On lead-lag estimation of non-synchronously observed point processes

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Highly relevant to quantitative trading. The paper directly addresses lead-lag estimation from high-frequency tick data, which is fundamental to statistical arbitrage, pairs trading, and market-making strategies. The empirical application demonstrates detection of sub-millisecond lead-lag relationships between exchanges (NASDAQ vs BATS), consistent with physical transmission times. The proposed estimator provides stable, accurate lead-lag estimates that can inform trading decisions at ultra-high frequencies. The theoretical guarantees (minimax rates) provide confidence in the estimator's performance.

The kernel estimator itself is conceptually straightforward (maximize a kernel-smoothed CPCF), but implementation requires careful handling: (1) efficient computation via binary search over timestamp pairs (Algorithm 1), (2) Lepski bandwidth selection with a grid of candidate bandwidths, (3) handling of unbounded CPCFs (alpha < 1), (4) tie-breaking for multiple maximizers, (5) proper edge correction. The computational complexity is O(T log T + T^2 h) for bounded CPCF and O(T log T + T^2 h^alpha) for unbounded CPCF. The theoretical assumptions (mixing conditions, moment bounds) are non-trivial to verify in practice.

The paper provides detailed mathematical proofs, algorithm pseudocode (Algorithm 1), and specifies all simulation parameters (model families, parameter values, bandwidth grids, number of Monte Carlo replicates). However, no code repository is explicitly linked. Empirical data (Daily TAQ) is publicly available but requires specific access. The theoretical framework is fully specified with all assumptions clearly stated.