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

Author

Listed:
  • Richard A. Ashley

    (Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA)

  • Kwok Ping Tsang

    (Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA)

Abstract
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. However, post-sample model testing requires an often-consequential a priori partitioning of the data into an “in-sample” period – purportedly utilized only for model specification/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 ≤ 150 – as is common in both quarterly data sets and/or in monthly data sets where institutional arrangements 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 both eliminates the aforementioned a priori partitioning and which also substantially ameliorates this power versus credibility 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 always 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 andWest [1] study of the causal relationship between macroeconomic fundamentals and the exchange rate; several of their conclusions are changed by our analysis.

Suggested Citation

  • Richard A. Ashley & Kwok Ping Tsang, 2014. "Credible Granger-Causality Inference with Modest Sample Lengths: A Cross-Sample Validation Approach," Econometrics, MDPI, vol. 2(1), pages 1-20, March.
    • Handle: RePEc:gam:jecnmx:v:2:y:2014:i:1:p:72-91:d:34391
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    References listed on IDEAS

    as
    1. Rossi, Barbara, 2005. "Optimal Tests For Nested Model Selection With Underlying Parameter Instability," Econometric Theory, Cambridge University Press, vol. 21(5), pages 962-990, October.
    2. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    3. Peter Reinhard Hansen & Allan Timmermann, 2012. "Choice of Sample Split in Out-of-Sample Forecast Evaluation," CREATES Research Papers 2012-43, Department of Economics and Business Economics, Aarhus University.
    4. Todd Clark & Michael McCracken, 2005. "Evaluating Direct Multistep Forecasts," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 369-404.
    5. 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 650-660, October.
    6. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November.
    7. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
    8. Barbara Rossi & Atsushi Inoue, 2012. "Out-of-Sample Forecast Tests Robust to the Choice of Window Size," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 432-453, April.
    9. 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.
    10. Ashley, R & Granger, C W J & Schmalensee, R, 1980. "Advertising and Aggregate Consumption: An Analysis of Causality," Econometrica, Econometric Society, vol. 48(5), pages 1149-1167, July.
    11. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    12. Diks, Cees & Panchenko, Valentyn, 2006. "A new statistic and practical guidelines for nonparametric Granger causality testing," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1647-1669.
    13. 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.
    14. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
    15. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    16. 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.
    17. 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.
    18. 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.
    19. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    20. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    21. Larry D. Haugh & David A. Pierce, 1977. "Causality in temporal systems: characterizations and a survey," Special Studies Papers 87, Board of Governors of the Federal Reserve System (U.S.).
    22. 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.
    23. 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.
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    1. April Reading List
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2014-04-01 20:43:00

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    Cited by:

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    3. Xiaojie Xu, 2019. "Price dynamics in corn cash and futures markets: cointegration, causality, and forecasting through a rolling window approach," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 33(2), pages 155-181, June.
    4. Kyriazakou, Eleni & Panagiotidis, Theodore, 2017. "Causality analysis of the Canadian city house price indices: A cross-sample validation approach," The Journal of Economic Asymmetries, Elsevier, vol. 16(C), pages 42-52.
    5. Gary J. Cornwall & Jeffrey A. Mills & Beau A. Sauley & Huibin Weng, 2019. "Predictive Testing for Granger Causality via Posterior Simulation and Cross-validation," Advances in Econometrics, in: Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part A, volume 40, pages 275-292, Emerald Group Publishing Limited.
    6. Jindamas Sutthichaimethee & Kuskana Kubaha, 2018. "The Relationship of Causal Factors Affecting the Future Equilibrium Change of Total Final Energy Consumption in Thailand’s Construction Sector under a Sustainable Development Goal: Enriching the SE-VA," Resources, MDPI, vol. 8(1), pages 1-18, December.
    7. Harvey, David I. & Leybourne, Stephen J. & Whitehouse, Emily J., 2017. "Forecast evaluation tests and negative long-run variance estimates in small samples," International Journal of Forecasting, Elsevier, vol. 33(4), pages 833-847.
    8. Ye, Haichun & Ashley, Richard & Guerard, John, 2015. "Comparing the effectiveness of traditional vs. mechanized identification methods in post-sample forecasting for a macroeconomic Granger causality analysis," International Journal of Forecasting, Elsevier, vol. 31(2), pages 488-500.
    9. Xiaojie Xu, 2018. "Cointegration and price discovery in US corn cash and futures markets," Empirical Economics, Springer, vol. 55(4), pages 1889-1923, December.

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