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Transcranial Magnetic Stimulation for Investigating Causal Brain-behavioral Relationships and their Time Course

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Detecting causal relations among symbolic time series.

Fernando Delbianco¹, Federico Contiggiani², Andrés Fioriti¹

¹Department of Economics and INMABB-CONICET, Universidad Nacional del Sur, San Andres 800, 8000 Bahía Blanca, Argentina.

Chaos (Woodbury, N.Y.)

|January 26, 2026

Summary

Symbolic time series analysis can obscure or falsely indicate causal relationships. Common causality tests like Granger

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Area of Science:

Social Sciences
Economics
Time Series Analysis

Background:

Symbolic time series analysis simplifies data by reducing noise.
It aims to clarify the evolution of time series dynamics.

Purpose of the Study:

To evaluate the reliability of causality tests on symbolic time series data.
To identify potential failures and artifacts in these methods.

Main Methods:

Application of established causality detection methods.
Testing methods including transfer entropy, Granger's test, and Peter-Clark Momentary Conditional Independence (PCMCI).

Main Results:

Causality tests on symbolic series may fail to detect true relationships.
These methods can frequently generate spurious causal findings.
Method performance varies with lag structure, alphabet size, and data characteristics.

Conclusions:

Caution is advised when interpreting causality from symbolic time series.
The choice of parameters significantly impacts the validity of causal inference.