Optimal Cross-Correlation Estimates from Asynchronous Tick-by-Tick Trading Data

Paper: arXiv 2303.16153

Authors: William H. Press

Abstract

Given two time series, A and B, sampled asynchronously at different times {t_A_i} and {t_B_j}, termed “ticks”, how can one best estimate the correlation coefficient ρbetween changes in A and B? We derive a natural, minimum-variance estimator that does not use any interpolation or binning, then derive from it a fast (linear time) estimator that is demonstrably nearly as good. This “fast tickwise estimator” is compared in simulation to the usual method of interpolating changes to a regular grid. Even when the grid spacing is optimized for the particular parameters (not often possible in practice), the fast tickwise estimator has generally smaller estimation errors, often by a large factor. These results are directly applicable to tick-by-tick price data of financial assets.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a novel, mathematically rigorous linear-time estimator for asynchronous tick data without relying on ad-hoc interpolation techniques. Its simulated benchmarks demonstrate significant variance reduction over traditional grid-binning methods, making it highly valuable for high-frequency finance applications.

Research Flowchart

  flowchart TD
    A[Research Goal: Estimate Correlation ρ from Asynchronous Tick Data] --> B[Inputs: Time Series A and B at Asynchronous Ticks t_A_i and t_B_j]
    B --> C[Derive Minimum-Variance Estimator: No Interpolation or Binning]
    C --> D[Develop Fast Tickwise Estimator: O N Linear-Time Algorithm]
    D --> E[Simulation & Evaluation: Compare vs. Optimized Grid Interpolation]
    E --> F[Outcomes: Superior Accuracy, Lower Estimation Error, High Efficiency for Financial Data]