics Letters, Elsevier, vol. 74(3), pages 313-319, February.
    4. Corradi, Valentina & Swanson, Norman R., 2006. "The effect of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo results and a simple test," Journal of Econometrics, Elsevier, vol. 132(1), pages 195-229, May.
    5. Gary Madden & Scott J. Savage, 1998. "Sources of Australian Labour Productivity Change 1950–1994," The Economic Record, The Economic Society of Australia, vol. 74(227), pages 362-372, December.
    6. Helmut Lütkepohl & Fang Xu, 2012. "The role of the log transformation in forecasting economic variables," Empirical Economics, Springer, vol. 42(3), pages 619-638, June.
    7. Héctor Manuel Záarte Solano & Angélica Rengifo Gómez, 2013. "Forecasting annual inflation with power transformations: the case of inflation targeting countries," Borradores de Economia 10462, Banco de la Republica.
    8. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    9. Beenstock, Michael & Szpiro, George, 2002. "Specification search in nonlinear time-series models using the genetic algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 811-835, May.
    10. Dilip M. Nachane, 2011. "Selected Problems in the Analysis of Nonstationary & Nonlinear Time Series," Journal of Quantitative Economics, The Indian Econometric Society, vol. 9(1), pages 1-17.
    11. Krämer Walter, 2002. "Statistische Besonderheiten von Finanzzeitreihen / Statistical Properties of Financial Time Series," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 222(2), pages 210-229, April.
    12. Aparicio, Felipe M., 2003. "On the record properties of integrated time series," DES - Working Papers. Statistics and Econometrics. WS ws036414, Universidad Carlos III de Madrid. Departamento de Estadística.

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