Accurate estimator of correlations between asynchronous signals

The estimation of the correlation between time series is often hampered by the asynchronicity of the signals. Cumulating data within a time window suppresses this source of noise but weakens the statistics. We present a method to estimate correlations without applying long time windows. We decompose the correlations of data cumulated over a long window using decay of lagged correlations as calculated from short window data. This increases the accuracy of the estimated correlation significantly and decreases the necessary efforts of calculations both in real and computer experiments.

💡 Research Summary

The paper addresses a fundamental problem in time‑series analysis: estimating the Pearson correlation between two signals that are sampled asynchronously. When observations from the two series do not occur at the same moments, the conventional Pearson estimator suffers from a systematic downward bias, a phenomenon well known in finance as the Epps effect. The standard remedy is to aggregate data over a large time window Δt, thereby “smoothing out’’ the asynchrony. While this reduces the bias, it also dramatically reduces the effective sample size, leading to large statistical uncertainties.

To overcome this trade‑off, the authors propose a decomposition technique that allows one to reconstruct the correlation at any large time scale Δt from high‑resolution data collected at a much finer scale Δt₀. The key insight is that, for a stationary process, the correlation over a window that is an integer multiple of the fine scale (Δt = n·Δt₀) can be expressed as a weighted sum of lagged autocorrelations and cross‑correlations measured at the fine scale. Equation (4) in the paper formalises this relationship:

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