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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

Listed:
  • 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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    2. Patrick Gagliardini & Elisa Ossola & O. Scaillet, 2019. "Estimation of Large Dimensional Conditional Factor Models in Finance," Swiss Finance Institute Research Paper Series 19-46, Swiss Finance Institute.
    3. Marica Valente & Timm Gries & Lorenzo Trapani, 2023. "Informal employment from migration shocks," Working Papers 2023-09, Faculty of Economics and Statistics, Universität Innsbruck.
    4. Gagliardini, Patrick & Ossola, Elisa & Scaillet, Olivier, 2019. "A diagnostic criterion for approximate factor structure," Journal of Econometrics, Elsevier, vol. 212(2), pages 503-521.
    5. 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.
    6. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    7. 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.
    8. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    9. Lorenzo Trapani & Emily Whitehouse, 2020. "Sequential monitoring for cointegrating regressions," Papers 2003.12182, arXiv.org.
    10. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    11. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
    12. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    13. Sun, Yucheng & Xu, Wen & Zhang, Chuanhai, 2023. "Identifying latent factors based on high-frequency data," Journal of Econometrics, Elsevier, vol. 233(1), pages 251-270.
    14. Esposti, Roberto, 2024. "Dating common commodity price and inflation shocks with alternative approaches," Bio-based and Applied Economics Journal, Italian Association of Agricultural and Applied Economics (AIEAA), vol. 13(2), July.
    15. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2020. "Determining the rank of cointegration with infinite variance," Discussion Papers 20/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    16. Roberto Esposti, 2022. "Who Moves First? Commodity Price Interdependence Through Time-Varying Granger Causality," Working Papers 471, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.

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    More about this item

    Keywords

    common cycles; common trends; nonlinear transformation; non stationarity; randomised procedure;
    All these keywords.

    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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