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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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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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“Cross‐correlation applied to nonstationary and autocorrelated time series, such as cardiac signals, may lead to spurious results (Dean and Dunsmuir 2016).”
From Interpersonal Physiological Synchrony During Dyadic Joint Action Is Increased by Task Novelty and Reduced by Social Anxiety (2025) · cites this paper as Dean and Dunsmuir 2016
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“Indeed, physiological signals, especially heart rate, often exhibit autocorrelation.”
From Interpersonal Synchronization of Autonomic Physiology via Mere Visual Contact (2026) · cites this paper as [110]
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Metadata
- Authors
- Dean, R. T., & Dunsmuir, W. T. M.
- Affiliations
- Western Sydney University (AU)
- UNSW Sydney (AU)
- Corresponding author
- Dean, Roger T.
- Venue
- Behavior Research Methods
- Published
- 2015-06-23
- Volume
- 48
- Issue
- 2
- Pages
- 783-802
- ISSN
- 1554-351X (ISSN-L)
- 1554-3528
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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