Dynamic Time Warping: The Algorithm That Could Rewire How Psychology Tracks Time

Psychology has a timing problem, and a team of Belgian researchers believes an algorithm borrowed from speech recognition could solve it. In a new methods paper published in Frontiers in Organizational Psychology, Juul Vossen, Evy Kuijpers and Joeri Hofmans of the Vrije Universiteit Brussel introduce Dynamic Time Warping, or DTW, to behavioral research. Their argument is deceptively simple: the statistical models psychologists use to study delayed effects assume that time behaves identically for everyone, when in reality it does not. The same behavior can trigger a consequence immediately in one person, hours later in another, and at different moments within the same individual across a single day. Traditional lag models, which shift one variable forward by a fixed number of measurement occasions, cannot capture that variability. DTW can, and the authors show it does so with striking gains in explanatory power.

The problem the researchers target has grown alongside the explosion of intensive longitudinal data. Smartphones and wearable sensors now allow scientists to collect high-frequency time series from hundreds of people, capturing fluctuating moods, stress levels and personality states three or more times a day. To analyze how past experiences shape current states, researchers overwhelmingly rely on lag models, including dynamic structural equation modeling, known as DSEM, and vector autoregressive approaches. But these techniques share a hidden assumption: that the onset and duration of a lagged effect are identical across and within individuals. As the authors point out, that assumption may routinely fail. A person who starts a demanding task well-rested might experience the depleting effect of conscientious behavior only later in the day, while someone already close to exhaustion feels it immediately. A fixed one-occasion lag improves alignment for the second scenario while worsening it for the first.

Dynamic Time Warping emerged long before it reached psychology. Hiroaki Sakoe and Seibi Chiba introduced the technique in the early 1970s to compare speech signals that were distorted by variations in speaking speed. The core idea is intuitive when illustrated with human growth: children’s height curves all follow the same general shape, with steady growth, a pubertal spurt and a plateau, but the timing of the spurt varies enormously. Comparing children at the same chronological age exaggerates their differences even though the underlying developmental process is essentially the same. Time warping resolves this by stretching or compressing the time axis so that comparable features align, revealing the shared trajectory beneath the timing differences. DTW operationalizes this idea by minimizing the Euclidean distance, or mismatch, between two time series, allowing similar observations to be matched even when they occur at slightly different moments.

Technically, the algorithm works through a cost matrix, a map of every possible mismatch between observations of the two series. Each cell records the momentary dissimilarity of pairing one observation with another. Dynamic programming then searches for the path through this matrix with the lowest cumulative cost, producing what is formally called the warping path, the alignment trajectory that specifies how observations from the two series are matched over time. Crucially, the procedure is constrained: the path cannot move backward in time, and it typically must respect the ordered nature of the data. Researchers can tune three key parameters. The step function determines whether one series is warped to match the other, the asymmetric option, or whether both are warped toward a common time scale, the symmetric option. The window size sets how far apart in time two observations may be matched, and the window type determines whether matching is allowed only forward, only backward, or in both directions.

A critical conceptual point, and one the authors emphasize throughout, is that DTW is not a statistical model at all. It is a preprocessing technique, comparable to data imputation or z-score standardization. It identifies an optimal alignment trajectory without estimating parameters or making distributional assumptions, after which researchers are free to apply any statistical model they choose, from multilevel regression to structural equation modeling. This model-agnostic quality is what makes DTW so versatile: it complements rather than replaces conventional pipelines. It also sidesteps a persistent headache in intensive longitudinal research, missing data. While DSEM handles incomplete observations through Bayesian estimation and traditional approaches often resort to imputation or listwise deletion, DTW simply excludes missing points during alignment, matching only the available data directly.

To demonstrate the technique, the team first ran a simulation comparing DTW with DSEM on data deliberately constructed to contain both lagged and leading relations. The results were revealing. DSEM with three lags achieved an explained variance of 0.64, but its lag coefficients changed sign across lags, a well-known instability of distributed-lag models in which correlated predictors compete for unique variance. DTW coefficients, by contrast, remained uniformly positive and increased steadily in magnitude, making them considerably easier to interpret. Most strikingly, when the algorithm was allowed to warp in both forward and backward directions within a window of three, explained variance jumped to 0.83, closely approximating the true data-generating process. When the warped data were fed into a DSEM model, the same pattern held, with explained variance rising from 0.33 to 0.83. These findings replicated in a version of the dataset with missing observations, where DTW again reached an explained variance of roughly 0.82.

