Temporal Lag estimation and Granger Causality on time series.
Abstract : The goal of Causal Inference problems is to use observations to infer the underlying causal structure of the data generating process. The input to these problems is either a multivariate time series or i.i.d sequences and the output is a {\em Feature Causal Graph} where the nodes correspond to the variables and edges capture the direction of causality. For high dimensional data, determining the causal relationships becomes a challenging task because of the curse of dimensionality. Graphical modeling of temporal data based on the concept of "Granger Causality" has gained much attention in this context. The blend of Granger methods along with model selection techniques, such as LASSO, enables efficient discovery of a "sparse" subset of causal variables in high dimensional settings. These temporal causal methods use an input parameter, L, the maximum time lag. This parameter is the maximum gap in time between the occurrence of the output phenomenon and the causal input stimulus. However, in many situations of interest, the maximum time lag is not known, and indeed, finding the range of causal effects is an important problem. In this work, we propose and evaluate a data-driven and computationally efficient method for Granger causality inference in time series without foreknowledge of the maximum time lag parameter. We present two algorithms here viz. Lasso Granger++ and Group Lasso Granger++ which alongside inferring the hypothesis feature causal graph, also estimates a value of max-lag by balancing the trade-off between "goodness of fit" and "model complexity".
The source code is uploaded in the folder titled "Final_Version_with_Comments". To run the Synthetic experiments, execute the matab script files runSynth_expNum.m