Tests For Causality In Time Series: Modification, Comparison And Application
Author: Rizwan Fazal

Causality is a central problem in all social sciences and primary question facing researcher is to find the casual direction. This central question has no reliable answer. There have been several approaches to test causality i.e. Simon (1953) approach, Wold (1954) approach, Granger causality (1969), Sims causality (1972) and Peter and Clark (PC) algorithm of Graph Theoretic Approach (GTA) developed by Spirtes et al (1993) and Pearl (2000). But there are serious theoretical and empirical weaknesses attached to some of these causality tests. After development of Granger causality, it was thought, initially, that the issue of determining the causal relation would be resolved, but it, too, has major flaws, as Granger causality determines predictability, not the causality; sometime the cause occurs later than the consequences. Among these approaches; theoretically PC algorithm of GTA looks sound and can be held as a preferred approach for testing causality. Because the recent development in graphical models and logic of causality show potential for alleviating difficulties of causal modeling (Pearl, 1998). But how it performs empirically? The literature carries no answer to this question. As it is not known, to what extent the PC algorithm is capable to differentiate between genuine and spurious causal assumption. So current study investigated the size and power properties of PC algorithm of GTA. This study also modifies the PC algorithms with different measure of correlations and evaluated the performance of Modified PC algorithm that how much it is capable of uncovering the true and spurious causal relationship. This study used Monte Carlo simulations to evaluate performance of PC and Modified PC algorithms of graph theoretic approach. Results of Monte Carlo simulations indicate that PC algorithm (treating VAR residuals as original variables) and Modified PC algorithm (treating Haugh-ARMA residuals as original variables) continuously maintains the size but does not have reasonable power. It is also evident from the simulated results that stationary and non-stationary series with different specifications (drift and trend) and autoregressive coefficients do not affect the size of PC algorithm (using VAR residuals) and Modified PC algorithms (using Haugh-ARMA residuals). The size of Modified PC algorithm (using Modified R recursive residuals) inflates for nonstationary series but it has good power. In case of stationary series when the auto regressive coefficients are near to unity, it also performs well, having high power. But when the auto regressive coefficients in the data generating process tend towards zero, Modified PC algorithm (using Modified R recursive residuals) fails to maintain power. The performance of these procedures is also evaluated when there is confounding variable in the data generating process. The results indicate that performance of Modified PC algorithm (using Modified R recursive residuals) in finding the correct causal path is better than PC algorithm (using VAR residuals) and Modified PC (using Haugh-ARMA residuals). After evaluating the performance of PC and Modified PC algorithms, causal determinants of inflation are estimated using appropriate causality approach having optimal statistical size and power properties. Supervisor:- Dr. Atiq-ur-Rehman

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Keywords : Graph Theoretic Approach, Time-series
Supervisor: Atiq Ur Rahman

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