The real-world test came next, using two Experience Sampling Method datasets collected in Belgium. The first comprised 157 employees with 1,699 repeated observations, measured three times daily across five workdays; the second comprised 96 employees with 2,151 observations over ten workdays. Both studies examined whether momentary conscientious behavior, working in a productive and industrious manner, predicts later feelings of depletion, a link suggested by prior theory on counterdispositional acting. The comparison between approaches was stark. In the second sample, a traditional fixed-lag model found no statistically significant effect of state conscientiousness on depletion, with p-values hovering around 0.07. When DTW was applied, allowing conscientiousness to match depletion one measurement moment later, both the linear and curvilinear effects became clearly significant, with p-values of 0.007 and 0.006 respectively. The fixed-lag approach had not merely missed an effect; it had reversed the sign of a trait-by-state interaction, while DTW reproduced the pattern of the unlagged baseline.

Exploratory analyses added another twist. Because depletion might also cause people to fail to act conscientiously, the researchers tested bidirectional warping, allowing lagged effects in both directions simultaneously. In both samples, the bidirectional model fit best, suggesting that the relationship between conscientious behavior and depletion is genuinely reciprocal. The authors argue this capability makes DTW a powerful tool for theory development, particularly for frameworks built on recursive cycles. The Job Demands-Resources theory posits gain spirals, in which engagement and resources reinforce one another, and loss spirals, in which strain and demands do the same. Conservation of Resources theory emphasizes the timing of resource loss and gain. DTW, with its person-specific alignment trajectories, is uniquely suited to examine how such spirals unfold at the individual level, and it may even help resolve long-standing puzzles such as the mixed evidence on ego depletion, where self-regulatory failure may be real but slow to materialize over hours rather than minutes.

The technique is not without caveats, and the authors are candid about them. Unconstrained warping can produce what is known as pathological warping, where the algorithm exploits its flexibility to reduce mismatch without reflecting meaningful temporal correspondence. Constraints such as window size and step function serve not only to encode theoretical assumptions but also to prevent this excess. The researchers recommend evaluating whether improvements in fit diminish as flexibility increases, and they suggest permutation-based checks that compare observed alignments against randomized ones. They also stress that temporal precedence detected by DTW is not evidence of causality, and that when warping is extensive, fixed effects become a mixture of concurrent and lagged relationships that demand careful interpretation. The algorithm’s underlying assumption, that observed mismatch is always caused by a lagged effect between the two variables, is admittedly an oversimplification of psychological reality.

Still, the implications are considerable. The timing of assessment in the social sciences has often been driven more by convenience and tradition than by theory, and using lags that are too long can underestimate the very effects researchers seek to measure. DTW offers a way to let the data reveal their own temporal rhythm, testing whether certain situations elicit stronger concurrent effects or more pronounced delayed ones, and whether individuals differ systematically in the timing of their responses. To lower the barrier to entry, the team has released a free interactive Shiny application that lets researchers explore how different DTW settings, step patterns, window types and window sizes, shape the resulting alignment, without requiring any programming experience. For a discipline increasingly awash in high-frequency data but still analyzing it with tools that treat time as uniform, the arrival of Dynamic Time Warping may mark the moment behavioral science finally learns to bend time to fit the people it studies.

Subject of Research: Capturing the rhythm of time: introducing Dynamic Time Warping in behavioral research

Article Title: Capturing the rhythm of time: introducing Dynamic Time Warping in behavioral research

Article References: Vossen, J., Kuijpers, E., & Hofmans, J. (2026). Capturing the rhythm of time: introducing Dynamic Time Warping in behavioral research. Frontiers in Organizational Psychology, 4, Article 1892016. https://doi.org/10.3389/forgp.2026.1892016

Image Credits: AI Generated

DOI: 10.3389/forgp.2026.1892016

Keywords: Capturing, rhythm, time, introducing, Dynamic, Warping, behavioral, research, scientific research