The estimation of causal relationships from time series data is an important factor in predicting or regulating control in various fields. Usually, when estimating causal relationships, either a causality or a correlation measure is used. However, many studies fail to adequately consider qualitative differences and relations between these measures when applied to time series. In this paper, we present a unified formulation of the causality measure based on information theory as well as relationships and disparities between correlation and causality measures. An advantage of our approach is that the formulated causality measure can extract linear subspaces with strong causal relationships. A significant contribution is the verification that time-delayed mutual information (TDMI) is not appropriate for nonindependent and identically distributed (non-i.i.d.) time series, which is done by demonstrating the behavior of projection vectors in an experiment with synthetic data.