Causal inference in time series is an important problem in many fields. Traditional methods use regression models for this problem. The inference accuracies of these methods depend greatly on whether or not the model can be well fitted to the data, and therefore we are required to select an appropriate regression model, which is difficult in practice. This paper proposes a supervised learning framework that utilizes a classifier instead of regression models. We present a feature representation that employs the distance between the conditional distributions given past variable values and show experimentally that the feature representation provides sufficiently different feature vectors for time series with different causal relationships. Furthermore, we extend our framework to multivariate time series and present experimental results where our method outperformed the model-based methods and the supervised learning method for i.i.d. data.