How long does a brain region “remember” its own recent past? The Autocorrelation Window (ACW) quantifies this by measuring how quickly the temporal autocorrelation of neural activity decays. A long ACW means the signal is predictable far into the future — the region integrates information over a wide temporal window. A short ACW means the signal decorrelates quickly — the region responds rapidly to new inputs.
Intrinsic Neural Timescales
The Cortical Hierarchy of Time
The brain is organized as a temporal hierarchy. Early sensory areas (V1, A1) operate on fast timescales (~tens of milliseconds) to track rapidly changing stimuli. Higher-order association areas (prefrontal cortex, temporal pole) operate on slow timescales (~hundreds of milliseconds to seconds) to maintain contextual representations over time.
This gradient was first described using fMRI by Murray et al. (2014), but EEG can capture it at much finer temporal resolution using the ACW.
Analogy: Imagine a chain of workers on an assembly line. The first worker (sensory cortex) handles items as they arrive and immediately passes them on — short memory. The last worker (prefrontal cortex) needs to hold many items in mind to make decisions about the whole batch — long memory. The ACW measures each worker’s “holding time.”
Computing the ACW
Autocorrelation → Decay → Threshold
Step 1: Divide the EEG signal into overlapping windows (typically 20 seconds, 50% overlap).
Step 2: Compute the autocorrelation function (ACF) within each window. The ACF at lag τ
measures the correlation between the signal and a copy shifted by τ time points.
Step 3: Determine the ACW as the lag at which the ACF decays to a threshold.
ACW-0
The lag at which the autocorrelation first crosses zero. Captures the full decay cycle. More robust, better test-retest reliability.
ACW-50
The lag at which the autocorrelation drops to 50% of its maximum. Captures the initial decay rate. More sensitive to fast dynamics.
import numpy as np def compute_acw(signal, sfreq, win_sec=20, overlap=0.5): """Compute ACW-0 and ACW-50 for a 1-D signal.""" win_samples = int(win_sec * sfreq) step = int(win_samples * (1 - overlap)) max_lag = win_samples // 2 acw0_list, acw50_list = [], [] for start in range(0, len(signal) - win_samples, step): chunk = signal[start:start + win_samples] chunk = chunk - chunk.mean() # Full autocorrelation, normalized acf = np.correlate(chunk, chunk, mode='full') acf = acf[len(acf)//2:] # positive lags only acf = acf / acf[0] # normalize to 1 at lag 0 # ACW-0: first zero crossing zero_cross = np.where(acf[:max_lag] <= 0)[0] acw0 = zero_cross[0] / sfreq if len(zero_cross) > 0 else np.nan # ACW-50: first drop below 0.5 half_cross = np.where(acf[:max_lag] <= 0.5)[0] acw50 = half_cross[0] / sfreq if len(half_cross) > 0 else np.nan acw0_list.append(acw0) acw50_list.append(acw50) return np.nanmean(acw0_list), np.nanmean(acw50_list)
Clinical & Cognitive Relevance
Consciousness, Aging & Psychiatric Disorders
ACW is gaining traction as a neural biomarker across multiple domains:
• Disorders of consciousness: Patients in minimally conscious states show
significantly shorter ACWs than healthy controls, reflecting reduced temporal integration.
• Aging: ACW generally shortens with age in association areas, mirroring
the flattening of the 1/f exponent.
• Schizophrenia: Altered ACW patterns suggest disrupted temporal binding.
• Meditation: Long-term meditators show altered ACW hierarchies.
Key references: Murray et al. (2014) — cortical timescale hierarchy. Watanabe et al. (2019) — ACW in EEG. Wolff et al. (2022) — ACW and consciousness. Golesorkhi et al. (2021) — test-retest reliability.