Cited by 216Time Series Analysis and ForecastingComplex Systems and Time Series AnalysisStatistical Methods and Applications

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Dangers and uses of cross-correlation in analyzing time series in perception, performance, movement, and neuroscience: The importance of constructing transfer function autoregressive models

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Dean, Roger T., Dunsmuir, William T. M.·2016·Behavior Research Methods

DOI 10.3758/s13428-015-0611-2

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Abstract

Many articles on perception, performance, psychophysiology, and neuroscience seek to relate pairs of time series through assessments of their cross-correlations. Most such series are individually autocorrelated: they do not comprise independent values. Given this situation, an unfounded reliance is often placed on cross-correlation as an indicator of relationships (e.g., referent vs. response, leading vs. following). Such cross-correlations can indicate spurious relationships, because of autocorrelation. Given these dangers, we here simulated how and why such spurious conclusions can arise, to provide an approach to resolving them. We show that when multiple pairs of series are aggregated in several different ways for a cross-correlation analysis, problems remain. Finally, even a genuine cross-correlation function does not answer key motivating questions, such as whether there are likely causal relationships between the series. Thus, we illustrate how to obtain a transfer function describing such relationships, informed by any genuine cross-correlations. We illustrate the confounds and the meaningful transfer functions by two concrete examples, one each in perception and performance, together with key elements of the R software code needed. The approach involves autocorrelation functions, the establishment of stationarity, prewhitening, the determination of cross-correlation functions, the assessment of Granger causality, and autoregressive model development. Autocorrelation also limits the interpretability of other measures of possible relationships between pairs of time series, such as mutual information. We emphasize that further complexity may be required as the appropriate analysis is pursued fully, and that causal intervention experiments will likely also be needed.

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Authors: Dean, R. T., & Dunsmuir, W. T. M.
Affiliations: Western Sydney University (AU)
UNSW Sydney (AU)
Corresponding author: Dean, Roger T.
ORCID: Dean, Roger T.
Dunsmuir, William T. M.
Venue: Behavior Research Methods
Publisher: Springer Science and Business Media LLC
Published: 2015-06-23
Volume: 48
Issue: 2
Pages: 783-802
ISSN: 1554-351X (ISSN-L)
1554-3528
DOI: 10.3758/s13428-015-0611-2
OpenAlex: W815444466
Cited by: 215
References: 53
Citations by year: 2026: 10 · 2025: 27 · 2024: 26 · 2023: 20 · 2022: 32 · 2021: 38 · 2020: 25 · 2019: 17 · 2018: 12 · 2017: 6 · 2016: 2
FWCI: 8.12
Type: journal article
Language: en
Open access: hybrid
doi.org
Licence: other-oa
www.springer.com/tdm (tdm)
Locations: Behavior Research Methods (publishedVersion, other-oa)
PubMed (publishedVersion)
Topics: Physical Sciences › Computer Science › Signal Processing › Time Series Analysis and Forecasting
Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Complex Systems and Time Series Analysis
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords: cross correlation function, autocorrelation, spurious correlations, transfer function, autoregressive models, Granger causality, prewhitening, stationarity, mutual information, time series analysis, perception, performance, psychophysiology, motion analysis, neuroscience
MeSH terms: Data Interpretation, Statistical, Humans, Movement, Neuropsychological Tests, Neurosciences, Perception, Psychomotor Performance, Software, Models, Statistical

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Dangers and uses of cross-correlation in analyzing time series in perception, performance, movement, and neuroscience: The importance of constructing transfer function autoregressive models

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