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Credible Granger-Causality Inference with Modest Sample Lengths: A Cross-Sample Validation Approach

  • Richard A. Ashley
  • Kwok Ping Tsang

Credible Granger-causality analysis appears to require post-sample inference, as it is well-known that in-sample fit can be a poor guide to actual forecasting effectiveness. But post-sample model testing requires an often-consequential a priori partitioning of the data into an 'in-sample' period - purportedly utilized only for model specifi- cation/estimation - and a 'post-sample' period, purportedly utilized (only at the end of the analysis) for model validation/testing purposes. This partitioning is usually infeasible, however, with samples of modest length – e.g., T less than 100 - as is common in both quarterly data sets and/or in monthly data sets where institutional arrange- ments vary over time, simply because there is in such cases insufficient data available to credibly accomplish both purposes separately. A cross-sample validation (CSV) testing procedure is proposed below which substantially ameliorates this predicament - preserving most of the power of in-sample testing (by utilizing all of the sample data in the test), while also retaining most of the credibility of post-sample testing (by al- ways basing model forecasts on data not utilized in estimating that particular model's coefficients). Simulations show that the price paid, in terms of power relative to the in-sample Granger-causality F test, is manageable. An illustrative application is given, to a re-analysis of the Engel and West (2005) study of the causal relationship between macroeconomic fundamentals and the exchange rate.

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File URL: ftp://repec.econ.vt.edu/Papers/Ashley/Ashley_Tsang_Cross_Sample_Validation_Granger_Causality.pdf
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Paper provided by Virginia Polytechnic Institute and State University, Department of Economics in its series Working Papers with number e07-41.

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Length: 20 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:vpi:wpaper:e07-41
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  1. Kenneth D. West & Todd Clark, 2006. "Approximately Normal Tests for Equal Predictive Accuracy in Nested Models," NBER Technical Working Papers 0326, National Bureau of Economic Research, Inc.
  2. Ashley, Richard, 1998. "A new technique for postsample model selection and validation," Journal of Economic Dynamics and Control, Elsevier, vol. 22(5), pages 647-665, May.
  3. Hamilton, James D., 2003. "What is an oil shock?," Journal of Econometrics, Elsevier, vol. 113(2), pages 363-398, April.
  4. Barbara Rossi & Atsushi Inoue, 2011. "Out-of-sample forecast tests robust to the choice of window size," Working Papers 11-31, Federal Reserve Bank of Philadelphia.
  5. Ashley, Richard, 2003. "Statistically significant forecasting improvements: how much out-of-sample data is likely necessary?," International Journal of Forecasting, Elsevier, vol. 19(2), pages 229-239.
  6. Richard Ashley & Kwok Ping Tsang & Randal J. Verbrugge, 2010. "Frequency Dependence in a Real-Time Monetary Policy Rule," Working Papers e07-21, Virginia Polytechnic Institute and State University, Department of Economics.
  7. Kilian, Lutz, 2006. "Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," CEPR Discussion Papers 5994, C.E.P.R. Discussion Papers.
  8. Richard Ashley & Haichun Ye, 2012. "On the Granger causality between median inflation and price dispersion," Applied Economics, Taylor & Francis Journals, vol. 44(32), pages 4221-4238, November.
  9. Hamilton, James D., 1996. "This is what happened to the oil price-macroeconomy relationship," Journal of Monetary Economics, Elsevier, vol. 38(2), pages 215-220, October.
  10. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
  11. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  12. R. F. Engle, 1972. "Band Spectrum Regressions," Working papers 96, Massachusetts Institute of Technology (MIT), Department of Economics.
  13. Jiménez-Rodríguez, Rebeca & Sánchez, Marcelo, 2004. "Oil price shocks and real GDP growth: empirical evidence for some OECD countries," Working Paper Series 0362, European Central Bank.
  14. Breitung, Jorg & Candelon, Bertrand, 2006. "Testing for short- and long-run causality: A frequency-domain approach," Journal of Econometrics, Elsevier, vol. 132(2), pages 363-378, June.
  15. Clark, Todd E. & West, Kenneth D., 2006. "Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 155-186.
  16. J. Isaac Miller & Shawn Ni, 2010. "Long-Term Oil Price Forecasts: A New Perspective on Oil and the Macroeconomy," Working Papers 1012, Department of Economics, University of Missouri.
  17. Hamilton, James D, 1983. "Oil and the Macroeconomy since World War II," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 228-48, April.
  18. Kiseok Lee & Shawn Ni & Ronald A. Ratti, 1995. "Oil Shocks and the Macroeconomy: The Role of Price Variability," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 39-56.
  19. Pesaran, M. Hashem & Timmermann, Allan, 2007. "Selection of estimation window in the presence of breaks," Journal of Econometrics, Elsevier, vol. 137(1), pages 134-161, March.
  20. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
  21. Diks, C.G.H. & Panchenko, V., 2004. "A new statistic and practical guidelines for nonparametric Granger causality testing," CeNDEF Working Papers 04-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  22. David A. Pierce & Larry D. Haugh, 1977. "Causality in temporal systems: characterizations and a survey," Special Studies Papers 87, Board of Governors of the Federal Reserve System (U.S.).
  23. Steven J. Davis & John Haltiwanger, 1999. "Sectoral Job Creation and Destruction Responses to Oil Price Changes," NBER Working Papers 7095, National Bureau of Economic Research, Inc.
  24. Richard A. Ashley & Randall J. Verbrugge., 2006. "Mis-Specification in Phillips Curve Regressions: Quantifying Frequency Dependence in This Relationship While Allowing for Feedback," Working Papers e06-11, Virginia Polytechnic Institute and State University, Department of Economics.
  25. Hooker, Mark A., 1996. "What happened to the oil price-macroeconomy relationship?," Journal of Monetary Economics, Elsevier, vol. 38(2), pages 195-213, October.
  26. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, July.
  27. Jeffrey S. Racine & Christopher F. Parmeter, 2012. "Data-Driven Model Evaluation: A Test for Revealed Performance," Department of Economics Working Papers 2012-13, McMaster University.
  28. Mork, Knut Anton, 1989. "Oil and Macroeconomy When Prices Go Up and Down: An Extension of Hamilton's Results," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 740-44, June.
  29. Ashley, Richard, 1981. "Inflation and the Distribution of Price Changes across Markets: A Causal Analysis," Economic Inquiry, Western Economic Association International, vol. 19(4), pages 650-60, October.
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