Testing Granger Causality in Non-Stationary VAR Systems Using Bootstrap Method

Year 2025, Volume: 7 Issue: 2, 200 - 217, 30.12.2025

Savaş Gayaker , Yeliz Yalçın

https://doi.org/10.56668/jefr.1819576

https://izlik.org/JA66DH39ZN

Abstract

Understanding the causal structure between variables is challenging issue in economics. Granger (1969) defined causality based on predictability and tested it among stationary variables using the Wald statistic. Later, Sims et al. (1990) showed that for non-stationary series the Wald statistic does not follow the χ² distribution, making the test invalid. Toda and Yamamoto (1995) solved this by adding lags equal to the maximum integration order, though their approach suffers from size and power problems in small samples. This study addresses these limitations by applying the Bootstrap Granger Causality test and comparing it with the TY test. Results indicate that the bootstrap method yields more accurate significance levels and higher power in small samples.

Keywords

Granger Causality , Toda-Yamamato , Bootstrap

Durağan Olmayan VAR Sistemlerinde Bootstrap Yöntemi ile Granger Nedensellik Sınaması

https://izlik.org/JA66DH39ZN

Abstract

Değişkenler arasındaki nedensellik yapısını anlamak ekonomide önemli ve hala zor konulardan birisidir. Granger (1969) durağan serilerde öngörülebilirliği esas alarak Granger nedensellik tanımını geliştirmiştir. Ancak Sims vd. (1990), durağan olmayan serilerde Wald istatistiğinin asimptotik olarak χ^2dağılımına yakınsamadığını göstermiştir. Toda ve Yamamoto (1995) ise maksimum bütünleşme derecesi kadar gecikme ekleyerek bu soruna çözüm önermiştir. Bununla birlikte, yöntemin küçük örneklemlerde güç kaybı ve anlamlılık düzeyinden sapma gibi sınırlılıkları bulunmaktadır. Bu çalışmada, bu sorunları azaltabileceği düşünülen bootstrap yöntemiyle Granger nedensellik testi incelenmiştir. Durağan olmayan seriler için bootstrap ve Toda–Yamamoto yaklaşımları Monte Carlo simülasyonu ile karşılaştırılmış; sonuçlar, bootstrap testinin nominal anlamlılık düzeyine daha yakın ve küçük örneklemlerde daha güçlü olduğunu göstermiştir.

Keywords

Granger Nedensellik , Toda-Yamamato , Bootstrap

References

• Balcilar, M., Ozdemir, Z.A. and Arslanturk, Y. (2010). Economic growth and energy consumption causal nexus viewed through a bootstrap rolling window. Energy Economics, 32(6): 1398-1410.
• Di lorio, F. and Triacca, U. (2013). Testing for Granger non-causality using the autoregressive metric. Economic Modelling, 33: 120-125.
• Dolado, J.J. and Lütkepohl, H. (1996). Making Wald tests work for cointegrated VAR systems. Econometrics Reviews, 15(4): 369–86.
• Emirmahmutoğlu, F. and Köse, N. (2010). Testing for Granger causality in heterogeneous mixed panels. Economic Modelling, 28: 870-876.
• Engle, R.F. and Granger, C.W.J. (1987). Co-integration and error correction: Representation, estimation and testing. Econometrica, 55: 251-276.
• Giles, D.E. and Godwin, R.T. (2012). Testing for multivariate cointegration in the presence of structural breaks: p-values and critical values. Applied Economics Letters, 19(16): 1561-1565.
• Granger, C.W.J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 36: 424-438.
• Granger, C.W.J. and Newbold, P. (1974). Spurious regression in econometrics. Journal of Econometrics, 2: 111–20.
• Granger, C.W.J. (1988). Some recent developments in the concept of causality. Journal of Econometrics, 39: 199–211.
• Hacker, R.S. and Hatemi, J.A. (2006). Tests for causality between ıntegrated variables using asymptotic and bootstrap distributions: Theory and application. Applied Economics, 38: 1489-1500.
• Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12: 231-254.
• Kónya, L. (2006). Exports and growth: Granger causality analysis on OECD countries with a panel data approach. Economic modelling, 23(6): 978-992.
• Lütkepohl, H. (2007). General-to-specific or specific-to-general modelling? An opinion on current econometric terminology. Journal of Econometrics, 136(1): 319-324.
• Manap, T.A.A., Abduh, M. and Omar, M.A. (2012). Islamic banking-growth nexus: Evidence from Toda-Yamamoto and bootstrap Granger causality test. Journal of Islamic Finance, 1(1): 59-66.
• Mantalos, P. (2000). A graphical investigation of the size and power of the Granger-causality tests in integrated cointegrated var systems. Studiesin Nonlinear Dynamics and Econometrics, 4(1): 17-33.
• Mantalos, P. and Shukur, G. (1998), Size and power of the error correction model cointegration test. A bootstrap approach. Oxford Bulletin of Economics and Statistics, 60(2): 249–255.
• Mavrotas, G. and Kelly, R. (2001). Old wine in new bottles: Testing casuality between savings and growth. The Manshester School, 69: 97-105.
• Sims, C.A. (1972). Money, income, and causality. The American Economic Review, 62(4): 540-552.
• Sims, C.A., Stock, J.H. and Watson, M.W. (1990). Inference in linear time series models with some unit roots. Econometrica, 58(1): 113–144.
• Toda, H.Y. and Yamamoto, T. (1995). Statistical inference in vector auto regressions with possibly integrated processes. Journal of Econometrics, 66: 225-250.
• Zapata, H.O. and Rambaldi, A.N. (1997). Monte Carlo evidence on cointegration and causation. Oxford Bulletin of Economics and Statistics, 59(2): 285-298.