Bootstrap Inference in Autoregressive Duration Models

Battle Count: 50

ACD models are directly relevant to high-frequency trading and market microstructure. The paper's empirical application to cryptocurrency ETFs demonstrates practical relevance. Bootstrap inference for duration models is important for: (1) estimating and testing persistence in trading durations, (2) constructing valid confidence intervals for ACD parameters under heavy tails, (3) testing integrated duration hypotheses relevant to market efficiency. However, the paper is primarily theoretical/methodological rather than directly providing trading strategies. The robustness to distributional misspecification is practically valuable for real-world trading data which rarely follows exponential distributions.

The bootstrap algorithms themselves are relatively straightforward to implement (recursive generation of bootstrap durations, resampling scaled residuals). However, the theoretical underpinnings are complex, involving renewal theory, random sample sizes, and heavy-tailed distributions. The fixed-count bootstrap is computationally simpler than the random-count version. Key implementation challenges include: (1) proper scaling of residuals to maintain unit mean, (2) handling the random sample size in the bootstrap world, (3) computing the observed information matrix correctly, (4) determining the appropriate tail index kappa for inference, (5) implementing restricted bootstrap for hypothesis testing. The Monte Carlo study requires careful calibration of observation windows to achieve target event counts.

The paper provides detailed mathematical proofs in the appendix, specifies all simulation parameters (M=10000 replications, B=399 bootstrap replications, burn-in d=1000), and provides a GitHub repository for processed data. The Monte Carlo design is fully described with specific parameter values. However, the theoretical proofs are complex and require careful implementation. The empirical application uses publicly available LOBSTER data.