Causality quantification and its applications: structuring and modeling of multivariate time series

ABSTRACT

Time series prediction is an important issue in a wide range of areas. There are various real world processes whose states vary continuously, and those processes may have influences on each other. If the past information of one process X improves the predictability of another process Y, X is said to have a causal influence on Y. In order to make good predictions, it is necessary to identify the appropriate causal relationships. In addition, the processes to be modeled may include symbolic data as well as numerical data. Therefore, it is important to deal with symbolic and numerical time series seamlessly when attempting to detect causality.

In this paper, we propose a new method for quantifying the strength of the causal influence from one time series to another. The proposed method can represent the strength of causality as the number of bits, whether each of two time series is symbolic or numerical. The proposed method can quantify causality even from a small number of samples. In addition, we propose structuring and modeling methods for multivariate time series using causal relationships of two time series. Our structuring and modeling methods can also deal with data sets which include both types of time series. Experimental results demonstrate that our methods can perform well even if the number of samples is small.

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INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Time series analysis

General Terms:
Algorithms, Theory

Keywords:
autoregressive model, entropy, information theory, markov chain, time series prediction