Learning maximum lag for grouped graphical granger models

Abstract

Temporal causal modeling has been a highly active research area in the last few decades. Temporal or time series data arises in a wide array of application domains ranging from medicine to finance. Deciphering the causal relationships between the various time series can be critical in understanding and consequently, enhancing the efficacy of the underlying processes in these domains. Grouped graphical modeling methods such as Granger methods provide an efficient alternative for finding out such dependencies. A key parameter which affects the performance of these methods is the maximum lag. The maximum lag specifies the extent to which one has to look into the past to predict the future. A smaller than required value of the lag will result in missing important dependencies while an excessively large value of the lag will increase the computational complexity alongwith the addition of noisy dependencies. In this paper, we propose a novel approach for estimating this key parameter efficiently. One of the primary advantages of this approach is that it can, in a principled manner, incorporate prior knowledge of dependencies that are known to exist between certain pairs of time series out of the entire set and use this information to estimate the lag for the entire set. This ability to extrapolate the lag from a known subset to the entire set, in order to get better estimates of the overall lag efficiently, makes such an approach attractive in practice. © 2010 IEEE.