Granger causality analysis and applications based on penalized estimators

The concept of causality introduced by Clive W. Granger (1969) into the literature was initially defined to test the relationship between the two time series. However, how to apply the test for more than two variables was not directly addressed. In graphical Granger causality models developed by Eichler (2005), the concept of Granger causality is extended for more than two number of variables. Most of the algorithms used in the literature for the Granger causality test are based on a statistical significance test. The fact that the number of variables included in the model is sufficiently large may pose major problems in the calculation of Granger causality tests. Lozano et al. (2009) emphasizes that it is very important for Granger causality methods to formulate the group structure appropriately among lagged values of any time series. Bahadori and Liu (2013) stated that the Granger causality approach may not provide consistent results for a high-dimensional data set with insufficient number observations. In order to solve such problems in Granger causality tests, Granger causality approaches based on various penalized estimators are developed. In the literature, the applications of Granger causality approaches based on various penalized estimators in the context of economic variables are almost non-existent. In this study, two different economic data groups in the context of time series and panel data are examined with Granger causality approaches based on various penalized estimators. In the context of time series, the relationship between goverment domestic debts and some basic macroeconomic indicators in Turkey is analyzed. In the context of panel data, the relationship between economic growth, energy consumption, foreign trade balance and financial development in 30 developing countries are investigated. Keywords: LASSO Granger, Elastic net Granger, Copula Granger, Truncating LASSO