An Examination of Practical Granger Causality Inference

Abstract

Learning temporal causal structures among multiple time series is one of the major tasks in mining time series data. Granger causality is one of the most popular techniques in uncovering the temporal dependencies among time series; however it faces two main challenges: (i) the spurious effect of unobserved time series and (ii) the computational challenges in high dimensional settings. In this paper, we utilize the confounder path delays to find a subset of time series that via conditioning on them we are able to cancel out the spurious confounder effects. After study of consistency of different Granger causality techniques, we propose Copula-Granger and show that while it is consistent in high dimensions, it can efficiently capture non-linearity in the data. Extensive experiments on a synthetic and a social networking dataset confirm our theoretical results. IntroductionIn the era of data deluge, we are confronted with largescale time series data, i.e., a sequence observations of concerned variables over a period of time. For example, terabytes of neural activity time series data are produced to record the collective response of neurons to different stimuli; petabytes of climate and meteorological data, such as temperature, solar radiation, and precipitation, are collected over the years; and exabytes of social media contents are generated over time on the Internet. A major data mining task for time series data is to uncover the temporal causal relationship among the time series. For example, in the climatology, we want to identify the factors that impact the climate patterns of certain regions. In social networks, we are interested in identification of the patterns of influence among users and how topics activate or suppress each other. Developing effective and scalable data mining algorithms to uncover temporal dependency structures between time series and reveal insights from data has become a key problem in machine learning and data mining.There are two major challenges in discovering temporal causal relationship in large-scale data: (i) not all influential confounders are observed in the datasets and

Discovery of Causal Time Intervals

“…In [14], variables which mediate the impact of an action on the outcome are identified to reduce the bias in assessing the causal effect for online advertising. [5] exploits confounder path delays in an attempt to cancel out the spurious confounder effect. However, a principled solution to this problem remains elusive.…”

“…While the original Granger causality test was designed for two time series, several methods [2,18,17] have been proposed to analyze time series data involving many features and to learn a causal graph structure. Following the work [2], [20] detects causality of spatial time series, [18] proposes to use hidden Markov Random Field method, [17] handles extreme values in time series, [4] detects Granger causality from irregular time series, and [5] presents Copula-Granger method to efficiently capture non-linearity in the data. Learning temporal causal graph has been applied to biology applications [25], climate analysis [9], microbiology [19], fMRI data analysis [24], anomaly detection [23], and longitudinal analysis [26].…”

Prediction Model of the Stock Market Index Using Twitter Sentiment Analysis

“…In this method, time series X is said to cause time series Y, if it can be proved that time series X provide statistically significant info rmat ion about the future values of t ime series Y, than Y alone [21] series X will have a statistically significant correlat ion with time series Y. It tested whether Twitter sentiments (pos, and neg) has a causative effect ("Granger causal") on the movement of the stock market Index.…”

Validating niche-construction theory through path analysis

“…Linear methods enable us to use some of the simplest concepts from time-series analysis to begin to scratch the surface of this difficult identification-and-quantitative-estimation problem in settings where data availability is lean and data quality is low. We can consider Granger causality testing as applied to the niche-construction context in a minimalist dynamic linear system of regression equations (nonparametric and nonlinear versions can be found in Diks and Panchenko (2006) and Bahadori and Liu (2013). We restrict ourselves to linear vector autoregressive systems as a workable approximation (at the initial stage where the frequency of the LP t allele is close to zero), but we point out that a variable such as allele frequency, LP t , lies in the interval [0,1], so clearly, we must use a general nonlinear Granger causality approach that respects this basic nonlinearity 2 in a more realistic approach.…”

“…(1b) can be done using the methods of Diks and Panchenko (2006) and Bahadori and Liu (2013). Lee et al (1993) discuss testing for the presence of neglected nonlinearity.…”