Dynamic cross-autocorrelation in stock returns

I investigate whether the cross-autocorrelation pattern of US small- and large-firm returns changes with the variance of returns using an exponential vector autoregressive model with volatility. The model allows the testing of dynamic cross-autocorrelation effects, while controlling for own time-varying autoregressive coefficients. Using daily and weekly data from 1965 to 2015, a constant cross-autocorrelation pattern is rejected. Returns on a large-firm portfolio are found to lead returns on a small-firm portfolio. The lead-lag relation changes over time with the variance of the large-firm returns. Traditional vector autoregressions with constant cross-autoregressive coefficients appear to be overly restrictive when testing lead-lag relations in stock markets.