correlograms

A correlogram is a graphical representation of how a signal correlates with a delayed version of itself (autocorrelogram) or with another signal (cross-correlogram) as a function of time lag. It summarizes temporal structure in neural firing data or other time series and is widely used to study rhythmicity, timing, and functional relationships.

In spike train analysis, the signal is often represented as a binary or count sequence obtained by binning spike times into fixed-width intervals. The autocorrelogram at lag k is typically computed as R[k] = (1/N) Σ_n (x[n] − μ)(x[n+k] − μ), where μ is the mean firing rate and N is the number of valid bins after edge handling. The cross-correlogram between two spike trains x and y uses a similar formula, C[k] = (1/N) Σ_n (x[n] − μx)(y[n+k] − μy). These expressions can be adapted with normalization or alternative estimators.

Practical considerations include the choice of bin size and lag window. Small bins (e.g., 0.5–2 ms) provide high temporal resolution but require sufficient firing, while larger bins smooth the result. Auto-correlograms reveal refractory periods and periodicities; cross-correlograms indicate whether one neuron tends to fire in relation to another with a certain delay or in a specific order.

Normalization and significance testing are common: normalizing by firing rates or using z-scores allows comparisons across cells or sessions; significance is often assessed with surrogate data such as jittered or shuffled spike trains or shift-predictor analyses.

Limitations include non-stationarity, rate modulations, edge effects, and potential misinterpretation of correlations as causality. Correlograms are valuable for insights into neural coding, synaptic connectivity, and network dynamics, as well as for analyzing temporal structure in other time series.