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

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

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

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