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

Author

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  • 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.

Suggested Citation

  • Valentina Corradi & Norman R. Swanson, 2003. "The Effect of Data Transformation on Common Cycle, Cointegration and Unit Root Tests: Monte Carlo Results and a Simple Test," Departmental Working Papers 200322, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:200322
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    References listed on IDEAS

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    Cited by:

    1. Patrick Gagliardini & Elisa Ossola & O. Scaillet, 2016. "A Diagnostic Criterion for Approximate Factor Structure," Swiss Finance Institute Research Paper Series 16-51, Swiss Finance Institute, revised Dec 2016.
    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. 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.
    4. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    5. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
    6. Matteo Barigozzi & Lorenzo Trapani, 2017. "Sequential testing for structural stability in approximate factor models," Papers 1708.02786, arXiv.org, revised Mar 2018.

    More about this item

    Keywords

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

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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