Abstract
Although Granger causality is a widely used technique to detect the causal relationship between time series, its direct application for nonlinearly modeled data is not appropriate. There have been proposed several extensions to nonlinear cases, but there is no method appropriate for detecting relations between time series in general. We present a new measure for evaluation of a causal effect between two time series, which is calculated on the selected local approximations of time-delay embedding reconstruction of state space by a linear regression model. The novel causal measure, called the modified Granger causality in selected neighborhoods (MGCiSN), reflects the proportion of the explained variation of the modeled variable by the past of the second variable only. The proposed procedure for evaluating the direct causal link between two nonlinearly modeled time series is applied to four data sets with different known nonlinear causal structures. Our experimental results support that the MGCiSN correctly detects underlying causal relationship in many cases and does not detect false causality, regardless of the number of samples.
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Acknowledgements
The work was supported by the Slovak Research and Development Agency, project APVV-15-0295, and by the Scientific Grant Agency VEGA of the Ministry of Education of the Slovak Republic and the Slovak Academy of Sciences, by the projects VEGA 2/0081/19 and VEGA 2/0054/18.
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Chvosteková, M. (2019). Modified Granger Causality in Selected Neighborhoods. In: Valenzuela, O., Rojas, F., Pomares, H., Rojas, I. (eds) Theory and Applications of Time Series Analysis. ITISE 2018. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-26036-1_3
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DOI: https://doi.org/10.1007/978-3-030-26036-1_3
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