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Testing for unit roots in the context of misspecified logarithmic random walks

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  • Kramer, Walter
  • Davies, Laurie
Abstract
Testing for unit roots has been among the most heavily researched topics in Econometrics for the last quarter of a century. Much less researched is the equally important issue of the appropriate transformation if any of the variable of interest which should preceed any such testing. In macroeconometrics and empirical finance (stock prices, exchange rates) there are often compelling arguments in favor of a logarithmic transformation. Elsewhere, for instance in the modelling of interest rates, a levels specification automatically suggests itself. In many applications, however, it is not a priori clear, given that one suspects a unit root, whether this unit root is present in the levels or the logs, so there is certainly some interest in the testing for unit roots in the context of an incompletely specified nonlinear transformation of the data . This issue can be approached from various angles: One is to check which transformations leave the I (1)-property of a time series intact, the presumption being that any such transformation could then do little damage to the null distribution of a test for unit roots (Granger and Hallmann 1991; Ermini and Granger 1993 Corradi 1995). A related one is to use tests whose null distribution is robust to monotonic transformations, whether the transformed data are I (1) or not (Granger and Hallmann 1991 , Burridge and Guerre 1996 , Gourieroux and Breitung 1999) or to embed the levels and log specifications respectively in a general Box-Cox-framework and to estimate the transformation parameter before testing (Franses and McAleer 1998, Franses and Koop 1998 , Kobayashi and McAleer 1999). The present paper continues along the lines of Granger and Hallmann (1991) by focussing on a conventional test procedure, the standard Dickey-Fuller-test, and by investigating its properties under a misspecified nonlinear transformation in particular, investigating whether an existing unit root is still detected, i.e. the null hypothesis of an existing
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  • 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.
    • Handle: RePEc:eee:ecolet:v:74:y:2002:i:3:p:313-319
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    1. Ermini, Luigi & Granger, Clive W. J., 1993. "Some generalizations on the algebra of I(1) processes," Journal of Econometrics, Elsevier, vol. 58(3), pages 369-384, August.
    2. Stock, James H., 1994. "Deciding between I(1) and I(0)," Journal of Econometrics, Elsevier, vol. 63(1), pages 105-131, July.
    3. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    4. 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.
    5. Breitung, Jorg & Gourieroux, Christian, 1997. "Rank tests for unit roots," Journal of Econometrics, Elsevier, vol. 81(1), pages 7-27, November.
    6. Burridge, Peter & Guerre, Emmanuel, 1996. "The Limit Distribution of level Crossings of a Random Walk, and a Simple Unit Root Test," Econometric Theory, Cambridge University Press, vol. 12(4), pages 705-723, October.
    7. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    8. 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.
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    2. 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.
    3. Yoon, Gawon, 2005. "An introduction to I([infinity]) processes," Economic Modelling, Elsevier, vol. 22(3), pages 473-483, May.
    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.
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