Granger-causality inference in the presence of gaps: An equidistant missing-data problem for non-synchronous recorded time series data

Abstract

The inference of causal interactions from incomplete data represents a major issue in many areas of applications. The incompleteness of data has different directions. The direction of interest in this manuscript is the collection of data whose measurements are sampled at equally spaced intervals with missing observations. This direction has two different scenarios: either for synchronously or non-synchronously recorded data. There are many known gap-filling techniques, however, each has its own limitations. In addition, the presence of gaps violates the underlying assumptions of the existing standard time series analysis techniques especially in the framework of Granger-causality concept, such as Directed Partial Correlation (DPC). This results in incorrect misleading conclusions about the inferred interaction structure. Therefore, the implications of applying the concept of Granger-causality based DPC are presented. To this end, a new extended methodology is proposed based on a specific shifting technique to overcome the shortcomings of the standard DPC technique. The proposed methodology provides an evidence that it is possible to infer the underlying causality structure even in the presence of gaps for non-synchronously recorded data. This manuscript presents the problem at hand for stock market time series analysis, as a case study.