autocorrelograms

An autocorrelogram is a graphical representation of the autocorrelation of a signal as a function of time lag. It is commonly used to examine how the values of a signal at different times are related to one another. In neuroscience, it is often constructed from spike train data to assess whether neuronal firing shows periodicity, refractory effects, or rhythmic structure.

To compute an autocorrelogram, the data are typically transformed into a time series with a chosen bin width, producing a binary or count sequence. The autocorrelation function is then estimated for a range of time lags, usually normalizing the result so that the value at lag zero reflects the variance of the series. For point-process data such as spike trains, specialized approaches may be used that account for nonuniform firing rates, including binless methods or rate-normalized measures. It is common to apply bias corrections, such as subtracting a shift predictor or using surrogate data, to control for slow rate fluctuations and trial structure.

Interpretation focuses on the patterns in the autocorrelogram. A peak at a nonzero lag suggests rhythmic or periodic firing at that interval, while a peak at zero lag reflects immediate self-similarity. A dip just after zero lag can indicate refractory periods. Broad, flat patterns imply a lack of serial dependence, while structured oscillations point to underlying rhythms or synchronized activity.

Applications span neuroscience and time-series analysis. In neuroscience, autocorrelograms help characterize neuronal firing patterns, identify oscillations, and assess temporal structure within and across trials or conditions. Limitations include sensitivity to bin size, nonstationarity, finite data length, and rate nonuniformity, which can bias the estimate if not properly controlled.