A response surface analysis of critical values for the lead-lag ratio with application to high frequency and non-synchronous financial data

Granger causality tests are being supplanted by new methods such as the Lead-Lag Ratio, particularly in finance where data arrives at random times and systematic sampling often produces spurious results. Existing approaches are insufficient; outside of block-sampling using a bootstrap, the lead-lag ratio has generally been assessed against a benchmark of 1 without regard for statistical significance. We use simulations to generate a response surface for the Lead-Lag Ratio. Our modelled critical values are applied to reassess the findings of three previous studies of lead/lag relations between financial return series with high frequency data. Our response surface method proves to be a convenient and efficient alternative to using a bootstrap.