Papana, A., Kyrtsou, C., Kugiumtzis, D. and Diks, C. (2016). Detecting Causality in Non-stationary Time Series Using Partial Symbolic Transfer Entropy: Evidence in Financial Data Computational Economics, 47(3):341--365.

In this paper, a framework is developed for the identification of causal effects from non-stationary time series. Focusing on causality measures that make use of delay vectors from time series, the idea is to account for non-stationarity by considering the ranks of the components of the delay vectors rather than the components themselves. As an exemplary measure, we introduce the partial symbolic transfer entropy (PSTE), which is an extension of the bivariate symbolic transfer entropy quantifying only the direct causal effects among the variables of a multivariate system. Through Monte Carlo simulations it is shown that the PSTE is directly applicable to non-stationary in mean and variance time series and it is not affected by the existence of outliers and VAR filtering. For stationary time series, the PSTE is also compared to the linear conditional Granger causality index (CGCI). Finally, the causal effects among three financial variables are investigated. Computations of the PSTE and the CGCI on both the initial returns and the VAR filtered returns, and the PSTE on the original non-stationary time series, show consistency of the PSTE in estimating the causal effects.